Biomechanical Analysis of Hand Grip Motion for Optimal Handle Design Using a Cadaver Model

The Pennsylvania State University The Graduate School College of Engineering

BIOMECHANICAL ANALYSIS OF HAND GRIP MOTION FOR OPTIMAL HANDLE DESIGN USING A CADAVER MODEL

A Dissertation in Industrial Engineering by Shihyun Park  2009 Shihyun Park

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy August 2009

The Dissertation of Shihyun Park was reviewed and approved* by the following:

Andris Freivalds Professor of Industrial and Manufacturing Engineering Dissertation Advisor Chair of Committee

David J. Cannon Associate Professor of Industrial and Manufacturing Engineering

Ling Rothrock Associate Professor of Industrial and Manufacturing Engineering

Neil A. Sharkey Professor of Kinesiology, Orthopaedics and Rehabilitation Associate Dean of Research and Graduate Education

M. Jeya Chandra Professor of Industrial and Manufacturing Engineering Graduate Program Coordinator

*Signatures are on file in the Graduate School

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ABSTRACT

Forceful exertion of tendons while gripping hand tools may be one of the factors that lead to the development of work-related musculoskeletal disorders (WRMSDs). Also, the ratio between internal tendon force and externally applied grip force is necessary to design an optimal handle size to maximize efficiency of the force and reduce an excessive tendon force. Previous research has indicated that flexor digitorum profundus (FDP) and flexor digitorum superficialis (FDS) forces can be up to 3.7 times the external forces predicted by a biomechanical model. However, these values were indirect estimates derived from the biomechanical model to predict internal tendon forces. Although anatomically precise, the model was challenging to implement in practice, since it requires input parameters that are often difficult or impossible to measure. Therefore, it is imperative that the model is validated with direct measurement of tendon forces using human cadaver forearms. The cadaver model with hand motion simulator allowed the application of controlled forces to the flexor tendons by the force delivery unit while the resulting grip forces were measured with force sensitive resistors. Consequently, the actual tendon forces generated by the actuators were compared with externally applied force (grip force and finger force distribution) in power grip motion with various diameter handles. Moreover, the effect of different tendon force ratios of FDP to FDS was investigated to explore kinematic role of the ratio in power grip motion. Also, the resulting data were compared to similar measures reported in the literature and input to mathematical model to validate. Results of validation of the hand motion simulator with showed that actual tendon forces activated by the system had an average of 0.97N error compared to target forces input. It was acceptable to use the hand motion simulator for the experiments. In terms of tendon force ratios of FDP to FDS, 40% of FDS to total tendon force (3:2 FDP to FDS) showed highest grip force and contact force distribution. The ratio of internal tendon force and externally applied force showed that the tendon force was on average 5.3 times higher than grip force and the efficiency of the forces was best at the 3:2 FDP to FDS force ratio and the smallest diameter handle. Grip force generated by pulling tendons was iv highest with small diameter handle (30mm) and lowest with large handle (60mm). The index and middle fingers contributed an average of 57.6% of total contact force of each phalange and the contribution of ring finger was smaller, followed by the little finger with the smallest contribution. Most phalange forces in power grip motion were concentrated on the distal phalange (72.4%) and others were notably low. In the assessment of finger joint angle, the joint angles were changed according to the tendon force ratios of FDP to FDS. Higher FDP force ratio made DIP joint flex and PIP joint straight. On the other side, high proportion of FDS force in flexor tendon showed stretched DIP joint and flexed PIP joint angle. Finally, the result of this study was input to the mathematical model to validate the model. The predicted FDP force calculated by the model was 61% higher than the actual FDP force directly measured by the cadaver model and the predicted FDS force was 38% less than the actual FDS force. Despite some differences, in general the hand motion simulator with a cadaver model produced finger kinematics closely resembling those that occur in normal human grasping and showed similar hand biomechanics result with previous studies that investigated grip force and finger force distribution with handles.

TABLE OF CONTENTS

LIST OF FIGURES ...... viii

LIST OF TABLES ...... xi

ABBREVIATIONS ...... xii

ACKNOWLEDGEMENTS ...... xiii

Chapter 1 INTRODUCTION ...... 1

1.1. Problem Statement ...... 1 1.2. Study Objectives ...... 4

Chapter 2 BACKGROUND ...... 7

2.1. Review of Work-Related Musculoskeletal Disorders (WMSDs) ...... 7 2.1.1. Occupational injuries in the U.S...... 7 2.1.2. Work-Related Musculoskeletal Disorders (WMSDs) ...... 9 2.1.3. Risk factors associated with WMSDs ...... 10 2.2. Anatomy of the Hand and Wrist ...... 12 2.2.1. Skeleton of the hand ...... 12 2.2.2. Joint of the hand ...... 13 2.2.3. Muscles of the hand ...... 15 2.2.4. Pulley system of the flexor tendon sheath ...... 24 2.3. Biomechanical analysis of the hand ...... 26 2.3.1. Analytic models ...... 26 2.3.2. Experimental analysis ...... 29 2.3.3. Tendon force ratio of the FDP and FDS ...... 33 2.3.4. A Two dimensional hand model ...... 39

Chapter 3 THE HAND MOTION SIMULATOR ...... 45

3.1. Support Frame ...... 45 3.1.1. Forearm fixators ...... 47 3.1.2. Cylindrical handle and handle fixture ...... 49 3.2. Motion System ...... 51 3.2.1. Force delivery unit ...... 51 3.2.2. Muscle force control ...... 53 3.2.3. Muscle forces in the experiment ...... 56 3.3. Data Acquisition System ...... 58 3.3.1. Tendon and grip force measurement ...... 58 3.3.2. Finger force distribution measurement ...... 61 3.4. Machine Vision System ...... 63 3.4.1. Vision system ...... 63 vi

3.4.2. Image process ...... 65 3.5. Software ...... 66 3.6. Calibration ...... 68 3.6.1. Motion calibration ...... 68 3.6.2. Force transducer calibration ...... 72

Chapter 4 EXPERIMENTS ...... 74

4.1. Overview ...... 74 4.2. Specimen ...... 74 4.2.1. Anthropometric data ...... 76 4.3. Experimental Procedure ...... 77 4.3.1. Tendon forces ...... 77 4.3.2. Procedures ...... 77

Chapter 5 RESULT ...... 79

5.1. Overview ...... 79 5.2. Validation of the Hand Motion Simulator ...... 79 5.2.1. System summary ...... 80 5.3. Grip Force Analysis ...... 84 5.3.1. Handle size analysis ...... 88 5.3.2. Tendon force ratio analysis ...... 90 5.4. Finger Force Distribution Analysis ...... 95 5.4.1. Finger and phalange forces ...... 95 5.4.2. Tendon force ratio ...... 99 5.5. Finger joint angle analysis ...... 104 5.6. Validation of mathematical model ...... 109

Chapter 6 SUMMARY AND DISCUSSION ...... 112

6.1. Hypothesis 1: The hand motion simulator ...... 112 6.2. Hypothesis 2: The tendon force ratio ...... 114 6.3. Hypothesis 3: The efficiency of internal force to external force ratio ...... 115 6.4. Hypothesis 4: The handle size effect ...... 116 6.5. Hypothesis 5: Finger Force Distribution ...... 120 6.6. Hypothesis 6: Finger Joint Angles ...... 122 6.7. Mathematical Model Validation ...... 123

Chapter 7 SUGGESTION FOR FUTURE RESEARCH...... 125

7.1. Handle Design ...... 125 7.2. Finger Force Distribution ...... 126 7.3. Intrinsic Muscles ...... 126 7.4. Passive Force-Length Relationship ...... 127

REFERENCES ...... 128 vii

APPENDIX A: Hand Motion Simulator control block diagram ...... 137

APPENDIX B: Calibration of Force Transducer (FSRs) ...... 141

APPENDIX C: Result of Statistical Analysis ...... 144

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LIST OF FIGURES

Figure 2.1. Incidence rates of injury and illness in manufacturing industry, 1982- 2001 (Adapted from Bureau of Labor Statistics, 2001) ...... 8

Figure 2.2. Bones of wrist and hand (source: Netter, 1989) ...... 14

Figure 2.3. Muscles of the hand (source Higgins and Mandiberg, 2000) ...... 16

Figure 2.4. Individual muscles of forearm: Flexors of Digits (source: Netter,1989) .. 17

Figure 2.5. FDP and FDS tendons of a typical digit (source: Netter, 1989) ...... 23

Figure 2.6. Pulley Structure of the Finger (A = annular, C = cruciate)...... 25

(source: Nordin and Frankel, 2001) ...... 25

Figure 2.7. Free-body diagram for a two-dimensional hand model. (source: Kong, 2001) ...... 40

Figure 3.1. Schematic drawing of the hand motion simulator ...... 46

Figure 3.2. Schematic drawing of the hand motion simulator ...... 47

Figure 3.3. Fixators for fastening the pins cross-drilled into radius and ulna ...... 48

Figure 3.4. Adjustable wrist fixator (Wristjack®, Source: Surgeon’s Manual) ...... 48

Figure 3.5. Split cylindrical handles with five different diameters ...... 50

Figure 3.6. Handle fixture with a height adjustable knob and handle fixing clamps .. 50

Figure 3.7. The Components of Force Delivery Unit (DFU) ...... 52

Figure 3.8. Motor and motion controller in FDU ...... 52

Figure 3.9. Workflow of the force feedback control system ...... 55

Figure 3.10. Data acquisition system of the Hand Motion Simulator ...... 59

Figure 3.11. Data acquisition system with force transducers ...... 60

Figure 3.12. Split cylindrical handle with force transducer inserted ...... 60

Figure 3.13. FlexComp system with FSRs ...... 62

Figure 3.14. FSRs attached on each phalanges ...... 62 ix

Figure 3.15. Image Process to compute finger joint angles ...... 65

Figure 3.16. Hand motion simulator monitoring panels ...... 67

Figure 3.17. Hand motion simulator controlling panels ...... 67

Figure 3.18. Calibration setting for force delivery unit and force transducers ...... 70

Figure 3.19. Regression of the displacement and axial rotation of the stepper motors ...... 71

Figure 3.20. The regression of the voltage (mV) and actual force (Kg) ...... 73

Figure 3.21. The regression of the raw signals and actual force (N) ...... 73

Figure 4.1. Specimen mounted on a custom fixation device in hand motion simulator ...... 75

Figure 4.2. Diagram for phalange length measurement for each finger ...... 76

Figure 5.1. Sample data plots showing performance of the force feedback control in the Hand Motion Simulator. FDP, FDS, Grip force plotted in the graph according to time sequential. Target Force was 100N and 50N for FDP and FDS, respectively...... 80

Figure 5.2. Boxplot of Actual FDP Force ...... 83

Figure 5.3. Boxplot of FDS Force ...... 83

Figure 5.4. The grip force variation on each handle ...... 88

Figure 5.5. The interaction of the Internal force and the handle ...... 89

Figure 5.6. The effect of the tendon force ratio between the FDP and FDS ...... 91

Figure 5.7. The interaction between the relative FDS percentage and the handle size ...... 93

Figure 5.8. The interaction between the relative FDS percentage and the handle size ...... 94

Figure 5.9. The main effects (Finger) for grip force. The number of finger is the order of finger from the index to the little finger, respectively...... 97

Figure 5.10. The main effects (Phalange) for grip force. The number of phalange is the order of phalange from the distal to the metacarpal phalange, respectively...... 97

Figure 5.11. The interaction effects for grip force (Finger * Phalange) ...... 98 x

Figure 5.12. Main Effects Plot (data means) for Total ...... 99

Figure 5.13. The interaction effects for grip force (Finger * %FDS) ...... 103

Figure 5.14. The interaction effects for grip force (%FDS * Finger) ...... 103

Figure 5.15. Finger joint angles on tendon force ratio and handle ...... 107

Figure 5.16. Inter phalangeal joint angles on handle size and %FDS ...... 108

Figure 6.1. The main effect of handle with mean grip force ...... 118

Figure 6.2. Mean contact force of each finger and phalange ...... 121 xi

LIST OF TABLES

Table 2.1. Extrinsic muscles of the hand and wrist (Source: Spence, 1990) ...... 18

Table 2.2. Intrinsic muscles of the hand and wrist (Source: Spence, 1990) ...... 19

Table 2.3. In vivo tendon forces (kg) of FDP and FDS ...... 34

Table 2.4. Ratios of tendon and joint forces in power grip function ...... 35

Table 3.1. Fundamental parameter of an imaging system ...... 64

Table 4.1. Dimension of phalanges on each finger ...... 76

Table 5.1. Comparison of target forces to actual forces ...... 82

Table 5.2. One sample t-test actual FDP to target force 100N ...... 82

Table 5.3. ANOVA for Grip Force, using Adjusted SS for Tests ...... 84

Table 5.4. Tukey tests on the difference in the grip force ...... 86

Table 5.5. The total/individual finger forces and contributions on each %FDS ...... 87

Table 5.6. ANCOVA for Grip Force, using Adjusted SS for Tests ...... 92

Table 5.7. The individual phalange forces contributions on each finger ...... 96

Table 5.8. Tukey procedure comparing the fingers ...... 96

Table 5.9 Tukey procedure comparing the phalanges ...... 96

Table 5.10. The total/individual finger forces and contributions on each %FDS ...... 102

Table 5.11.The total/individual phalange forces and contributions on each %FDS .... 102

Table 5.12. Finger Joint Andlge flexion on %FDS and handle ...... 106

Table 5.13. Each phalange force on 40% FDS level ...... 109

Table 5.14. Comparison of predicted flexor tendon forces and actual finger forces ... 111

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ABBREVIATIONS

WMSD Work related Musculo-Skeletal Disorder

FDP Flexor Digitorum Profundus

FDS Flexor Digitorum Superficialis

FPL Flexor Pollicis Longus

DIP Distal Inter-Phalangeal

PIP Proximal Inter-Phalangeal

MCP MetaCarpo-Phalangeal

HMS Hand Motion Simulator

FDU Force Delivery Unit

DAQ Data Acquisition

FSR Force Sensitive Resistor

GF Grip Force

FA Actual Force

FT Target Force

%FDS Percent FDS force

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ACKNOWLEDGEMENTS

The work presented here would not have been possible without the support of my family, friends and mentors over the years. First and foremost, I would like to thank my advisor, Professor Andris Freivalds for his constant guidance throughout the whole period of my doctoral studies. I sincerely believe that studying and working under his supervision have been the largest achievements in my career, and I am glad that I had that opportunity. I am also grateful to Professor Neil Sharkey, who gave me the opportunity to expand my expertise on the biomechanics study of Kinesiology, committee members, Professor David J. Cannon and Ling Rothrock for providing valuable comments and suggestions and Professor Chang Min Lee, who was the first mentor in academic studies. Andrew Hoskins, Yatin Kirane and Jesun Hwang, for sharing their scientific knowledge and for enthusiastic discussion. I would also like to thank the faculty, staff and students of the department of Industrial and Manufacturing Engineering, both past and present, who have had a profound effect on my life through their generosity, intellect, friendships and dedication to research. To my grandmother and parents, Jin Soon Cho, Maeng Ro Park and Jung Ok Kim, for patiently supporting me through all of the ups and downs we have encountered along the way. Lastly and most importantly, I am deeply grateful to my wife, Jung Soo, for her love, support, and encouragement during these years. The best experiences of this period were the births of our son and daughter, Jude and Sarah, who had thence dramatically changed and enriched our life.

Chapter 1

INTRODUCTION

1.1. Problem Statement

Failure to properly consider tendon and applied forces in designing a hand tool can have harmful effects on users. These effects may range from minor discomfort and fatigue to work related disorders or cumulative trauma disorders (CTDs) of the finger, hand and forearm (NIOSH, 1997). In this vein, forceful exertion of the upper extremities is widely recognized as one of the physical risk factors associated with the development of upper extremity Work Related Musculoskeletal Disorders (WMSDs), which are of increasing concern to employers as a source of Worker Compensation claims, lost work time and reduced productivity (National Research Council & Institute of Medicine, 2001).

Especially, work related musculoskeletal symptoms and injuries; such as carpal tunnel syndrome and tendonitis are common among operators of hand-held tools (Nathan et al.,

1992).

For quantifying peak exertion intensity with hand tools, biomechanical modeling of the hand is important for understanding how exerted forces act on the internal tissues for various hand functions. The National Institute for Occupational Safety and Health

(NIOSH) has been supporting the development and validation of models for the quantitative assessment of exposure to ergonomic risk factors including forceful exertion

(NIOSH, 2001). However, the mechanisms leading to risk of WMSDs have not been identified. 2

Quantitative mechanical hand modeling has been considered since the early 1960s

(Landsmeer, 1961) and has increased in complexity (An et al., 1979; Spoor, 1983;

Valero-Cuevas et al., 1998; Kong, 2001). Some extensive studies included all known intrinsic and extrinsic muscles involved in grasp (Chao et al., 1976; An et al., 1979;

Spoor, 1983; Valeo-Cuevas et al., 1998; Li et al., 2001). Although anatomically precise, these models are challenging to implement in practice, since they require input parameters that are often difficult or impossible to measure. Assumptions regarding muscle recruitment and optimization methods sometimes produce results that have been found inaccurate (Dennerlein et al, 1998).

Electromyography can investigate muscle activation patterns (Bendz, 1980;

Darling and Cole, 1990; Darling et al., 1994; Dennerlein et al., 1998; Vallbo and

Wessberg, 1993), but this method yields only an estimate of muscle activation, as many motor units may be active (Basmajian and Luca, 1985).

The most reliable assessment of the effects of external loading conditions on tendon forces is obtained by directly measuring tendon forces in human body. Direct measurement of tension in the tendon provides a measure of forces within the human musculoskeletal system that have been earlier predicted by isometric force models.

Validating the mathematical models by experimental measurement in vivo was undertaken in previous researchers (Schuind et al. 1992; Dennerlein et al., 1998; Kursa et al, 2005). However, Schuind et al. did not record finger joint positions, while Dennerlein et al. measured force in only one tendon. In addition, Kursa et al.(2005) measured force in only one finger. Also, in vivo test, true tendon forces are probably lower than the predicted results because these experiments were performed during carpal tunnel surgery. 3

In such case, the muscles are partially inactive and weaken pinch and power grip forces

(Chao, 1989).

Therefore, cadaveric experiments make no limitation of finger motion and measuring extrinsic muscles. Cadaveric studies have focused on the flexor tendon forces in both tip pinch and power grip actions (Bright and Urbaniak, 1976) or the relationship between tendon pulley integrity and flexor tendon excursion (Armstrong et al., 1978;

Idler et al., 1986; Lin et al, 1990). Also, Brand et al. reported the relative tension capacities of forearm and hand muscles with cross-sectional area of the muscles in cadaver hand (1981). However, no method has solved the force ratio between the tendon force and the externally applied force in power grip motion with various handles. In addition, no simultaneous comparison of kinematic data with tendon forces exists in the literature of power grip.

In this study, a hand motion simulator: a cadaver model was developed to investigate hand biomechanics of power grip motion and examine grip force and finger force distribution of the hand generated by extrinsic flexor muscles (FDP and FDS).

Moreover, the interaction effect of tendon force ratio (FDP to FDS) with finger joint motion was also investigated with the cadaver model using various sizes of cylindrical handles to find optimal handle size. Finally, contact forces and kinematic data were used to validate the biomechanical hand model.

1.2. Study Objectives

In terms of hand biomechanics research, many studies have focused on hand tool design based on simple experiments with an EMG or a force sensor. Most studies have focused on the externally applied force and the magnitude of muscle exertion in power grip on cylindrical handles. Also, anatomical and biomechanical studies of the human hand have been investigated to understand the tendon and muscle forces that correspond to externally applied forces. However, no such models have been employed to define the kinematic role of flexor muscles in grasping various sizes handles.

In the previous study performed in our laboratory, a mathematical hand model was developed to estimate tendon forces of the flexor muscles (FDP and FDS) in each finger (Kong and Freivalds, 2003). The biomechanical model showed that the internal tendon force were about 3.7 times higher than the externally applied force in the gripping task. However, the model only used the externally applied forces to estimate the FDP and

FDS tendon forces and the prediction model was not validated. Consequently, to validate the biomechanical hand model, the cadaver model with hand motion simulator was developed to measure internal tendon forces directly with a cadaver hand. This hand motion simulator allowed the application of controlled forces to the FDP and FDS tendons, resulting in the closing of the fingers around the handle with concurrent application of forces to the handle.

Therefore, this study focused on the work that has gone into developing the cadaver model as well as the work necessary to refine it as a comprehensive research tool.

Furthermore, quantified data from the cadaver model was used to investigate the 5 relationship between internal flexor tendon forces and externally applied forces in power grip with various handles and validated the mathematical model as well.

This thesis addressed the following research objectives:

1. The cadaver model: The Development of a hand motion simulator with a cadaver hand to generate the tendon forces (FDP and FDS) associated with power grip motion on various cylindrical handle sizes.

2. Force ratio: Analyses of the relationship between two flexor tendons (FDP and FDS) and between internal tendon forces (FDP and FDS) and externally applied forces (grip force and finger force distribution).

3. Handle size effect: Investigation of the optimal handle diameter for maximizing applied grip force generated by constant tendon forces.

4. Validation of the mathematical model: Validation of the biomechanics hand model through quantification of internal tendon forces and results of grip forces and finger motions in power grip motion.

To accomplish these objectives, the following hypotheses were proposed

Hypothesis 1.

Actual tendon forces generated by this cadaver model equal to the target forces input.

Hypothesis 2.

Tendon force ratios of FDP to FDS force affect grip force and finger force distribution.

Hypothesis 3.

Flexor tendon-to-grip force ratios are different depending on handle diameters.

Hypothesis 4.

Small diameter handle has higher grip force than larger diameter handles.

Hypothesis 5.

Middle finger and distal phalange have highest contact force among all fingers and phalanges.

Hypothesis 6.

The tendon force ratios of FDP to FDS affects finger joint angles in power grip.

Chapter 2

BACKGROUND

2.1. Review of Work-Related Musculoskeletal Disorders (WMSDs)

2.1.1. Occupational injuries in the U.S.

The term ‘musculoskeletal disorders’ (MSDs) refers to conditions that involve the nerves, tendons, muscles, and supporting structures of the body. These include such ailments as low back pain, shoulder disorders, and distal upper extremity disorders, including tendonitis and carpal tunnel syndrome (Waters, 2004). Work-related musculoskeletal disorders (WMSDs) are included as a class of musculoskeletal disorders.

They represent a wide range of disorders, which can differ in severity from mild periodic symptoms to severe chronic and debilitating conditions. Usually WMSDs are associated with occupational factors (i.e., repeated and highly forceful stresses, awkward or static postures and vibrations) (Silverstein et al., 1986; Putz-Anderson, 1988; Armstrong, 1994).

The report from the Bureau of Labor Statistics (BLS, 2001) that in 2001 there were 522,528 MSD cases, 75% of those were due to overexertion and another 11.5% were due to repetitive motion disorders (OSHA, 2001). Also, 60,099 injuries or illnesses occurred as a result of repetitive motion, including typing or key entry, repetitive use of tools, and repetitive placing, grasping, or moving of objects other than tools. Based on these investigations, it is clear that work-related injuries and illnesses represent a significant health problem for the industrial labor force in the United States. Trends in the numbers of cases of reported injuries and illnesses have steadily declined in the last 10 8 years. According to the BLS, the number of injury and illness cases that resulted in lost work days in manufacturing industries steadily decreased since about 1990, as can be seen in Figure 2.1. During that same period of time, however, the number of cases resulting in restricted work activities steadily increased. The reasons for these declines in lost day injuries and illnesses are unclear, but may include: a smaller number of disorders could be occurring because of more intensive efforts to prevent them; more effective prevention and treatment programs could be reducing days away from work; employers or employees may be more reluctant to report or record disorders; or the criteria used by health care providers to diagnose these conditions could be changing (NIOSH, 1997).

Lost workday cases incidence rates, injuries and illnesses Manufacturing, 1982-2001

Incidence rates per 100 full-time workers 7

Lost workday cases 6

4 Cases with days away from work 3

2 Cases with days of restricted work activity only

0 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001

Figure 2.1. Incidence rates of injury and illness in manufacturing industry, 1982-2001 (Adapted from Bureau of Labor Statistics, 2001) 9

2.1.2. Work-Related Musculoskeletal Disorders (WMSDs)

Work related musculoskeletal disorders (WMSDs), also known as Cumulative

Trauma Disorders (CTD), Repetitive Strain Injuries, or Overuse Syndrome, are a group of health problems caused by over-use or misuse of muscles, tendons and nerves. Usually, WMSDs can be classified into three basic types by anatomical characteristics: Tendon disorders, Muscle injuries and Nerve disorders. Tendon disorders occur at or near the joints where the tendons irritate nearby ligament and bones. Tendons without sheaths are vulnerable to repetitive motions and awkward postures. In fact, when a tendon is repeatedly tensed, some of its fibers can tear apart. The tendon becomes inflamed, thickened and bumpy. Tendonitis is the general term indicating inflammation of the tendon. The most frequently noted symptoms are a dull aching sensation over the tendon, discomfort with specific movements and tenderness to touch. Recovery is usually slow and condition may easily become chronic if the cause is not eliminated (Lipscomb,

1995).

Muscle injuries arise from excessive force exertions. The mechanism of injury for muscle disorders is quite different from tendon disorders. Typically, muscle injury occurs as the result of excessive external forces on the passive structures, mainly connective tissue, rather than from overuse. Excessive contractions also cause structural damage and loss of force generating capacity (McComas, 1968). Nerve disorders occur when repeated or sustained work activities expose the nerves to pressure from hard, sharp edges of the work surface, tools or nearby bones, ligaments, and tendons (Feldman et al., 1983). The symptoms include pain, tingling, and numbness in the hand. Carpal tunnel syndrome

(CTS) is the most common nerve disorder. The carpal tunnel is formed by the bony 10 carpal arch and the overlying transverse carpal ligament and flexor retinaculum. Typical symptoms of CTS include pain, numbness, tingling and clumsiness in the affected area of the hand and fingers resulting in difficulties performing normal activities (Phalen, 1972).

Careful job and hand tool designs and work place re-designs are recommended to reduce the incidence of CTS.

2.1.3. Risk factors associated with WMSDs

The WMSDs of the distal upper extremities may result from the interaction between physical and personal factors. Specific risk factors of WMSDs are difficult to identify because many risk factors may interact simultaneously to induce the condition

(Moore, 1992; NIOSH, 1997).

2.1.3.1. Physical risk factors

Repetitive motions

There is strong evidence for a positive association between highly repetitive works with WMSDs. Highly repetitive work may directly damage tendons with repeated stretching and elongation as well as increase muscle fatigue and decrease the time for fatigue recovery Numerous studies identified repetitive motions as a risk factor associated with development of CTS (Keyserling et al., 1993; Silverstein et al., 1987).

Many workers perform the same tasks and stereotyped motions over and over, sometimes thousands or tens of thousands time each day. Highly repetitive motions require fast muscle contractions, which become less efficient and demand greater recovery time 11 because muscle capacity to produce force diminishes with increasing contraction speed.

Silverstein et al. (1987) reported that odds ratios for risk of CTS and CTDs were 1.9 and

3.6, respectively, in high repetition jobs compared to jobs that requires a low number of repetitions. Based on these results, they indicated that jobs which have a basic cycle time of 30 seconds or less, and jobs in which over 50 percent of the work cycle are spent performing the same basic motions pattern have been associated with elevated rates of

CTS.

Forceful exertion

The forceful exertion required to do the task plays an important role in the onset of WMSDs. More force equals more muscular effort, and consequently, a longer time is needed to recover between tasks. Since in repetitive work, as a rule, there is not sufficient time for recovery, the more forceful movements develop fatigue much faster (Chaffin,

1973). Exerting force in certain hand positions is particularly hazardous. The amount of force needed depends on the weight of the tools and objects that the worker is required to operate or move, and their placement in relation to the worker's body in manual material handling tasks (Keyseling et al., 1993). Forceful exertions of the upper extremities (i.e., using knives, wrenches and other hand tools; using fingers and hands to shape or surface finish materials and parts, etc.) may cause upper extremity musculoskeletal disorders such as joint inflammation, muscle spasms, sprains, tendinitis, or diseases of the peripheral nerves (Armstrong et al., 1979; Silverstein et al., 1987).

Awkward posture

Awkward posture is one of the most frequently cited risk factors for CTS

(Armstrong, 1978, 1994; Moore, 1992). Common examples of awkward wrist postures include excessive flexion, extension, radial and ulnar deviation, and pinch grips (Keir,

1999). Awkward postures overload muscles and tendons, loads joints in an asymmetric manner, thereby inhibiting blood flow (VanWely, 1970). The median nerve may be under considerable risk during awkward hand postures that place extreme pressure on the flexor tendon. In fact, sizable compressive forces have been demonstrated in the median nerve when hand movements involve simultaneous pinching and extreme wrist flexion (Rempel and Horie, 1994).

2.2. Anatomy of the Hand and Wrist

2.2.1. Skeleton of the hand

The skeleton of the hand consists of a series of bones. The proximal rows are in articulation with the carpal bones and are called metacarpals; these in turn are in articulation with the phalanges. Each phalange and each metacarpal consists of a base, a shaft and a head; each finger has three phalanges; the thumb has only two. Figure 2.2 shows the skeletal structure of the hand.

There are eight carpal bones at the wrist, arranged in two transverse rows of four bones each. The bones of the proximal row, from lateral to medial, are the scaphoid, lunate, triquetrum, and pisiform. Those of the distal row, from lateral to medial, are the 13 trapezium, trapezoid, capitate, and hamate. The scaphoid and lunate articulate with the distal end of the radius to form the wrist joint.

Five metacarpal bones form the skeleton of the palm of the hand. They are numbered from lateral to medial. Proximally, the metacarpals articulate with the distal row of the carpal bones and with each other. Distally, each articulates with the proximal end of a phalange.

The skeleton of the fingers is formed by 14 phalanges. Each finger contains three phalanges: proximal, middle, and distal. An exception is the first digit (thumb), which has only proximal and distal phalanges (Spence, 1990).

2.2.2. Joint of the hand

There are four joints in each finger, in sequence from the proximal to distal: carpometacarpal joints (CMC), metacarpophalangeal (MCP), proximal interphalangeal

(PIP), and distal interphalangeal (DIP) joints (see Figure 2.2.). The CMC joints are composed of the articulations between the distal carpal row and the bases of four medial metacarpals, and are united by articular capsule and three types of ligaments (volar, dorsal, interosseus). The movement of this joint is more regulated by the ligaments, and consists of flexion-extension, abduction-adduction and some axial rotation, which take places concurrently with the other motions (Norkin, 1989). The MCP joints consist of the convex metacarpal head and the concave base of the proximal phalange and stabilized by a joint capsule and ligaments. The movements permitted at this joint are flexion- extension, abduction-adduction and circumduction (Norkin, 1989). Steindler (1955) reported that the range of the dorsovolar movement in this joint is approximately 110-120 14 degrees (90 degrees for flexion and 20 degrees for extension) and the range of the lateral movement is approximately 40-60 degrees. However, this type of movement has different ranges with the individual fingers (index: 60 deg., little: 50 deg., middle and ring: 45 deg.). The IP joints are true hinge joints, having one degree of freedom. Each finger has two IP joints (proximal and distal); the thumb has only one IP joint which is structurally and functionally identical to the distal IP joints of the finger (Norkin, 1989). The excursion ranges of dorsovolar direction in the proximal IP and in the distal IP joints are approximately 110-130 and 45-90 degrees. Generally, this range of movement at each joint (IP joint) increases ulnarly and proximally (Steindler, 1955).

Figure 2.2. Bones of wrist and hand (source: Netter, 1989) 15

2.2.3. Muscles of the hand

Based on the origin of the muscles, the muscle groups associated with movement of the forearm and the hand can be divided into extrinsic and intrinsic muscle groups. The extrinsic muscles originate in the forearm while the intrinsic muscles are entirely contained in the hand. In this regard, extrinsic muscles are long and large so as to provide greater excursion and strength while intrinsic muscles are short and small so as to provide precise coordination of the fingers.

Extrinsic muscles of the forearm and hand can be divided into two groups, which are named as anterior muscles and posterior muscles based on the locations. Again, each muscle group can be separated further into superficial and deep muscle groups based on its location. The anterior muscle groups serve as flexors. Most anterior muscles originate from the medial epicondyle of the humerus and insert on the carpal bones, metacarpals or phalanges. Among the anterior superficial muscles, the flexor digitorum superficialis serves for flexion of the fingers. The flexor carpi ulnaris both flexes and adducts the wrist while the flexor carpi radialis flexes and abducts the wrist. The palmaris longus flexes the wrist and tenses the palm. Among the anterior deep muscles, the flexor pollicis longus flexes the thumb. The extrinsic muscles of anterior and flexors are illustrated in

Figure 2.4, and summarized in Table 2.1. The pronator teres performs pronation of the forearm so that the palm turns downward when the elbow flexed and forearm horizontal.

The brachioradialis performs flexion of the forearm and it also serves as a synergist of the biceps brachii of the upper, which is a strong supinator muscle. The posterior forearm muscles serve as extensors. Most of these muscles originate from the lateral epicondyle 16 of the humerus and insert on the carpus, metacarpals or phalanges. Each muscle group can be divided further into superficial and deep muscle groups. Intrinsic muscles whose origin and insertion are both in the hand make possible the fine and precise movements that are typical of the fingers. They are divided into three groups: the thenar, the hypothenar and midpalmar muscle groups acting on the thumb, on the little finger, and on the all phalanges except the thumb, respectively. The intrinsic muscles are illustrated in

Figure 2.3, and the locations and actions of extrinsic and intrinsic muscles are listed in

Table 2.2.

Figure 2.3. Muscles of the hand (source Higgins and Mandiberg, 2000)

Figure 2.4. Individual muscles of forearm: Flexors of Digits (source: Netter,1989)

Table 2.1. Extrinsic muscles of the hand and wrist (Source: Spence, 1990)

Group Layer Name Function Flex and abduct the hand Flexor carpi radialis Support flexion of forearm Superficial Palmaris longus Flex hand

Flexor carpi ulnaris Flex and adduct hand Anterior Flexor digitorum Middle Flex phalanges and the hand superficialis Flexor digitorum profundus Flex phalanges and the hand Deep Flex the thumb Flexor pollicis longus Support flexion of the hand Extensor carpi radialis Extend and abduct hand longus Extensor carpi radialis brevis Extend hand Extensor digitorum Superficial Extend fingers and hand communis Extensor digiti minimi Extend little finger Posterior Extensor carpi ulnaris Extend and adduct hand Extend thumb and abduct Abductor pollicis longus hand Extend thumb and abduct Extensor pollicis brevis Deep hand Extend thumb and abduct Extensor pollicis longus hand Extensor indicis Extend index finger

Table 2.2. Intrinsic muscles of the hand and wrist (Source: Spence, 1990)

Group Name Abbrev. Function

Abductor pollicis AbPB Abducts thumb

Pulls thumb in front of the palm to meet Opponents pollicis OP Thenar little finer muscles Flexor pollicis FPB Flexes and adducts thumb

Adductor pollicis AdPB Adducts thumb Pulls the skin toward the middle of the Palmaris brevis PB palm

Hypothenar Abductor digiti ADM Abducts little finger muscles Flexor digiti FDM Flexes little finger Minimi brevis Opponens digiti ODM Brings little finger out to meet thumb minimi Flex proximal phalange Lumbricales L Extend the middle and distal phalanges of the second through fifth fingers Midpalmar Abduct fingers from the middle finger, Dorsal interossei DI muscles flex the proximal phalange

Adduct fingers toward the middle Palmar interossei PI finger, flex the proximal phalange

2.2.3.1. General characteristics of the flexors

As the main flexor muscles, the flexor digitorum profundus (FDP) and flexor digitorum superficialis (FDS) are the principal muscles involved in most repetitive work- related functions. Long et al. (1970) have studied these flexors using electromyography

(EMG). They showed that the FDP is the muscle that performs most of the unloaded flexion movement of the fingers and that the FDS comes in when more strength is needed.

The resting fiber length of the FDP tendon is slightly shorter than that of the FDS tendon.

In general, the lengths of resting muscle fibers vary by finger. The FDP comprises about

12% of the total muscle capability below the elbow. Although, in the middle finger, the tension capabilities of the FDP and FDS are equal, the average tension capability of the

FDP is about 1.5 times as strong as the FDS. The FDP of the little finger may be three times stronger than the FDS. There is significant variation (range: 0.9~3.4%) in the tension capabilities of the FDS tendons for each finger, while there is fairly constant tension capabilities for the FDP tendons of each finger (2.7~3.4%). It is generally agreed that the middle finger is the strongest and the little finger is the weakest finger for both the FDP and FDS.

2.2.3.1. Flexor Digitorum Profundus (FDP)

Flexor Digitorum Profundus (FDP) is a strong broad muscle that originates from the upper three-fourths of the volar surface of the ulna and gives rise to tendons that are inserted into the base of the distal phalange of each finger. The fiber bundles of FDP descend nearly vertically and give rise to a common belly nearly at the wrist that soon divides into four portions. After the division, tendons pass side by side under the 21 transcarpal ligament to the base of each finger (see Figure 2.5). Specially, FDP tendons pass through the slit in the superficial tendon on the volar surface of the proximal phalange (see Figure 2.6). In the palm, each profundus tendon gives rise to the lumbrical muscle which diverts some profundus power away from PIP flexion and DIP flexion to the extensor side of these joints, thus allowing the MCP joints to precede and dominate the beginning of the sequence of finger closure. The FDP muscles of the middle, ring and little fingers are somewhat dependent upon each other since there is a close connective tissue binding them together. However, the index finger is capable of greater functional independence since it has a fairly individual muscle belly (Brand et al., 1993). At the level of the carpal tunnel, profundus muscles are interconnected by tendinous cross- connection.

The lengths of muscle fibers for each finger varies between 6.2~6.8cm (Brand et al., 1981) and are on average 0.5cm shorter than that of FDS. The main function of the

FDP is the flexion of distal interphalangeal (DIP) joint, proximal interphalangeal (PIP) joint and metacarpo-phalangeal (MCP) joints.

2.2.3.1. Flexor Digitorum Superficialis (FDS)

FDS arise from the medial epicondyle of the humerus and from the radius and the ulnar, and sends tendons into the sides of the volar surface of the shafts of the middle phalange of each finger. In the forearm, a large flat common tendon connects the single proximal muscle belly to the three separate distal muscles, thus forming a complex muscle unit (see Figure 2.5). The four tendons pass together through the carpal tunnel under the transverse carpal ligament to the index and little finger such that the middle and 22 ring finger tendons lie at first superficial. All of these tendons within the carpal tunnel have a degree of freedom. After passing through the carpal tunnel, the FDS tendon diverges together with a FDP tendon, and passes over the MCP joint into an osteofibrous tunnel on the palmer surface of the middle phalange such that FDP tendon can pass through, and fold about the FDP tendon so that their lateral edges come to meet in the midline beneath this tendon. Then they again separate, extend distally, and attach to a ridge on each side of the middle phalange. The FDS tendon of the middle finger is always independent while ring finger is sometimes independent. However, FDS tendons of the index and little fingers are closely linked to each other. The nerve of the FDS is supplied by the median nerve (Steinberg, 1992).

The length of the muscle fibers of the FDS is between 7.0~7.3cm, which is a little longer than that of FDP (Brand et al., 1981). The main action of the FDS muscle is to flex the middle phalange on the proximal interphalangeal joint, to flex the fingers on the hand and the hand on the forearm. There is wide variation in the tension capabilities of the

FDS muscles. 23

Figure 2.5. FDP and FDS tendons of a typical digit (source: Netter, 1989)

2.2.4. Pulley system of the flexor tendon sheath

The tendon sheath is an important physiologic and biomechanical element of the flexor tendon mechanism. The sheath, a double walled tube, surrounds the tendons and contains synovial fluid. The synovial sheath provides a low-friction gliding environment for the flexor tendon and nutrients for maintenance of the tendon and tenocytes, along with the intrinsic blood supply. The flexor tendon sheath begins at the neck of the metacarpal phalange and ends at the distal interphalangeal joint. In each finger, two main flexors (FDP & FDS) are surrounded by their synovial sheath and held against the phalanges by the fibrous tendon sheath. Overlaying the synovial sheath is the pulley.

The pulley can be divided into three types according to the locations: a palmar aponeurosis pulley, five annular pulleys (A1, A2, A3, A4 and A5) and three cruciate pulleys (C1, C2 and C3). The A2 and A4 pulleys are located on the proximal and middle phalanges, respectively. The A1, A3 and A5 pulleys are located at the palmar surface of the MCP, PIP and DIP joints (Figure 2.6).

These pulleys maintain a relatively constant moment arm and prevent tendon bowstringing across the joints during flexion. In detail, the broader and denser annular pulleys prevent tendon bowstring to provide optimal joint flexion for a given amount of tendon excursion. The more variable and thinner cruciate pulleys provide flexibility of the flexor sheath.

Many researchers (Doyle, 1989; Idler, 1985; Lin et al., 1990) have clinically and anatomically studied the finger pulley system. Mostly they underscored the importance of the A2 and A4 pulleys for normal function and a stable joint. The other pulleys such as palmar aponeurotic and A3 pulleys become important only when the A2 and A4 pulleys 25 have been damaged. Marco et al., (1998) performed a study for rupture of the flexor tendon pulleys in the crimp (or cling) grip with 21 cadaver fingers. In most of cases, the initial failure occurred either in the A2 or A4 pulleys followed by the rupture of A3 pulley despite its relative weakness and its location at the center of the proximal interphalangeal (PIP) joint. Based on a review of the videotapes, they explained that the

A3 pulley stretched to the volar side as the force increased in the flexor tendons. The forces were transferred from the A3 pulley to the stiffer A2 and A4 pulleys, then these two pulleys were damaged before the more flexible A3 pulley.

C3 C2 C1

A5 A4 A3 A2 A1

Figure 2.6. Pulley Structure of the Finger (A = annular, C = cruciate). (source: Nordin and Frankel, 2001) 26

2.3. Biomechanical analysis of the hand

The relationship between the finger tendon forces and the externally applied forces to the fingers is essential to understand the mechanisms of hand disorders.

Studying tendon forces can help us understand how external forces are transmitted to the internal tendons and identify which tendons are highly exposed to these external forces.

In addition, these studies can help the clinician in planning and optimizing interventions for the best recovery of mechanical function. (Weightman and Amis, 1982; Schuind et al.,

1992). .

There are two common methods for quantification of tendon forces: analytic models experimental and analysis. Several analytic biomechanical finger models that are based on the equations of static equilibrium at each joint of the finger have been developed to evaluate tendon forces based on externally applied forces. Experimental direct tendon force measurement models also have been applied for more comprehensive understanding of the mechanism of these tendons inside of the fingers.

2.3.1. Analytic models

In the field of biomechanics, there has been continued interest in quantitative evaluation of the forces imposed on the human body. Many analytic models that predict muscle forces by applying mechanical laws have been formulated. In these models, the human body was considered as a system of rigid, articulating segments on which known external forces and unknown muscle and joint force acted. The objective of the analytic 27 model is to determine the muscle forces that are required for static and dynamic equilibrium.

However, one of most restrictive problems in analytic modeling is the redundant nature of the system being analyzed, in which more muscles than are strictly necessary to obtain equilibrium normally cross a joint. Accordingly, the number of muscles crossing the joint exceeds the number of equilibrium conditions at the joint and no unique solution can be obtained. To solve this indeterminate problem, two methods have been employed; the reduction method and the optimization method. The reduction method is performed either by grouping functionally similar muscles, or by eliminating them based on EMG observation while the optimization method is performed by applying an optimization algorithm with respect to selected optimization criterion.

2.3.1.1. Reduction methods

The reduction method that reduces excessive unknown variables has been one of the most commonly used methods in this area. The main objective of this method is to reduce the number of excessive variables until the number of unknown forces is equal to the number of required equilibrium equations, thus eliminating static indeterminacy.

Borelli was the first researcher who applied Newton’s law to the human body to calculate muscle forces and used the reduction method (Dul, 1983). Since then, several researchers (Hirsch et al., 1974: thumb, Smith et al., 1964: finger; Chao et al, 1976: finger) used the reduction method to estimate muscle forces.

Smith et al. (1964) analyzed index finger metacarpophalangeal (MCP) joint forces during tip pinch with a two dimensional model. The authors assumed (i) that the extensor 28 muscles were relaxed, (ii) that the radial and ulnar interossei could be treated as a single force and (iii) that the lumbrical muscle exerted a force of one sixth of the total interosseous force. Solution of three moment equilibrium equations, for an external load of P, produced values of 3.8P, 2.5P, and 2.1P for the flexor digitorum profundus (FDP), flexor digitorum superficialis (FDS) and intrinsic tensions, respectively.

Chao et al. (1976) used a three dimensional model to analyze the forces at all three finger joints during tip, lateral, and ulnar pinch, and grasp. Particularly, in this paper, the joint and tendon orientations were well defined. In order to determine tendon and joint forces, unknown tendon forces were systematically eliminated on the basis of EMG and physiological assessment. They found that flexor muscles have greater strength during pinch, whereas intrinsic muscles have greater strength during grasp. However, they did not verify their results. As seen in the above two studies, the reduction method has beeen appreciated by many researchers for its simplicity. However, the anatomical simplification inevitable for the reduction method might have induced considerable errors.

2.3.1.2. Optimization method

The optimization method is an alternative solution method for the analytical model. Instead of eliminating unknown muscle forces in the redundant equation system, an unique solution can be obtained from a mathematical formulation and optimization algorithm. The most influencing factor in this approach is an optimization criterion

(usually physiological criterion in muscle force calculation) which corresponds to the objective function. Hence the optimization criterion is decided first. Second, objective functions and constraints which represent the system considered are formulated. Then, an 29 optimization algorithm is applied to decide the best solution among candidate solution provided by the objective function.

Chao and An (1978) studied the middle finger during tip pinch and power grip actions, with an aid of three-dimensional analysis. They analyzed the same problem using the optimization and linear programming (LP) technique of Chao et al. (1976) instead of the previously described EMG and permutation-combination method. The predicted middle finger muscle and joint forces were very similar to those of the previous study

(Chao et al., 1976), except for the intrinsic muscle forces whose predicted values were considerably lower. They found that the highest joint contact forces for all three joints occurred for pinch grip rather than power grip. They also found that the main flexors

(FDP and FDS) were most active in both pinch and power grip functions, whereas the intrinsic muscles were less active in power grip than in pinch.

However, in terms of optimization methods, these models were unable to predict synergistic muscle action. Thus, cautions must be imposed on drawing conclusions about the validity of an optimization criterion when the results are correlated with EMG observations.

2.3.2. Experimental analysis

2.3.2.1. EMG studies

The EMG method is a readily available technique which can be applied to the force analysis and the muscle function analysis. Also, it is used to validate the analytical model. Generally, muscle activity is recorded either via a surface electrode on the skin or 30 via a needle or wire electrode in the muscles. The biggest problem in using electromyographic technique was in locating the electrodes. While it has been relatively easy to identify large, superficial muscles, considerable difficulty has been experienced with small and deep muscles.

Chao et al. (1989) first used EMG technique to quantify the amount of force exerted in hand muscles under isometric contraction. Their initial motivation for this study was in the verification of predicted results from their mathematical model. They conducted two experiments: an isolated isometric test and a pinch/grasp function test. In the former study, they derived maximum EMG signals of tested muscles in the naturally extended position and established the muscle tension and EMG relationship. In the latter part of the study, the forces were measured simultaneously with EMG signals during pinch/grasp functions. They developed an algorithm for force analysis, based on the polynomial relationship between tension and integrated EMG. Absolute muscle forces during several pinch/grasp functions were calculated by using this algorithm, and were normalized against the applied force. Particularly, ranges of the forces in FPL (Flexor

Pollicis Longus) and EPL (Extensor Pollicis Longus) muscles showed a good accordance with the results from the analytical math model.

2.3.2.2. in vivo Studies

Directly measured tendon forces under isometric finger function were first reported by Bright and Urbaniak (1976). They developed a force transducer to measure the tendon forces in both tip pinch and power grip actions during operative procedures.

Flexor tendon forces were found to be in the range of 4.0 to 20.0 kg and 1.25 to 15.0 kg 31 for the Flexor Digitorum Profundus (FDP) and Flexor Digitorum Superficialis (FDS), respectively in power grip action, while 2.5 to 12.5 kg for the FDP and 1.0 to 7.5 kg for the FDS in pinch action. Since they directly measured the tendon forces only, they did not report the actual applied pinch and power grip force and the ratio of tendon force to the externally applied force.

Schuind et al. (1992) directly measured forces in the flexor tendons (FPL, FDP and FDS) during various finger functions. They developed an s-shaped tendon force transducer and measured flexor tendon forces in pinch and power grip functions. Also, a pinch dynamometer was used to record the applied loads in pinch action. The tendon forces showed proportionality to the externally applied forces. To compare their results with the previously published mathematical finger models, they normalized their tendon forces, as a ratio of the tendon force to the applied forces. In tip pinch, the ratios were

3.6P, 7.92P and 1.73P, for the externally applied force P, for the FPL, FDP and FDS, respectively. In lateral pinches, the ratios were 3.05P, 2.9P and 0.71P for the FPL, FDP and FDS, respectively. Although the FDP and FPL showed high forces during tip and lateral pinch, the maximal values recorded are probably on the lower side of the potential forces and it could be explained by the significantly weaker pinch and power grip forces during carpal tunnel surgery due to the denervation or partial anesthesia of the sensory area of the median nerve. However, generally the magnitude of tendon forces in this study was similar to values reported by Bright and Urbaniak (1976), although direct comparison is not possible since the applied force was not recorded in their study.

In another in vivo tendon force measurement study, Dennerlein et al. (1998) measured only FDS tendon forces of the middle finger at three finger postures, which 32 ranged from extended to flexed pinch postures using a gas-sterilized tendon force transducer (Dennerlein et al., 1997) and a single axis force transducer (GreenLeaf

Medical Pinch Meter, Palo Alto, CA). The investigation was centered upon the average ratio of the FDS tendon tension to the externally applied force. The average ratio ranged from 1.7P to 5.8P, with a mean of 3.3P, in the study. Tip pinches with the DIP joint flexed were also studied with the tendon-to-tip force ratio being 2.4P. These ratios were compared with the results of their own three finger models as well as other contemporarily published isometric tendon force models. These ratios were larger than those of other studies. The average values were also slightly higher than that (1.73P) of

Schuind et al.'s (1992) in vivo tendon force measurement study. It was found that the tendon force ratios and muscle strength varied substantially from individual to individual, although the ratio of force from tendon to tendon was relatively constant within the same limb for all studies (Brand et al., 1981; Dennerlein et al., 1998).

2.3.2.3. Cadaveric Studies

Brand et al. (1981) measured the mass or volume of a muscle that is proportional to its work capacity, and the fiber length of a muscle that is proportional to its potential excursion. The mass fraction of FDP was 29.4% higher than the FDS and tension fraction of FDS was 30.3% less than the FDP. Consequently, the tendon force ratio of FDP to

FDS was 3:2 FDP to FDS. An et al. (1985) also measured the volume and fiber length of muscles. By dividing the volume of the muscle by the fiber length of the muscle, the

Physiological Cross-Sectional Area (PCSA) of the muscle was determined. The PCSA of 33 all fibers was proportional to maximum tension. Thus, he reported the FDP had 12.3% larger than the FDS in analysis of PCSA.

Valero-Cuevas et al. (2000) measured tip pinch motion of cadaver hands to estimate fingertip force reduction following peripheral nerve injuries. For the tension of tendons, they used springs pulling extrinsic and intrinsic tendons and anchoring Nylon cords tied to the proximal end of a spring. Thus, known tensions could then be applied to individual tendons, and simultaneously to several tendons, and the fingertip force output measured. The comparison of the ratio of tendon tension to fingertip force was 2.8 and

1.33 for FDP and FDS, respectively. Therefore, flexor tendon force was 4.13 times higher than the external fingertip force.

2.3.3. Tendon force ratio of the FDP and FDS

Although the intrinsic muscles are more active in pinch action than in power grip action, the relative magnitudes of the main flexor tendon forces (such as FDP and FDS) are usually high in both actions. The in vivo tendon forces of the flexors measured in previous studies, are presented in Table 2.3. In general, the averages and ranges of tendon forces are similar with a few exceptions. Schuind et al. (1992) showed lower FDS tendon forces in power grip action than those of other types of grips. They also indicated significant differences between FDP and FDS tendon forces in both pinch and power grip, whereas the others showed that the force of FDP tendon was only slightly larger than that of the FDS tendon. These discrepancies can be explained by the different finger postures utilized in each study, since each finger could have various functional muscle 34

capacities depending upon its joint configuration (Chao and An, 1978). In all these in vivo tendon force studies, the muscle and tendon forces were proportional to the externally applied forces. However, the predicted maximum tendon forces are probably lower than the true potential forces because these experiments were performed during carpal tunnel surgery under local anesthesia in the median nerve innervation area. In such cases, the muscles are partially inactive and produce lower pinch and power grip forces.

To normalize these tendon forces, the ratios of the tendon force to the applied force, FDP to FDS, and joint forces are studied for both pinch and power grip functions (see Table

2.4). Average ratios of tendon forces to the applied forces in the tendon force prediction models were, for an external force of P, 3.5P (SD: 0.74), 1.8P (SD: 1.03) and 3.67P (SD:

2.29) for the FDP, FDS and I (intrinsic) tendons in pinch, while 3.14P (SD: 0.29), 3.48P

(SD: 0.72) and 11.4P (SD: 6.6) were for FDP, FDS and I tendons in power grip, respectively. Generally all data agreed with high contributions of flexor tendons (FDP and FDS) for both pinch and power grip actions, although intrinsic tendons showed high

Table 2.3. Cadaver (Kg) and in vivo tendon forces (N) of FDP and FDS

Finger Configuration FDP FDS

Brand et al., 1981 - 14.9* (13.5-17.0) 10.4* (4.5-17)

Ketchum et al., 1978 MCP joint flexion 5.7* (5.27-6.18) 6.12* (3.73-7.63)

Tip Pinch 2.5-12.5 1.0-7.5 Bright et al., 1979 Power grip 4.0-20.0 1.25-15.0

Tip Pinch 8.3 (2.0-12.0) 1.9 (0.3-3.5) Schuind et al., 1992 Power grip 4.0 (1.9-6.4) 0.6 (0.0-0.9)

(Note: *- average tendon forces for all fingers in cadaver studies) 35 variations among those data. The average ratios of FDP to FDS were also obtained,

2.92:1 and 0.93:1 for pinch and power grip, respectively. These data showed the significant strength of the FDP tendon for the pinch actions, whereas the fairly equal contributions of these two flexors to the overall power grips.

Validating these mathematical solutions by experimental measurement was undertaken by Schuind et al. (1992), although they did not measure the externally applied force at the same time with tendon forces in power grip. They only used the pinch dynamometer for measuring the amount of the applied force for pinch functions. Thus, the mean tendon forces were applied for validating power grip functions in this study.

In pinch actions, Schuind et al. (1992) reported the higher ratio of FDP to the applied force (7.92P) than the result (3.5P) of mathematical tendon force prediction models. The FDS ratio to the applied force (1.73P), however, was fairly similar to the

Table 2.4. Tendon and joint forces ratios to external forces in power grip function

Muscle Force Joint Force Finger FDP FDS FDP/FDS I DIP PIP MCP Bright et al., 1976 - 4.0-20.0* 1.25-15.0* - - - - - Schuind et al., 4.0** 0.6** 6.67 - - - - 1992 - Index 2.77 2.53 1.09 5.76 .09 4.35 12.7 Chao et al., 1976 Middle 3.05 4.23 0.72 .10 .17 7.11 3.9 Little 3.37 3.40 0.99 5.21 3.31 6.02 4.5 Chao and An, 3.37 3.75 0.9 1.64 3.89 6.8 5.18 1978 Middle An et al., 1985 Index 3.17-3.47 1.51-2.14 0-1.19 2.8-3.4 4.5-5.3 3.2-3.7 (Note1: *: tendon force, unit: kg; **: mean tendon forces, unit: kg) (Note2: I: intrinsic (interossei plus lumbrical) muscle) 36 average ratio (1.8P) in the finger model studies. Because of the large force measurement for the FDP tendon, higher ratio of FDP/FDS (4.6P) was presented in their study than that of finger model studies. As another direct measurement data, Dennerlein et al. (1998) found the higher tension ratio of the FDS tendon to the applied force (3.3P) than those of mathematical finger model studies.

In power grip actions, there were no in vivo tendon force data for the ratio of tendon force to the externally applied force. Thus, only the FDP: FDS ratio of direct measurement study can be used for the comparison with the finger model studies. They presented a 6.67:1 ratio based on their mean tendon forces of FDP and FDS. The force of

FDP was significantly larger than that of FDS in direct measurement study, whereas both

FDP and FDS had similar contributions to power grip (3.14P for FDP and 3.48P for FDS) and a FDP: FDS ratio of 0.93:1 was also calculated in finger force prediction models. The variability of these results may be expected since all researchers did not use the same finger characteristics: moment arms, finger configurations and angles of the applied forces to the finger tip or pulp area.

There are controversial issues for the functions of tendons (intrinsic muscles vs. flexors) during pinch and power grip actions in biomechanical finger models. Based on the solutions from the three moment equations, Smith et al. (1964) found that flexor tendons usually carry larger forces than the intrinsic muscles during tip pinch. Chao and

An (1978) also supported this result in their study. They showed that the flexors were most active and produced high tendon forces in both pinch and power grip actions.

However, Chao et al. (1976) and An et al. (1985) suggested contradictory results for the contributions of intrinsic muscles in finger actions. They presented higher contributions 37 of intrinsic muscles than those of the flexors in pinch and power grip functions. In general, although the magnitude of the intrinsic muscle force was less than that of the flexors, the intrinsic muscles were more active in pinches than in power grip. An et al.

(1985) also agreed with high intrinsic muscle forces in pinches and explained it by the need for these intrinsic muscles to balance and stabilize the large MCP joint forces.

Most of these studies showed similar trends for joint forces. Small constraint forces and moments were seen at both the DIP and PIP joints, while the constraint forces and moments were considerably higher at the MCP joint in both actions. DIP and PIP joint forces of the power grip actions were relatively lower than those of the pinch actions.

This may explained why hands are more adaptable in performing powerful grip actions rather than pinches since it is more difficult to maintain the proper stability requirements at the distal joints (Chao et al., 1976).

Through these two- or three-dimensional models, many researchers have tried to understand how the externally applied forces are transmitted across finger joint to the internal tendons of the human hand and how these tendon forces relate to the applied forces. Generally most studies agreed with high contributions of flexor tendons (FDP and

FDS) in power grips and good proportionality tendon forces to the external forces.

However, generally, the in vivo direct flexor tendon forces and the FDP to FDS ratios were larger than those predicted from the finger models.

In spite of the relatively low tendon forces predicted in biomechanical finger models, FDP and FDS tendon forces were 3.14~3.5 times and 1.8~3.48 times larger than the applied forces in pinches and power grips, respectively. Thus, large and repeated tendon forces can be a contributory factor in tendon disorder, especially in hand intensive 38 tasks. In addition, these tendon forces varied due to the finger joint configurations or finger postures utilized in each task. Therefore, properly designed hand tools, which optimize the hand posture to minimize tendon forces, can reduce and prevent work- related musculoskeletal disorders.

The essential part of the finger model is the basic assumptions to simplify the finger mechanism. From a mathematical point of view, the simpler the anatomy, the simpler the finger model. However, these simplifications of the finger mechanics can lead to misleading information on the joint and tendon forces calculated from the finger model.

In addition, most of these finger models have been developed for clinical and rehabilitation purpose to simulate the muscle and tendon forces involved in grasping an object (Chao et al., 1976; Cooney and Chao, 1977). There are only a few studies that have applied to the analysis and evaluations of the hand tool tasks and hand tool designs.

Therefore, the development of a more carefully and accurately designed biomechanical finger model is critical to understanding the mechanism of tendon disorders. The finger model should then be applied to more practical working conditions

(such as intensive hand tasks, hand tool designs).

Because of the limitations of the external force measurement system, it was not possible to truly analyze the ratio of each tendon force to the applied force in power grip function. Therefore, the development and application of better experimental systems are needed to do more reliable validation for the results from the theoretical finger models. 39

2.3.4. A Two dimensional hand model

From a biomechanical perspective, the extrinsic finger flexors, FDP and FDS, comprise the main sources of power for finger flexion in grasping type motions, especially power grip. Kong and Freivalds (2003) established static equilibrium equations for each phalange and for each finger (see Figure 2.7). Because most of the tendon-pulley attachments are in line with the long axis of the phalanges and there are small lateral force components, only two axis, the x and y, need to be defined. Therefore, a simple two-dimensional model utilizing those two tendons should be sufficient for most applications. To further define the model, several other assumptions need to be made. All assumptions and equations were quoted from Kong’s study (2001).

Assumptions of the hand model

In order to define and simplify the system of biomechanical analysis, these assumptions, which were adapted from Chen (1991), are necessary in this study.

1. No effects of intrinsic muscles and extensors: The effects of these muscles on the

finger flexion can be neglected since these muscles will relax their viscoelastic

property when the joint angles are within their normal range of motion during power

grip or grasp (Armstrong, 1978).

2. Hinge Joints: All of the interphalangeal and metacarpal joints (DIP, PIP and MCP

joints) are hinge joints; consequently, they only permit flexion and extension.

3. Flexor digitorum superficialis (FDS) insertion: Anatomic analysis shows that the FDS

is inserted by two slips to the sides of the proximal end of the middle phalange 40

(Steinberg, 1992). However, it is assumed that each FDS tendon is inserted to the

palmar side of the proximal end of the middle phalange. Furthermore the direction of

insertion is assumed to be parallel to the proximal phalange’s long axis in this study.

In a two-dimensional biomechanical model, the effect of having two splits inserted

along the sides of the bone is the same as having one tendon inserted on the palmar

side of the proximal end of the middle phalange.

Figure 2.7. Free-body diagram for a two-dimensional hand model. (source: Kong, 2001)

4. Tendons and tendon sheaths are modeled as frictionless cable and pulley system.

Therefore, a single tendon passing through several joints maintains the same tensile

force (Chao et al., 1976).

5. External load: The externally applied forces are assumed to be a single unit-force

exertedd at the mid-point pulp of a distal phalange for pinch or by three-unit forces 41

applied normally at the mid-point of each phalange and metacarpal bone for grasp as

seen in Figure 2.7. The direction of the force is assumed to be perpendicular to the

long axis of the bone. Also, any geometrical parameters of the axis of hand

musculature remain unaffected by the magnitude of the load.

6. No effect of finger deformations: Deformation of the bones and the tendons are

neglected since only healthy subjects were used with no injuries occurring during the

experimental grasp exertions.

7. No mass effect: The weight of the bones together with other soft tissues on the hand

was assumed to be negligible. In case of involving the external load, the mass effect

was a very small percentage of the external load.

8. The tendon force ratio of FDP to FDS at the each phalange: It is assumed 3:1 (that is,

 = 0.333 (Marco et al., 1998). Marco et al. used a 3:1 profundus-to-superficialis

tendon force ratio that resulted in rupturing the pulleys before avulsion of the flexor

digitorum superficalis tendon.

9. Tendon moment arms: Tendon moment arms of the two flexors (FDP & FDS) can be

estimated for distal and proximal interphalangeal and metacarpal phalangeal joints of

different thickness (Armstrong, 1978). The tendon moment equations for these

flexors are predicted by following equations:

FDP: PRik (mm) = 6.19-1.66X1-4.03X2+0.225X3 Eq. 0.1

FDS: SRik (mm) = 6.42+0.10X1-4.03X2+0.225X3 Eq. 0.2

where,

th th PRik = FDP moment arm for the i finger and k joints.

th th SRik = FDS moment arm for the i finger and k joints.

X1 = 1 for the proximal interphalangeal joint (PIP) and 0 for all others.

X2 = 1 for the distal interphalangeal joint (DIP) and 0 for all others.

X3 = Joint thickness (mm) measured according to Garrett (1970).

Consequently, these equations can be summarized as follows:

DIP joint: PRi (mm)= 2.16+0.225 X3 Eq. 0.3

PIP joint: PRi (mm)= 4.53+0.225 X3 Eq. 0.4

SRi (mm)= 6.52+0.225 X3 Eq. 0.5

MCP joint: PRi (mm)= 6.19+0.225 X3 Eq. 0.6

SRi (mm)= 6.42+0.225 X3 Eq. 0.7

Four Cartesian coordinate systems are established to define the locations and orientations of the tendons and to describe the joint configuration. There are two coordinate systems for both the middle and proximal phalanges and only one system for the distal and metacarpal phalanges. The y-axis is defined along the long axis of the each phalange, from the proximal end to the distal end. The x-axis is defined as perpendicular to the long axis of each phalange and in the palmar-dorsal plane, from the palmar side to the dorsal side of the finger bone. Both x- and y-axes have their origins at the center of the proximal end of phalange. In terms of notation, subscribe i refers to fingers, with 1 to

4 for the index, middle, ring, and little fingers, respectively, subscript j refers to joints, 43 with 1 to 4 for the DIP, PIP, MCP, and wrist joints, respectively, while subscript k refers to phalanges, with 1 to 4 for the distal, middle, proximal phalanges, and the metacarpal bone, respectively.

In terms of model input values, the external force on each phalange of each finger is indicated by F(i,j). The finger joint flexion angles, measured with reference to straight fingers as the hand is lying flat, are indicated by (i, j). The length of each phalange for each finger is indicated by L(i,k).

For the model output variables, the FDP tendon force for each phalange of each finger is indicated by TP(i,k). The FDS tendon force for each phalange and each finger is indicated by TS(i,k). Finally, joint constraint forces along the Xk- and Yk-axes are indicated by Rxk(i,j) and Ryk(i,j), respectively.

To solve for the above unknown model output variables, a static equilibrium analyses of each phalange in the x- and y-axes must be zero. Similarly, the summation of all moments acting on each phalange must also be equal to zero.

Therefore, joint forces and tendon forces for each phalange can be obtained: 44

DISTAL PHALANGE:

TP (i,1)= 0.5 [L(i,1) / PR (i,1)] F(i,1) Eq. 0.8

Ry1(i,1)= TP(i,1)cos(i, 1) Eq. 0.9

Rx1(i,1)= TP(i,1)sin(i, 1)-F(i,1) Eq. 0.10

MIDDLE PHALANGE:

TP (i,2)= Eq. 0.11 [0.5F(i,2)-Rx1(i,1)cos(i, 1)+Ry1(i,1)sin(i, 1)]L(i,2)/[ SR(I,2)+PR(i,2)]

TS (i,2)=  TP(i,2) Eq. 0.12

Ry2(i,2)= Rx1(i,1)sin(i, 1)+ Ry1(i,1)cos(i, 1)+ (+1) TP(i,2)cos(i, 2) Eq. 0.13

Rx2(i,2)= Rx1(i,1)cos(i, 1)- Ry1(i,1)sin(i, 1)+(1+ ) TP(i,2)sin(i, 2)-F(i,2) Eq. 0.14

PROXIMAL PHALANGE:

TP (i,)= Eq. 0.15 {0.5F(i,3)-Rx2(i,2) cos(i, 2)+Ry2(i,2)sin(i, 2)}L(i,3)/ [ SR(i,3) +PR(i,3)]

TS (i,3)=  TP (i,3) Eq. 0.16

Ry3(i,3)= Rx2(i,2)sin(i, 2)+ Ry2(i,2)cos(i, 2)+ (+1) TP(i,3)cos(i, 3) Eq. 0.17

Rx3(i,3)= Rx2(i,2)cos(i, 2)-Ry2(i,2)sin(i, 2)+ (1+)* TP(i,3)sin(i, 3)-F(i,3) Eq. 0.18

Therefore, final tendon forces of the FDP and FDS are calculated by following equation.

FDP = TP(1)+TP(2)+TP(3) Eq. 0.19 FDS = TS(2)+TS(3) Eq. 0.20 45

Chapter 3

THE HAND MOTION SIMULATOR

The Hand Motion Simulator (HMS) was built to simulate hand motions and postures in a cadaver hand. Muscle forces generated by linear actuators with force feedback control were applied to the tendons of the extrinsic muscles of the hand. The

HMS was composed of five essential parts: frame supporting a specimen, motion delivery unit through stepper motor driven linear actuators applying forces to the muscle tendons, data acquisition unit for force transducers measuring internal and external forces, kinematic vision measuring finger joint angles, and operating program to control the

HMS.

3.1. Support Frame

Aluminum T-slotted profile bars support the main structure of the frame (see

Figure 3.1, 3.2). The external fixation frame was incorporated into the inner-frame with two bars placed parallel to each other through the radius and the ulna. 6 fixators for securing the forearm were suspended from the bars with vertical shafts to adjust the height. An adjustable handle fixture was rigidly located on top of the frame. The handle fixture secured the handle to the frame to prevent shifting during power grip motion. All fixtures are adjustable to allow for vertical & parallel positioning. Fixtures are used to secure a forearm, fasten a handle, and attach a camera on the external cage. In terms of the motion capture, a CCD camera was placed on the side of external frame 46

perpendicular with lateral view to record finger joint angles. In the motion unit, two stepper motors were vertically installed on the side of frame, and faced each other on the inner & outer fame to arrange force delivery cables in a row. Force delivery metal wires connected the stepper motor to a clamp for each tendon. However, since the line from a motor was perpendicular to the line from a clamp, a pulley system was placed on the top of frame side. The pulley wheel had a non-friction ball bearing to minimize friction with a cable.

Figure 3.1. Schematic drawing of the hand motion simulator

FSRs

Freeze clamps

Force Deliver Unit Wristjack® (FDU) Load Cells Camera

Figure 3.2. Schematic drawing of the hand motion simulator

3.1.1. Forearm fixators

Fixators for a forearm were placed on the both sides of the frame. To adjust the forearm position, the fixture was designed with horizontal & vertical adjustability (Figure

3.3). To fasten the forearm in position, six Schanz screws (self-drilling

4.0mm/175mm(length)/40mm(thread), Synthes Inc.) were laterally cross-drilled into the radius and ulna, and the screws pins were thrust into fixators suspended from the sidebars.

An adjustable fixation system (Wristjack®, Hand Biomechanics Lab, Inc) was also secured to the forearm frame. It held the wrist in specific angles of flexion or extension, postures observed in power grip motion (Figure 3.4). Two small pins were screwed into the metacarpals through the metacarpal bar to fasten the hand to the fixator. The inner- frame with the wrist fixator allows incremental adjustment of palmar tilt, radial inclination, length and rotation.

Figure 3.3. Fixators for fastening the pins cross-drilled into radius and ulna

Figure 3.4. Adjustable wrist fixator (Wristjack®, Source: Surgeon’s Manual)

3.1.2. Cylindrical handle and handle fixture

A cylindrical force transducer dynamometer was designed and constructed to measure force in a single axis of sensitivity and to measure all forces applied along the handle length, independent of point of contact. It was split and a force transducer was inserted in between halves handles. This type of split cylindrical handle has been used to measure grip force by many researchers (Ayoub and Lo Presti, 1971; Dong et al., 2004;

Edgren et al., 2004; Irwin and Radwin, 2008). The force transducer signals were amplified and digitized using a 12-bit analog-digital converter. The data acquisition sample rate was 10 Hz. The handles included cylinders of 30, 37, 45, 50, and 60 mm diameter (see Figure 3.5). The handles were made of aluminum and were inter- changeable with a force transducer.

These handles were required to be fixed in position while pulling tendons for power grip motion. Since a cadaver hand did not have stable reaction force to a thumb and palm, the handle might be tilted by finger flexion for power grip motion. To prevent the undesired movement of the handle, the handle fixture was installed to keep the handle in place. The fixture consisted of vertical poles attached to the frame, a knob to adjust vertical position, and also a cross bar to fix the vertical poles on the main frame (see

Figure 3.6). A camera fixture was attached on the side of the cage in lateral view. The fixture could be slid on the side of cage to stand in line with the cross-sectional side of the handle. Thus, the camera vision kept a lateral view to the handle and grip posture and also captured the finger joint angle of power grip motion. 50

Figure 3.5. Split cylindrical handles with five different diameters

Figure 3.6. Handle fixture with a height adjustable knob and handle fixing clamps 51

3.2. Motion System

3.2.1. Force delivery unit

The excursion of the Flexor Digitorum Superficialis (FDS) and the Flexor

Digitorum Profoundus (FDP) was controlled by a two Force Delivery Units (FDU) (see

Figure 3.7). Each FDU consisted of a stepper motor driven linear actuator (model EC2H:

Industrial Devices. Novato, California) in series with a force transducer (model LCCA-

500; Omega Engineering). Each force transducer was attached to a cable (metal wire) connected to a freeze clamp in the line of force of each muscle. The freeze clamp was employed to maintain a secure couple between a force delivery cable and fresh musculotendinous tissues and without slippage. These devices have been successfully employed in other muscles (Sharkey et al. 1995). The freeze clamp was attached firmly to the tendons and liquid nitrogen was circulated through one half of the clamp in order to freeze the tendon solid at the interface to provide an extremely rigid connection between cable and tendon. The FDU frame was adjusted to maintain cable length irrespective of specimen size. The linear actuator of each FDU was powered and controlled by using a stepper motor controller that receives command input from a motion controller (UMI-

7764, NI) (see Figure 3.8). This motion controller residing in a controlling PC was coupled with a universal motion interface (UMI) card. Since the UMI had compatibility of different manufactured parts, the protocol was not a problem between the motor and motion controller. The UMI incorporated a host PC power monitor that inhibits the motion driver if the host PC loses power during motion control. In addition, The UMI monitored the +5 VDC from the PC and activated the inhibit signals if the voltage fell out 52

of tolerance. The controlling computer received a force feedback from force transducers measuring actual tendon forces and implemented a force-feedback control loop in order to reduce the steady state error between the actual force and the target force for the muscles to less than deadband offset. The controlling computer used a velocity control to converge the motion to the target force.

Stepper Motor Driven Linear Actuators Freeze clamps Load Cells

Tendons Cables

Controlling ForcePIC Stepper Motor Computer Micro-Controller Controller

Figure 3.7. The Components of Force Delivery Unit (DFU)

Figure 3.8. Motor and motion controller in FDU 53

3.2.2. Muscle force control

To control muscle force, the custom developed HMS Software (LabView,

National Instruments, Inc.) had two modes: the force feedback control loop and direct control. Muscle forces were controlled by a feedback control loop based on the actual force, FA, measured by each force transducer and the desired force, FD.

The HMS software read in three forces: actual force, FA, target force, FT, and adjustable deadband offset force, Fdb, used to control the sensitivity of the control loop.

The data acquisition system with analog to digital converters read these voltages and the motion controller kept pulling until reaching the target force, FT. Stepper motors in the feedback control loop could possibly overshoot and oscillate. For smoother convergence of the motion on the target force, a velocity control algorithm was incorporated in the force feedback control. When the actual force was greater than the target force in accordance with overshoot, the velocity of the actuator was reduced by a half of the original velocity the moment the actuator let the cable out. Likewise, when the actual force, FA went down below the target force, FT, the velocity of the actuator was decreased by a half of the already reduced velocity the moment the actuator pulled in. Through these successive repetitions of reducing velocity, the motion finally stopped at the convergent point balancing with the target force, FT. However, a ripple of force signals from force transducers made the stepper motors have infinite oscillated motions. To remove these small fluctuations of the motion of motors, the force feedback control loop were controlled by adjustable deadband offset, Fdb. The offsets force of the FDP and the

FDS was determined by the ripple variation of signals from force transducers, and could be regulated during the operation. Consequently, the motion of the Force Delivery Unit 54

was finally suspended on target forces with this force feedback control loop. The entire process is presented in Figure 3.9 and the following shows the simple flow of the force feedback control loop.

Input Target Force = FT1

Input Initial Pulling Speed = Vdefault

While 1

F1=Read Actual Force V = Vdefault

If F1 < FT1 Pull in

Else if F1 > FT1 Let out V = V / 2 Else Do nothing End

In terms of visco-elastic properties of tendon and muscle, the tensions of cables connected with suspended motors sometimes decreased with tendon creep, and the actual forces slowly went down below the target force with lapse of time. To compensate for loss of cable tensions, the actuator needed to re-activate the pulling motion by the force feedback control. According to the re-activation of the force feedback control loop, initial velocity was input to the feedback control after reset of the final zero velocity. The sensitivity of motion was also adjusted by Fdb on the front panel.

Figure 3.9. Workflow of the force feedback control system

The Force Delivery Unit (FDU) could be operated in direct modes as well. In this mode, the user has direct control of the each FDU and can move the actuators in and out directly. Hence, the operator could manually control the HMS in direct mode. This mode was used for tendon length adjustment when the specimen was being placed in the HMS and the freeze-clamps were being attached. In terms of safety, the operator is able to intervene and stop a test at any point.

3.2.3. Muscle forces in the experiment

Basically, tendon forces and ratios between the FDP and FDS might be diverse, depending on finger postures in power grip motion. As seen in section 2.3.3, the tendon forces and the ratio of FDP and FDS had a large variability that may be expected because all researchers did not use the same finger characteristics. Therefore, in this study, the hand motion simulator activated the flexor tendons with various tendon force ratios to define power grip mechanism, and the ratios were investigated with response variables

(grip force, finger force distribution and finger joint angle).

There were two types of experiments conducted with different ratios. In the first experiment, the FDP force was held constant at 100N, and the FDS force was increased in 20N increments from 20N to 100N. Hence, the total tendon force of the flexor tendons was also increased from 120N to 200N along with the FDS force increase as five different FDS forces applied. The tendon force ratio was simultaneously changed from

100:20 (5:1) FDP to FDS force to 100:100 (1:1) as well. The second experiment was conducted in a different way. The total flexor tendon force was a constant (200N) and both FDP and FDS forces were set at five different ratios whereby FDS increased from 57

20N to 100N by 20N increments. Simultaneously, the FDP force decreased from 180N to

100N. Consequently, the tendon force ratio was shifted at 180:20 (9:1) FDP to FDS force to 100:100 (1:1). That meant the relative FDS force ratios (%FDS) to the total tendon force were 10% at 9:1 FDP to FDS and 50% at 1:1 ratio. These different levels of FDP to

FDS ratios induced different mechanical behavior during power grip.

3.3. Data Acquisition System

A data collecting system was utilized to measure external forces and internal forces while grasping. External forces were defined as grip force measured from a force transducer inserted in a split cylindrical handle, and internal forces were determined as tendon forces taken by force transducers in line with the force delivery unit. The data acquisition system was designed for measuring internal and external forces coupled with force feedback control system.

3.3.1. Tendon and grip force measurement

To measure tendon tension and grip pressure during the grasping motion, the

HMS was composed of a SCXI Chassis system (National Instruments) with three force transducers (See figure 3.10). The SCXI chassis included an amplifier and an A/D converter. The stainless steel force transducers (LC202-500, Omega Inc.) had dual mounting studs for easy installation in the FDU or handle (see Figure 3.11) and with a range of 500 lb and accuracy of 0.25%. Two force transducers were connected in line of cable with a FDU to measure tendon tension as an internal force, and force transducer was inserted into a split cylindrical handle presented in section 3.1.2 to measure grip force as an external force (see Figure 3.12). The amplifier and A/D converter (SCXI-

1600, NI Inc.) required a terminal block (SCXI-1314, NI) and a strain gauge input module (8-ch. SCXI-1520, NI). SCXI-1600 amplifies and digitizes the signal with 16bit

A/D converter. The SCXI system was monitored and controlled by a custom programmed software (Labview, NI). 59

Figure 3.10. Data acquisition system of the Hand Motion Simulator

Figure 3.11. Data acquisition system with force transducer

Figure 3.12. Split cylindrical handle with force transducer inserted

3.3.2. Finger force distribution measurement

To explore the finger force distribution, contact forces on each phalange were measured by conductive polymer sensors with a data encoder. Force sensitive resistors

(FSRs) have been used previously to measure force and pressure distributions at the hand-handle interface (Fellows and Freivalds, 1989; Kong and Freivalds, 2003). Previous researchers have demonstrated the utility of FSRs have made it possible to measure the force distribution pattern in the hand during various activities. Furthermore, FSRs are well suited for the evaluation of the force or pressure distributions associated with different handle shapes and textures (Chang et al., 1999; McGorry, 2001). We employed the same type of FSR, FlexiForce™ resistance sensor (A201, Tekscan: Capacity: 25lb.) in this study since its flexibility and reliability of force measurement has been successfully demonstrated. Hence, FSRs were attached on each phalange (distal to metacarpal phalange) of all four fingers (index to little finger). Figure 3.13 and 3.14 illustrate the FlexComp Infiniti™ data collection system and a specimen with 16 channel

FSRs on each phalange. The contact forces were gathered via FlexComp Infiniti™ data collection system (Thought Technology). FlexComp Infiniti™ system could collect the data up to ten sensors. FlexComp Infiniti™ system consists of the FlexComp Infiniti™ encoder unit, the TT-USB interface unit, fiber optic cable, and operating software

(BioGraph Infiniti™ Ver. 2.1.). The FlexComp Infiniti™ encoder is a multi-modality device for real time data acquisition with ten channels. The FlexComp Infiniti™ encoder can render a wide and comprehensive range of objective physiological signs used in ergonomics, clinical observation, and biofeedback.

Figure 3.13. FlexComp system with FSRs

Figure 3.14. FSRs attached on each phalanges 63

3.4. Machine Vision System

The HMS used a machine vision instead of other traditional manual measurement tools because it offered unique abilities not found in many traditional tools. We can implement many other applications using traditional tools, but machine vision made these tasks much easier. In terms of measuring finger joint angles, a goniometer is the most traditional approach. However, it is not effective to measure every joint manually with repetition. It can be troublesome and inaccurate to read finger joint angle with a manual goniometer. Also, since electro goniometers can be unstable with small joint flexion, we needed to capture each finger joint angles of the index finger on different conditions while simulating power grip motions.

3.4.1. Vision system

The vision system consisted of a hardware part and a software part. To acquire, analyze, and process images, the imaging system was set up with the supporting frame.

Five factors comprise an imaging system: resolution, field of view, working distance, depth of field, and sensor size (See Table 3.1).

In the HMS, the images were captured using a small camera (Model Quickcam

Pro 9000, Logitech Corporation) with a 2,000,000 pixels CCD image sensor to get image, so it was ample resolution to process captured images with vision analysis algorithm. To read finger joint angles, the field of view was 160mm x 120mm showing finger flexions motions with each phalange angle. The captured image had a resolution of 960 pixels by

720 pixels. Thus, the resolution that the imaging system could distinguish was 1mm per 6 64

pixels. A total of 691,200 pixels are involved to process the image captured by the camera. It was enough to process the image data with vision analysis algorithm compared with 2,000,000 pixels capacity. The focal length of the camera is 3.7 mm and it offered wide angle with proper working distance.

The real-time video on the HMS control panel had a resolution of 600 pixels by

480 pixels and 15 frames per seconds. This video was used to monitor the movement of fingers controlled by motion delivery units. Upon clicking the capture button on the panel, captured images representing static grip postures of each condition are saved in an 8-bit stacked JPG format. As the post process, saved images were analyzed by the custom

Labview software to read finger joint angles on each condition.

Table 3.1. Fundamental parameter of an imaging system

Resolution The smallest feature size on your object that the imaging system can distinguish

Pixel resolution The minimum number of pixels needed to represent the object under inspection

Field of view The area of the object under inspection that the camera can acquire

Working distance The distance from the front of the camera lens to the object under inspection

Sensor size The size of a sensor’s active area, defined by the sensor’s horizontal dimension Depth of field The maximum object depth that remains in focus

3.4.2. Image process

Saved images were analyzed in post image process. The operation commonly used in machine vision applications is edge detection. Edge detection is an effective tool for many machine vision applications. It provides effective application with information about the location of object boundaries and the presence of discontinuities. Edge detectors locate the edges of an object with high accuracy. An edge is a significant change in the grayscale values between adjacent pixels in an image. We can use the location of the edge to make measurements, such as the angle of the detected line.

Moreover, we can use multiple edge locations to compute such measurements as intersection points. Thus, when a straight edge was located in a Region Of Interest (ROI), the angle of the line was measured by the edge detection process. Consequently, the finger joint angle was captured in the grasping motion is computed by the edge detection algorithm (See Figure 3.15).

Figure 3.15. Image Process to compute finger joint angles

3.5. Software

The Custom program by Labview software (National Instruments, Austin, Texas) controlled the motion delivery units and the data acquisition system. This program was designed to provide the user with complete control of the simulation from adjustment of calibration settings for force transducers and external triggering set-up (see Figure 3.16. and 3.17). The HMS software required manual input by manual to support the force feedback control. The input data comprised the target forces (FDP & FDS) and deadband force offset, and the output data were composed of actual tendon forces, tendon displacements and a grip force. Hence, operator can individually control the desired forces for FDP and FDS and change the force ratio between FDP vs. FDS. Moreover, operator could control the motion delivery unit by manual control buttons on the front panel. The output data were saved to an Excel format.

The entire process of the system was fully illustrated in the following chapter. In addition, the block diagrams of source codes showing the logic of force feedback control, velocity control and data saving are attached on the Appendix A.

Figure 3.16. Hand motion simulator monitoring panels

Figure 3.17. Hand motion simulator controlling panels 68

3.6. Calibration

Before conducting the experiment, all equipments were calibrated to validate the system. Motion calibration was conducted with an accurate linear measurement tool in terms of the stepper motor movement. Also, two types of force transducers (orce transducer and FSRs) were calibrated with an accurate digital force gauge. These calibration data were used to operate the hand motion simulator with the force feedback control.

3.6.1. Motion calibration

To validate the motion of the FDU, the calibration of the stepper motor is required to measure the displacement of a force delivery cable. According to pulling/pushing motion of the stepper motor, the cable tension would be changed by the motion. This tension force is used to provide a feedback control in the HMS system. Hence, the displacement of the motion is related with the force variation of the tension.

The stepper motor used in the experiment has 16mm/rev ballscrew with a drive/pulley system. However, since it is hard to say the real displacement of rod equals to the theoretical movement of the motor specification due to friction and gear slips. Thus, an accurate linear measurement tool (Mitutoyo ID-F150HE) was used to calibrate the linear motion of the motor (see Figure 3.18). The Digimatic Indicator (Mitutoyo ID-

F150HE) has an absolute linear encoder technology for measuring accurate tolerance in linear dimension. The accuracy is 0.0003mm and resolution is 0.001 mm. The linear measurement tool was fastened with a universal clamp in a straight line of the rod of 69

stepper motor. Also, the stem of the tool contacted with the end tip of the motor rod.

After rigidly fixing the position, the stepper motor was activated to test rectilinear motion.

To minimize the tolerance, a straight line between the tool and the motor was very important in the test. A calibration was conducted to test two stepper motors. Each stepper motor was calibrated individually with the linear measurement tool. The revolution of the screw in the motor was manually input on the control panel and the real displacement output was screened on the linear measurement tool. The linear measurement tool measured 10mm displacement as 246100 steps of the screw in the stepper motor. Thus, the calibration scale was 0 mm to 130 mm and the 246100 steps was repeated thirteen times to record the linear displacement of the motion. After the first sampling, the next known revolution was input on the panel. Based on the result, the motor moves 1 mm / 24610 steps. The result of calibration of actuators was shown in

Figure 3.19. Consequently, though the motor is controlled by the revolution of a ballscrew, we can monitor and record the real displacement of the motion. It will be very useful to verify the tendon characteristics.

Figure 3.18. Calibration setting for force delivery unit and force transducers

140 y = 0.00004x + 0.3828 120 S 0.119671 R-Sq 100% 100 R-Sq(adj) 100%

60 displacement

Displacement Linear (displacement) 40

0 0 1000000 2000000 3000000 4000000 Axial rotation

140 y = 0.000041x + 0.01662 120 S 0.0987486 R-Sq 100% 100 R-Sq(adj) 100%

60 displacement

Displacement Linear (displacement) 40

0 0 1000000 2000000 3000000 4000000 Axial rotation

Figure 3.19. Regression of the displacement and axial rotation of the stepper motors

3.6.2. Force transducer calibration

A calibration for force transducers and FSRs was conducted with the force delivery unit. Each force transducers and FSRs were individually calibrated by an accurate digital force gauge (Chatilon Co.; Accuracy: 0.5N) with a stepper motor. All force transducer were contacted with the digital force transducer to measure the force produced by a stepper motor pushing. The stepper motor was controlled by manual and the digital force transducer indicated the force in real time sequence. Based on the digital force transducer, the force range for the calibration was 0 to 225N with 42 steps separated sampling data points. According to increment of the pushing force by 5N, successively, from 0 to 225N, force transducer signal was recorded on the computer, respectively. All sampling were tested in three trials. The mean values at 42 calibration points were plotted as the linear graphs (see Figure 3.20).

The calibration for FSRs was conducted the same way, but the force range for calibration was 0 to 50N by 5N increments. Accordingly, 11 data points were measured by the digital force transducer in line with a stepper motor that generate pressure to the

FSR. This calibration was conducted for all 16 FSRs, and all regression plots and equations are shown in Appendix B. Figure 3.21 shows sample regression plots and equations for FSRs calibration.

25 25 y = ‐24045x + 0.041 y = ‐240405x + 0.0372 R² = 1 R² = 1 20 20

15 15

10 10

FDS 5 FDP 5 Linear (FDS) Linear (FDP) 0 0 ‐0.0001 ‐5E‐05 0 ‐0.0001‐0.00008‐0.00006‐0.00004‐0.00002 0

Figure 3.20. The regression of the voltage (mV) and actual force (Kg) for Force Transducers

1200 1200.00 y = 455.0ln(x) ‐ 853.8 y = 451.5ln(x) ‐ 796 1000 1000.00 R² = 0.987 R² = 0.994 800 800.00 600 600.00 400 400.00 200 200.00 0 0.00 ‐200 0204060‐200.00 0 204060 ‐400 ‐400.00 ‐600 ‐600.00 CH 1 CH 3 ‐800 ‐800.00 Log. (CH 1) Log. (CH 3) ‐1000 ‐1000.00

Figure 3.21. The regression of the raw signals and actual force (N) for FSRs

Chapter 4

EXPERIMENTS

4.1. Overview

The hand motion simulator was used to investigate the power grip motion with cylindrical handles on a cadaver model, and experiments were designed to determine the relationships between grip forces and handle size, flexor tendon forces, tendon force ratios and finger force distributions in power grip motion.

4.2. Specimen

One female fresh-frozen human cadaveric left hand specimen was used in this study. The specimen was amputated at the middle humerus and was free from apparent musculoskeletal disorders and anatomical abnormalities. After thawing overnight at room temperature, the specimen was minimally dissected to expose the musculotendinous junctions of the extrinsic muscles. The specimen was prepared with the entire forearm below the elbow joint and mounted into the Hand Grip Simulator after the preparation. In this experiment, since we only focused on flexor muscles among the extrinsic muscles, flexors of the extrinsic were grouped into each tendon. The flexor digitorum profundus

(FDP) and the flexor digitorum superficialis (FDS) were the main finger flexor muscles and were selected to simulate the power grip motion. To maintain the structure of interior tissues including muscles, tendons and vascular system, only the FDP and FDS were extracted and isolated from the other muscles in the forearm and other tissues left 75

undisturbed. After dissection of the forearm, three Schanz screws (4.0mm diameter) were drilled vertically into the proximal part of the radius and three additional Schanz screws were drilled into the ulnar aspect of the forearm for fastening the entire forearm into the simulator. Two small size Schanz screws (2.5mm diameter) were drilled into the metacarpal bone of index finger for the wrist fixator. The wrist fixator (Wristjack®) was attached on the radius side of the wrist through the Schanz screw on radius aspect of the hand. The wrist fixator maintained a functionally neutral wrist angle of 20° extension allowing free motion for all fingers (Li, 2006). Each flexor tendon separated from flexor muscles was securely coupled with a freeze clamp (Sharkey, 1994) and coolant tubes for liquid nitrogen were connected to the freeze clamps (see Figure 4.1).

Figure 4.1. Specimen mounted on a custom fixation device in hand motion simulator 76

4.2.1. Anthropometric data

Musculoskeletal modeling of hand requires anthropometric data such as the lengths of the segments. Hand length was measured using the method of Garrett (1971) as the distance from the wrist crease baseline to the tip of the middle finger with the hand extended. All phalange lengths were measured by a sliding caliper and showed hand length and segment lengths ranged from a 12th to a 73 th percentile female (see Table 4.1).

For computational phalange lengths, the length of each phalange was determined as shown in Figure 4.2 and it was used for input data for the biomechanical hand model

(Kong, 2001).

Table 4.1. Dimension of phalanges on each finger (Unit: cm) Phalange Index Middle Ring Little Palm length Hand length

Distal 2.04 2.13 1.81 1.29 - -

Middle 2.19 2.38 2.04 1.43 - -

Proximal 2.51 2.62 2.557 1.88 - -

Total 6.74 7.13 6.42 4.60 10.21 17.3

Percentile 45th %ile 12th %ile 32th %ile 19th %ile 73th %ile 42th %ile

Figure 4.2. Diagram for phalange length measurement for each fingeer 77

4.3. Experimental Procedure

4.3.1. Tendon forces

As already mentioned in section 3.3.2, the flexor muscle force was the independent factor for an analysis of variance (ANOVA) procedure and it was controlled by two experimental modes. In the first experiment, FDP force was fixed at 100N and

FDS force increased from 20N to 100N by 20N at once. Hence, the total tendon force was also increased as the FDS force increased. Secondly, total tendon force (sum of FDP and FDS force) was fixed at 200N and both FDP and FDS forces were adjusted with regular ratios: FDP force decreased from 180N to 100N and FDS simultaneously increased from 100N to 180N. Consequently, the total force was always 200N, but the tendon force ratio of FDP and FDS was different at the different combination of two tendon forces. Through these two conditions for the experiment, the grip force and finger force distribution were analyzed in this study, respectively.

4.3.2. Procedures

Before the experiment, coolant (liquid nitrogen) was delivered directly to the body of the freeze clamps that have separate linkages with cables to actuators. Coolant flow was hand-regulated at a liquid nitrogen tank and an initial freezing period of 3-5 min was required. Flow was maintained until the tissue was frozen 1cm distal to the clamp nose. This tissue was periodically checked and maintenance pulses of liquid nitrogen were given when required (10-15 min intervals) 78

One end of the pulling cable was connected to a freeze clamp at the musculotendinous junction and the other end of the cable was connected to the force transducer coupled with an actuator rod. Prior to actual pulling, the two cables were fully released from the actuator with no tension and all fingers were preconditioned to standardize the positions of the joints. During the preconditioning, fingers were manually moved for 10 seconds through their neutral postures and then placed in a position with minimal resistance to motion.

After setting the target forces input by the operator, loading was initiated from 0N to target in 30 seconds, and real time force signals (FDP, FDS and grip forces) were displayed on the screen by a custom Labview program. Also, contact forces on each phalange were also recorded and monitored on the second screen by a custom FlexComp program (Thought Technology). Real time videos of finger motion were monitored and recorded using a lateral view camera that recorded 15 frames per second during the experiment.

Three trials were run for each five different handles and five different tendon force ratios, with three minutes intervals between each trial. All of the 15 trials (5 tendon force ratios x 3 trials) were completely randomized for each handle. The reason that the handle could not be randomized was for the consistency of the initial handle position with a hand. A sequence of five handles was also randomized as 45, 60, 47, 30 and 37mm.

After each trial, tendon forces (FDP and FDS), Grip force and phalange forces were saved as an Excel file. 79

Chapter 5

RESULTS

5.1. Overview

This chapter presents the system validation to show the reliability of the hand motion simulator with the force feedback control. It also describes the relationship of the effect of tendon force ratio and handle size on response variables (grip force, finger force distribution and finger joint angle). The effect of tendon force ratio and the handle size are presented to evaluate the model performance as well. Also, these results were compared with the mathematical model to predict tendon forces for validation.

5.2. Validation of the Hand Motion Simulator

The hand motion simulator was operated under force feedback control to attain target forces and compensate for deviation of the tendon tension compared with the target forces during the operation. To validate the accuracy of the hand motion simulator, the target forces and actual forces over the duration of three repeated simulations for two flexor tendons (FDP and FDS) were compared. Also, the finger force distribution on each phalange was analyzed to validate the system.

5.2.1. System summary

Figure 5.1 shows how the HMS performed the motion with coordination of two stepper motors connected with two flexor tendons. In the sample motion, the target force of FDP and FDS were 100N and 50N, respectively. The real time tensions from the force transducers in line of tendon pulling cables went through the force feedback control to match the actual forces to the target forces. Since the input FDS force was less than the input FDP, the FDS force reached first to the target force during continuous pulling the

FDP tendon. Consequently, as shown in the Figure 5.1, the FDS motion usually rippled to compensate the deviation of real time actual force during pulling the FDP. However, it finally reached a stable condition as soon as the FDP reached the target force. The actual forces in stable condition were compared to the target forces, and the average error between the actual and target force was 1.0N.

Sample Data 120

100 FDP_F 80 FDS_F 60

Force (N) GF 40

0 0 20406080 Motion Time (sec.)

Figure 5.1. Sample data plots showing performance of the force feedback control in the Hand Motion Simulator. FDP, FDS, Grip force (GF) plotted in the graph according to time sequential. Target Force was 100N and 50N for FDP and FDS, respectively. 81

5.2.2. System reliability

To validate the accuracy and reliability of the force feedback control in the system, the actual force achieved was compared with the target force input by the operator. Table

5.1 shows the result of the validation experiment of the hand motion simulator. Box plots of variations of actual FDP and FDS forces are shown in the Figure 5.2 and 5.3, respectively.

FDP target forces were all 100N in the experiment, the target force (100) was compared with the actual force generated by the HMS. Table 5.2 suggests that is statistically significant difference between actual FDP force and target force, given p

<0.05. The average of the actual force was 99.07, which was statistically different from the target force of 100N. Nevertheless, this 0.93N of difference may not imply practical significance. In other words, the system had average 0.93N (SD: 0.42) error probability compared with the target force, and it seems to be negligible to operate the simulator that has diverse tendon tensions.

The experiment was also conducted for FDS actuator. The FDS force was separated by 20N increase (20, 40, 60, 80 and 100N). The differences of actual force and target force were similar with the result of FDP that showed about 1N error with the desired force. However, the error was increased at 100N level. It can be explained by the tension of both FDP and FDS. Since total force at 100N FDS force was 200N, balancing of both high-tension tendons made the accuracy a little bit lower. Of course, we could decrease the error range to increase the accuracy of the system through slowing the tendon pulling speed down. However, it would take too much time to get to the target force. 82

Table 5.1. Comparison of target forces to actual forces (unit: N)

Grip Force Experiment Finger Force Distribution Experiment

Target Actual FDP Target Actual FDS Target Actual FDP Target Actual FDS Force Force Force Force Force Force Force Force

20 - 20 19.04 ± 0.66 180 178.85 ± 0.83 20 19.19 ± 0.42

40 - 40 39.12 ± 0.41 160 159.01 ± 0.62 40 39.20 ± 0.19

60 - 60 59.03 ± 0.52 140 139.21 ± 0.68 60 59.17 ± 0.33

80 - 80 79.05 ± 0.43 120 119.01 ± 0.48 80 78.92 ± 0.58

100 99.07 ± 0.43 100 98.79 ± 0.78 100 99.21 ± 0.12 100 98.84 ± 0.68

Table 5.2. One sample t-test actual force to target force as 100N

One-Sample T: Actual Force Test of mu = 100 vs not = 100 Variable N Mean StDev SE Mean 95% CI T P Actual FDP 150 99.07180 0.4271 0.0349 (99.0029, 99.1407) -26.62 0.000

_ X

98.0 98.5 99.0 99.5 100.0 FDP Force

Figure 5.2. Boxplot of Actual FDP Force

100

Actual FDSForce 40

10 20 40 60 80 100 Desired FDS Force

Figure 5.3. Boxplot of FDS Force

5.3. Grip Force Analysis

The effect of the nominal internal force and handle size were studied based on the grip force measured by five different diameter cylindrical handles that was split with a force transducer in the handle. Analyses of variance were performed to test the significance of the main and interaction factors with the grip force. Data were analyzed by the Minitab. Table 5.4 shows the grip force on each handle and different tendon force ratio of the FDP and FDS. Before looking at the analysis result, the normality and homogeneity of variance assumption of data were checked for ANOVA analysis.

Because the shape of the histogram is bell-shaped and the normal probability plot is almost a straight line, the normality assumption can be accepted. In other words, any large variation was not detected in the diagnostic plot to check the normality and homogeneity of variance assumption for ANOVA analysis (See Appendix C.1).

Therefore, the results from the ANOVA model are reliable. Data analysis on grip force showed significant effects for handle size (p <0.001) and nominal internal tendon force (p <0.001), but not the interaction effect of handle and nominal internal force (See

Table 5.3).

Table 5.3. ANOVA for Grip Force, using Adjusted SS for Tests

Source DF SS MS F P Handle 4 1788.35 447.09 56.80 < 0.001 Nominal Int. Force 4 1518.45 379.61 48.23 < 0.001 Handle*Nominal Int. Force 4 142.70 8.92 1.13 0.353 Error 50 393.53 7.87

Total 74 3843.03

S = 2.0545 R-Sq = 89.76% R-Sq(adj) = 84.84% 85

All pair-wise comparisons among levels of finger (Tukey’s multiple comparisons procedure) showed that the grip force increased linearly according to the increment of the internal tendon force. Table 5.4 presents the results of Tukey mean test and the corresponding mean values. Those were grouped by vertical lines do not differ significantly at  < 0.05. In terms of the effect of the tendon force ratio, even when changing the tendon force ratio of the FDP and FDS, it seemed that the grip force was not affected by the ratio. Thus, we need to investigate this further in detail.

In the analysis of the relation between grip force and handle size, the smallest diameter handle (30mm) indicated significantly high grip force compared with other handles in power grip (p < 0.001). Also, the largest size handle (60mm) had significantly less force than the other handles (p < 0.001). However, the average grip force on 37mm,

45mm and 50mm handles were not different from each other. The previous studies of handle size with power grip also reported that grip force drops when increasing the handle diameter (Edgrenm 2004; Kong and Lowe, 2005; Seo and Amstrong, 2008). Table

5.5 shows the grip forces on five different diameter handles as response to different tendon force ratios. The handle size effect will be described in following section 5.3.1. in detail.

Table 5.4. Tukey tests on the difference in the grip force

Main Factor Grip Force (Mean: N) Grouping (Tukey’s) 120 22.92 140 26.25 Nominal 160 30.28 Internal Force 180 32.66 200 36.92 1 38.32 2 29.27 Handle 3 29.70 4 28.97 5 22.76

Table 5.5. The total/individual finger forces and contributions on each %FDS

Tendon force (N) Grip Force (N) on handle FDP FDS Total 1 [30mm] 2 [37mm] 3 [45mm] 4 [50mm] 5 [60mm] Mean 100 100 200 45.7 (4.4 F) 34.2 (5.9 F) 36.9 (5.4 F) 39.1 (5.1 F) 28.7 (7.0 F) 36.9 (5.5 F) 100 80 180 41.5 (4.3 F) 32.1 (5.6 F) 34.0 (5.3 F) 31.9 (5.6 F) 23.9 (7.5 F) 32.7 (5.7 F) 100 60 160 40.9 (3.9 F) 27.8 (5.7 F) 30.5 (5.4 F) 28.8 5.6 F) 23.4 (6.8 F) 30.3 (5.5 F) 100 40 140 32.5 (4.3 F) 26.3 (5.3 F) 25.7 (5.5 F) 26.2 (5.3 F) 20.6 (6.8 F) 26.3 (5.4 F) 100 20 120 31.1 (3.9 F) 26.3 (4.6 F) 23.4 (5.1 F) 22.6 (5.3 F) 18.2 (6.6 F) 24.3 (5.1 F) Mean 160 38.3 (4.2 F) 29.3 (5.5 F) 30.1 (5.3 F) 29.7 (5.4 F) 23.0 (7.0 F) 30.1 (5.3 F) (F: applied grip force unit)

* The value in ( ) indicates the efficiency of the internal force to external force 88

5.3.1. Handle size analysis

The relationship between the internal tendon force and the external grip force was analyzed to assess the effect of different diameter handle sizes. The number of handle from 1 to 5 represents 30mm, 37mm, 45mm, 50mm and 60mm cross-sectional diameter, respectively.

Data summary

Figure 5.4 presents the grip force variations with the box plots on each handle. As already discussed, the grip force for the smallest handle size was 20% (significant at p

<0.05) larger than the mean grip force and 23% lower force than the mean grip force for the largest handle size. The reason that there were high variations of the grip force in

Figure 5.4 was that the average grip force derived from different tendon force ratios.

30 Grip Force

10 1 2 3 4 5 handle

Figure 5.4. The grip force variation on each handle 89

Thus, we need to analyze the interaction effect of handle and nominal internal force with separated tendon force ratios.

Optimal handle size

The graph in Figure 5.5 shows clearly which handle had the highest grip force within each internal force level. Since the ANOVA output did not suggest an interaction effect between nominal internal force and handle size, we only need to check which handle has the highest grip force overall and also handle size effect was analyzed with all levels of internal force. The handle effect was already shown by the Tukey pairwise comparisons in Table 5.4 with handle 1 having significantly higher grip forces than the other handles (p-value compared with other handles are <0.001); handle 5 also had

handle 45 1 2 3 40 4 5

Mean 30

120 140 160 180 200 Int. Force

Figure 5.5. The interaction of the Internal force and the handle

90 significantly lower grip force than the other handles. Handle 2,3, and 4 are not significantly different from each other. Consequently, the smallest (30mm) handle diameter had maximum grip force, and it was the optimal handle size among five different diameter handles at least for this size hand. As shown in Table 5.5, the grip force was highest in the smallest handle (30mm) with highest grip force and the efficiency of internal tendon force (4.2F), for an external grip force F, was highest with the smallest handle as well. The largest diameter handle (60mm) had lowest grip force and worst tendon force efficiency (7.0F).

5.3.2. Tendon force ratio in Grip force

The relationship of two flexor tendon forces on different sizes of handles was analyzed to find the effect of different FDP and FDS ratios.

Data summary

Figure 5.6 shows the relationship between the grip force and the internal force as internal forces increase. FDP forces were always constant (100N) and FDS forces were increased from 20N to 100N. Thus, the internal force increase was due exclusively to increasing FDS tendon force. As shown in Figure 5.6, the mean grip forces increased linearly as the internal force increased, and it seems that the slope of grip force was constant,. That means that the ratio between the FDP and FDS does not affect grip force.

Hence, we need to analyze the tendon force ratio effect on each handle in detail. 91

30 Grip Force

10 120 140 160 180 200 Int. Force

Figure 5.6. The effect of the tendon force ratio between the FDP and FDS

To find the relationship between the tendon force ratio and grip force on different sizes of handle, Analysis of Covariance (ANCOVA) was used to solve the hypothesis.

ANCOVA is a technique that combines ANOVA and regression analysis to examine both the influence of categorical and continuous variables on the response. ANCOVA evaluates the influence of the continuous variable (covariate) on the response variable and at the same time enables the comparison of treatments on a common basis relative to the value of the covariates (Kuehl, 2000). In this experiment, the relative FDS force is a continuous variable on the grip force as the response.

Before statistical analysis, the diagnostic plots were presented to check whether the dataset achieves the normality and homogeneity of variance assumptions for

ANCOVA analysis (See Appendix C). From the residuals vs. fitted value plot, the variance is not different across each handle. The normal probability plot of studentized 92 residual appears to be a straight line that indicated that the residuals are approximately normally distributed. Therefore, the assumptions for ANCOVA analysis hold.

Table 5.6 shows the result of ANCOVA. Both handle type and relative FDS% have significant influence on grip force (p < 0.001). Moreover, the interaction of handle and relative FDS% is also significant with p-value <0.012. This term tests the hypothesis that the slopes of each regression line between relative FDS% and grip force are equal across five handle types. Its significance suggests that the regression lines of five handle types do not have identical slops (See Figure 5.7). The relationship between relative FDS% and grip force are different across five handles. Hence, we need to investigate this further for subtle differences.

Table 5.6. ANCOVA for Grip Force, using Adjusted SS for Tests

Source DF SS MS F P

Handle 4 193.03 48.26 5.23 0.001 Relative FDS% 1 1740.12 1740.12 188.74 < 0.001 Handle*Relative FDS% 4 128.94 32.23 3.50 0.012 Error 65 599.26 9.22

Total 74 4304.81

S = 3.3636 R-Sq = 86.08% R-Sq(adj) = 84.15%

50 handle 1 2 45 3 4 5 40

30 Grip Force

15 20 25 30 35 40 45 50 Relative FDS%

fg Figure 5.7. The interaction between the relative FDS percentage and the handle size

Since regression lines for five handles did not have equal slopes, to get the regression slope of each handle type, we can split the dataset based on handle types and conduct regression analysis of each handle size. The summarized output of the regression of each handle type is shown in the appendix C.2.3. The output suggests that the relationship between relative %FDS and grip force were all significant (p-value of the relative FDS% coefficient is <0.001) but the slopes (relative FDS% coefficient) are not identically the same. Handle 2 and 5 apparently have a slope that is much flatter

(regression coefficient 0.269 and 0.343, respectively) than other handles whose regression coefficients are at least 0.5.

However, when the model order of regression was plotted with the quadratic, the slope of each handle increased as relative FDS% increase. Especially, this was noticeable 94 at 40-50% of relative FDS%, most slopes of handles were drastically increased (see

Figure 5.8). This means that relatively higher FDS tendon force (40% to 50%) yielded a better grip force during the power grip motion. This result agrees with the study of mechanical characteristics of a muscle (Brand and Hollister, 1981). They analyzed the

FDP and FDS characteristics with the mass, average fiber length and cross-sectional area of all fibers. Based on the mass fraction (%) of the FDP and FDS, the ratio of two tendons was 3:2. In addition, the tension fraction (%) ratio of two tendons showed 3:2.3 profundus to superficialis tendon force ratio. The findings indicate that the physical FDS had 20% - 30% less force than the FDP. Thus, their study showed that the slope of grip force increased with 35% -50% FDS of the total internal force.

50 handle 1 2 45 3 4 5 40

30 Grip Force

15 20 25 30 35 40 45 50 Relative FDS%

Figure 5.8. The interaction between the relative FDS percentage and the handle size 95

5.4. Finger Force Distribution Analysis

To explore the reliability of the hand motion simulator, the finger force distribution was also measured by 16 FSRs attached on each phalange from distal phalanx to metacarpal of each finger. The individual finger force was defined as the sum of the four phalangeal segment forces for that finger, and the total finger force was defined by the sum of all four-finger forces, from index to little fingers (see Table 5.7).

Analyses of variance (ANOVA) were performed to test the significance of the man and interaction factors with gripping force.

5.4.1. Finger and phalange forces

Data analysis on contact force showed significant differences for each finger (p<

0.001) (Figure 5.9). As shown in Table 5.8, all pairwise comparisons among levels of finger (Tukey’s multiple comparisons procedure) showed that middle finger applied significantly more force (55.5%) than the other fingers. The index finger generated significantly more force (25.5%) than the other fingers. The ring finger (12.2%) and the little finger (6.7%) were not notably different from each other (see Table 5.8). These results are similar to those of previous studies (Kong, 2001).

Each phalange also indicated significantly different force distributions in power grip motion (Figure 5.10). In the Tukey test, the distal phalange (73%) had significantly more force than the other phalanges (p < 0.001). However, the average forces loaded on the middle (5%), proximal (5.6%), and metacarpal (16.3%) were not different from each other (see Table 5.9). The result of interphalangeal force distribution studies indicated as 96 well that the distal phalange always exerted more force and maintained a fixed lead over the other two phalanges (Amis, 1987; Kong et al., 2004, 2005).

Table 5.7. The individual phalange forces contributions on each finger

Total Mean forces of individual phalanges and percentage contribution (N) Finger Phalange Force (N) Distal Middle Proximal Metacarpal Index 9 6.6 (73.33%) 0.4 (4.44%) 0.1 (1.11%) 1.9 (21.21%) Middle 18.9 13.9 (73.54%) 1.4 (7.41%) 1.5 (7.94%) 2.1 (11.11%) Ring 4.2 2.6 (61.90%) 0 (0%) 0.1 (2.38%) 1.5 (35.71%) Little 2.3 1.8 (78.26%) 0 (0%) 0.4 (17.39%) 0.1 (4.35%) Total (N) 34.4 24.9 (72.38%) 1.8 (5.23%) 2.1 (6.11%) 5.6 (16.28%)

Table 5.8. Tukey procedure comparing the fingers

Finger Index Middle Ring Little Mean (N) 9 18.9 4.2 2.3

(Underlined means are not significantly different at 5% level)

Table 5.9 Tukey procedure comparing the phalanges

Phalange Distal Middle Proximal Metacarpal Mean (N) 24.9 1.8 2.1 5.6

(Underlined means are not significantly different at 5% level) 97

Contact Force (N) 10

0 1 2 3 4 FINGER

Figure 5.9. The main effects (Finger) for grip force. The number of finger is the order of finger from the index to the little finger, respectively.

10 Contact Force (N) Force Contact

1 2 3 4 Phalange

Figure 5.10. The main effects (Phalange) for grip force. The number of phalange is the order of phalange from the distal to the metacarpal phalange, respectively.

Figure 5.11 shows the interaction between finger and phalange. As described in pair-wise comparison analyses, the distal phalange (phalange 1) force on the middle finger (finger 2) had the highest force among other phalanges and the ring and little finger showed the lowest force, followed by the index finger. Otherwise, the force distributions of the middle, proximal and metacarpal phalange showed similar patterns along all fingers. This means that most contact force was generated by the distal phalange among all segments. In addition, the middle and index finger tip had significantly high contact force while the ring and little finger had a feeble contact force distribution.

The distal phalange force distribution had pattern similar to the previous study, but the middle and proximal phalange force patterns were quite low compared to other studies. It will be discussed in Section 6.5 in detail.

14 Phalange 1 2 12 3 4

Mean 6

1 2 3 4 FINGER

zx Figure 5.11. The interaction effects for grip force (Finger * Phalange) 99

5.4.2. Tendon force ratio in Finger force distribution

To explore the tendon force ratio of the FDP and FDS, the difference of finger forces were analyzed with the different tendon force ratios. The variation of each finger force summing phalange forces was significant with fingers and relative percentage of

FDS force (%FDS). However, there was no interaction effect of finger and %FDS. Also, all phalange forces were significantly different on each finger and distal and metacarpal had significant difference with %FDS. But there were no interaction effects for all phalanges as well (See Appendix C).

As shown in the Figure 5.12, the mean finger force was significantly higher at the

40% FDS force ratio. In the pair-wise comparison, the mean finger force at 40% FDS

8 Mean of Finger Force (N) Force Finger of Mean

6 10 20 30 40 50 %FDS

Figure 5.12. Main Effects Plot (data means) for Total 100 increased significantly (48%) from the 10% and 20% FDS force level. In terms of the efficiency of tendon force (internal force) vs. finger force (external force), Table 5.10 shows the highest ratio of flexor tendon force to the applied finger grip force was 7.9F generated with the 10% FDS force and the lowest ratio was 4.1F with the 40% FDS force

(3:2 PDF to FDS tendon force ratio). Thus, 4.1F was most efficient ratio between internal force and external force, and the ratio of FDP and FDS to the applied finger grip force was 2.5F and 1.6F, respectively.

Table 5.11 shows the individual phalange forces and total phalange forces on different tendon force ratios. Total phalange force was also highest (12.2N) at 40% FDS force and it was decreased with %FDS decreased (6.4N at 10% FDS). Most contact force

(66.24% - 75.41%) was concentrated on distal phalange with whatever tendon force ratios changed. All other phalanges had merely 25% - 34% contact force on fingers in power grip. In pair-wise comparison, the distal phalange force was significantly different with others ( < 0.001)

The finger forces increased significantly on the index and middle finger as the %FDS force increased, but those dropped slightly at the 50% of FDS. Also, finger forces at the 40% of FDS force showed more contact forces than other tendon force ratios.

Specifically, index and middle finger contact force increased significantly up to 40%

FDS, but the dropped at 50% FDS. In Figure 5.13, similar trends took place in each finger at the different tendon force ratios, but the 40% FDS force had better contact force distribution followed by the 50% FDS, and the contact force was the lowest at 10% FDS force. In Figure 5.14, the effect of the tendon force ratio is more clearly presented by mean finger contact forces for each tendon force ratio. Middle and index finger forces 101 peaked at 40% while the other fingers were similar. Therefore, 40% FDS generally showed best contact force distributions on all four fingers. The 40% FDS means that the optimal tendon force of the FDP vs. the FDS is 3:2 for the power grip. In other words, the

FDS force should be 33% less than the FDP force in power grip motion.

This conclusion derived from sum of finger force and finger force distribution is consistent with the result of the grip force of split handles that showed the force slope was increased for 40% of FDS force. Brand et al. (1981), who analyzed relative tension and potential excursion of muscles in the forearm and hand by dividing the fiber length into the volume of each muscle (the cross-sectional area of the muscle) and relative tension capacities of forearm and hand muscle, found a 3:2 profundus-to-superficialis tendon-force ratio, which agreed with my results. 102

Table 5.10. The total/individual finger forces and contributions on each %FDS (F: applied grip force unit)

Total Tendon Mean forces of individual fingers and percentage contribution (N) %FDS Finger FDP force FDS force Force Force (N) Index Middle Ring Little 50% 36.6 5.5F 2.7F 2.7F 11.1 (30.33%) 19.2 (52.46%) 4.3(11.75%) 2.0 (5.46%) 40% 48.8 4.1F 2.5F 1.6F 15.2 (31.15%) 24.4 (50.00%) 5.4 11.07%) 3.8 (7.79%) 30% 31.0 6.5F 4.5F 1.9F 8.6 (27.74%) 17.4 (56.13%) 3.1 (10.00%) 1.9 (6.13%) 20% 28.9 6.9F 5.3F 1.4F 6.3 (21.80%) 18.2 (62.98%) 2.6 (9.00%) 1.8 (6.23%) 10% 25.1 7.9F 7.2F 0.8F 3.7 (14.74%) 14.4 (57.37%) 5.2 (20.72%) 1.8 (7.17%)

Table 5.11.The total/individual phalange forces and contributions on each %FDS

Total Mean forces of individual phalanges and percentage contribution (N) %FDS Phalange Force (N) Distal Middle Proximal Metacarpal 50% 9.1 6.8 (74.73%) 0.4 (4.40%) 0.4 (4.40%) 1.5 (16.48%) 40% 12.2 9.2 (75.41%) 0.5 (4.10%) 0.7 (5.74%) 1.8 (14.75%) 30% 8.0 5.3 (66.25%) 0.4 (5.00%) 0.4 (5.00%) 1.9 (23.75%) 20% 7.2 5.3 (73.61%) 0.4 (5.56%) 0.5 (6.94%) 1 (13.89%) 10% 6.4 4.5 (70.31%) 0.5 (7.81%) 0.4 (6.25%) 1 (15.63%)

103

25 %FDS 10 20 30 20 40 50

15 Mean 10

0 1 2 3 4 FINGER

Figure 5.13. The interaction effects for grip force (Finger * %FDS)

25 FINGER 1 2 3 20 4

15 Mean 10

0 10 20 30 40 50 %FDS

Figure 5.14. The interaction effects for grip force (%FDS * Finger)

104

5.5. Finger joint angle analysis

The finger joint angles were generated by a custom developed program by

Labview for measuring the interphalangeal joint angles (Table 5.12). The effect of handle, the relative percentage of FDS force (%FDS) and the interaction of handle and %FDS were all significant (p <0.001). Figure 5.15 shows the captured grip postures representing finger joint angles in lateral view depending on different tendon force ratios and handle sizes. The main effects on DIP, PIP and MCP joint angles due to different handle sizes and the relative FDS forces (%FDS) are plotted in Figure 5.16.

In terms of handle size, the joint angles at the MCP and PIP joint showed a descending pattern as the handle diameter increased, but DIP joint angle showed convex pattern according to handle size increasing. Essentially, flexions of MCP and PIP joint decreased as the handle size increased, but the DIP joint angle was most flexed for the middle handle size.

The loading of the tendon forces with different ratio (FDP vs. FDS) produced different finger joint motions. According to increasing the percent FDS force from 10% to 50% of total tendon force, on average, the MCP joint angle gradually increased from

19.7 to 23.8; in contrast, the PIP joint angle showed a rapid rise from 70.1 to 83.4 in the high proportion of FDS while the DIP joint angle displayed a rapid decline from

32.8 to 2.7. These results clearly show that the tendon force ratio of FDP to FDS affects the finger joint motion while grasping a handle. Higher percent FDP force with less FDS force produced flat PIP joint angles and flexed DIP joint angles; In contrast, the same proportion of FDP to FDS force (i.e. PDF : PDS = 1 : 1) produced flexed PIP joints and flattened DIP joints. Thus, the DIP would be too flexed with low portion of FDS force 105 compared with FDP force, and would be too flat with same level of FDS to FDP force.

Therefore, 3:2 FDP to FDS tendon ratio that already concluded before can be supported by this mechanism of finger joint angles by different tendon force ratios. 106

Table 5.12. Finger Joint Andlge flexion on %FDS and handle

Handle 1 2 3 4 5 %FDS MCP PIP DIP MCP PIP DIP MCP PIP DIP MCP PIP DIP MCP PIP DIP 50% 33.5° 98.9° 0.1° 37.2° 89.4° 4.4° 23.2° 79.2° 5.7° 11.1° 83.1° -3.7° 14.0° 66.2° 9.4° 40% 34.9° 93.9° 8.8° 35.0° 90.6° 10.4° 19.7° 64.3° 13.6° 11.7° 81.1° 0.2° 14.7° 71.0° 10.1° 30% 35.7° 80.3° 23.6° 30.8° 89.8° 24.0° 12.1° 66.9° 30.7° 11.4° 73.1° 9.2° 10.5° 78.2° 9.9° 20% 33.1° 76.8° 34.1° 31.7° 84.0° 34.9° 8.4° 61.0° 47.7° 13.9° 67.0° 16.4° 14.5° 67.2° 12.0° 10% 32.6° 75.2° 38.4° 31.8° 80.2° 42.1° 6.6° 69.0° 52.3° 15.5° 55.5° 16.7° 15.1° 62.1° 14.1°

107

Figure 5.15. Finger joint angles on tendon force ratio and handle 108

Main Effects Plot (data means) for MP

handle %FDS 35

20 Mean of MP Angle

10 1 2 3 4 5 10 20 30 40 50

Main Effects Plot (data means) for PIP

handle %FDS 87.5

85.0

82.5

80.0

77.5

75.0 Mean of PIPAngle of Mean

72.5

70.0

1 2 3 4 5 10 20 30 40 50

Main Effects Plot (data means) for DIP

handle %FDS 35

30 ) 25

Meanof DIP Angle( 10

0 1 2 3 4 5 10 20 30 40 50

Figure 5.16. Inter phalangeal joint angles on handle size and %FDS 109

5.6. Validation of mathematical model

To validate the mathematical model described in the previous chapter, the actual anthropometric data, actual finger joint angles and finger force distributions of each finger were computed in the model with the manipulated forearm flexor tendon forces.

Since the optimal tendon force ratio for power grip that I found in this study was 3:2 FDP to FDS ratio, the input data set were selected from the data at 40% FDS force level. The specific phalange forces at the 40% FDS force level are shown in Table 5.13.

Table 5.14 shows the comparison of the ratio of tendon forces to the applied finger forces. Average ratios of predicted tendon forces to the applied finger forces in the tendon force prediction models were, for an external force of F, 9.29F, 9.38F, 8.51F and

4.51F for the index, middle, ring, and little finger in power grip, respectively, while 4.92F were for the ratio of actual tendon force measured by the simulator. Also, the FDP and

FDS tendon force were 7.6F and 1.2F to the external finger force F in the prediction model, while 3.0F and 2.0F were for the actual FDP and FDS forces in power grip, respectively.

Table 5.13. Each phalange force on 40% FDS level

Mean phalange force (N) Finger Distal Middle Proximal Index 12.41 0.40 0.00 Middle 18.98 1.52 0.50 Ring 3.22 0.00 0.07 Little 2.36 0.00 1.19

110

The predicted flexor tendon forces were, on average 44% higher than the actual tendon forces. Also, the predicted FDP force was 61% higher than the actual FDS force, but the FDS force was 38% less in the predicted FDS force, probably due to the α parameter used in the prediction model. The α parameter is the tendon force ratio of the

FDP to FDS assumed by 3:1. However, the mathematical model has contradiction in terms of the tendon force ratio. Kong already assumed that the FDP to FDS ratio is 3:1, but final FDP force ratio must be higher than 3 times to the FDS force, because the FDP force is the summation of three phalange forces (distal, middle, proximal) but the FDS force is the sum of two phalange forces (middle, proximal) divided by three (α = 0.3).

Moreover, the tendon force ratio was varied on the finger joint angle in power grip. As shown in the main effect plots of finger joint angles and the relative FDS force in Figure

5.15, the PIP joint angle increase as the %FDS increase, while the DIP joint angle decrease as the %FDS increase. Consequently, the α parameter (tendon force ratio) should be predetermined by the PIP and DIP joint angles in power grip motion.

These findings can be compared with the results from the other biomechanical finger models. Although researchers generally agreed on the proportion of muscle and tendon forces required for the externally applied forces, they presented various ranges of these ratios for the external force to internal tendon force. Average ratios were, for an external force of F, 2.27F-3.47F for the FDP and 1.51-4.23F for the FDS in power grip motion (An et al., 1985; Chao et al., 1976; Chao and An, 1978). The FDP and FDS ratio were smaller than the result of predicted tendon force ratio but similar with the result of this study.

111

Table 5.14. Comparison of predicted flexor tendon forces and actual finger forces

(F: applied finger force unit)

Predicted Tendon Force (N) Actual Finger Finger Ratio FDP FDS TOTAL Force (N) Index 102 (8.0F)17 (1.3F) 119 12.81 9.29F Middle 170 (8.1F)27 (1.3F) 197 21 9.38F Ring 24 (7.3F) 4 (1.2F) 28 3.29 8.51F Little 14 (3.9F) 2 (0.6F) 16 3.55 4.51F Total Predicted 310 (7.6F) 50 (1.2F) 360 8.86F Tendon Force (N) 40.65 Actual Tendon 120 (3.0F) 80 (2.0F) 200 4.92F Force (N)

112

Chapter 6

SUMMARY AND DISCUSSION

In this chapter, the results will be summarized and compared with previous studies. The main topics to be covered include the hand motion simulator, tendon force ratio, internal force and external force ratio, handle size effects, finger force distributions, finger joint angles, and validation of the prior mathematical model. Conclusions and suggestions for future research will follow.

6.1. Hypothesis 1: The hand motion simulator

To study forearm flexor tendons and hand motion in cadavers, the hand motion simulator (HMS) was built. The model was composed of a main frame, and force delivery, data acquisition and kinematic vision units. The main frame supporting a specimen and all equipment was constructed with an aluminum T-slotted profile providing very rigid structure. Six forearm fixators (Schanz screws, Synthes Inc.) were used to secure a forearm in position and stabilize it against pulling force of stepper motors. This mounting system did not interrupt the excursion of forearm muscles and there was no interference between the fixator and hand motion. To operate the system, a custom control program was developed in Labview for motion control, data monitoring, and data storage functions. Muscle forces generated by linear actuators under force feedback control were applied to the major flexor tendons in the forearm to produce a power grip motion. Also, two force transducers connected in line with the cables from 113 each stepper motor measured muscle tensions (internal tendon forces) and one was inserted in a split cylindrical handle to measure the hand grip force. The tendon forces measured by the force transducers provided force feedback to the motion delivery unit for comparison to target forces. To validate system reliability, the actual tendon tensions were compared with the target forces input into the system. Though significantly different in the desired target, the average error (0.93N) at different level of pulling forces was acceptable. It was concluded that the hand motion system provided very accurate motion control with the force feedback control.

The hand motion simulator provides great flexibility for hand and forearm researches. All parts in the system are adjustable vertically and horizontally depending on specimen size or the objective of studies. The handle fixture with a handle could be modified with other tools or equipment to cooperate with a hand such as a handle with vibration or a trigger for a power tool. Grip strength was measured using the split cylinder, in which the two halves of the cylinder were connected by a force transducer.

The split cylindrical handle was useful to measure grip force and provided grip forces on different handle diameters (Ayoub and Lo Presti, 1971; Dong et al., 2004; Edgren et al.,

2004; Irwin and Radwin, 2008). Also, the force trend on each handle was consistent with previous studies. However, the split handle employed only one directional sensor, which limits sensitivity. A modified handle with the ability to measure shear forces and moments in the three cardinal planes would be a great improvement. Nonetheless, most previous researches have used a split cylindrical handle with one directional force transducer (An, 1985; Edgren et al., 2004; Seo, 2008; Aldien, 2005, Welcome, 2004).

Furthermore, the split cylindrical dynamometer is much better than a Jamar dynamometer 114 which may not be reliably applicable to the assessment of tools with cylindrical handles, but more closely approximates a two-handled tool (pliers, etc). The dynamometer used in this study approximates a cylindrical handle for a power grip motion (Edgren, 2004).

Therefore, a three directional force transducer inserted in a split handle may increase the sensitivity for measuring different directional phalange forces on a cylindrical handle.

Alternatively, a cylindrical handle with three directional measuring arms can be used to measure overall grip strength, as well as show the grip force distribution around the circumference of the handle (Wimer, 2009).

6.2. Hypothesis 2: The tendon force ratio

The tendon force ratio was explored to validate the biomechanical model and also to better understand the power grip mechanics. Accordingly, the tendon force ratios of the FDP to the FDS were classified by adjusting each tendon. In the analysis of the grip force, the regression plot with the quadratic showed the slope of most grip forces dramatically increased at the segment from 35-50% of relative FDS%. That means relatively higher FDS tendon force (35% to 50%) shows better grip force during the power grip motion. Regarding the analysis of finger force distribution, the mean finger force was highest with a 40% FDS force ratio. In the pair-wise comparison, the mean finger force at 40% FDS (3:2 FDP to FDS ratio) increased significantly (48%) from the

10% and 20% FDS force (See Table 5.10). The index and middle fingers increased significantly as %FDS force increased, and finger forces were highest at the 40% FDS level (3:2 FDP to FDS force ratio). Consequently, the 40% FDS ratio generally showed best contact force distributions on four fingers. The 40% FDS ratio means that the 115 optimal tendon force of the FDP vs. the FDS is 3:2 for the power grip motion. These results supported Hypothesis 2 by showing the optimal tendon force ratio based on grip force and finger force distribution. Brand (1981) analyzed the FDP and FDS characteristics by measuring the mass, average fiber length and cross-sectional area of all fibers, and the ratio of two muscles was 3:2 (40% FDS force to FDP). Their finding was consistent with the result in this study (3:2 FDP to FDS force ratio).

6.3. Hypothesis 3: The efficiency of internal force to external force ratio

Ratios between tendon forces generated by the force delivery unit and the grip force applied by power grip motion were investigated during a task involving increasing tendon force linearly with five different diameter handles. The efficiency of internal forces to external forces was compared to understand the mechanisms of hand disorders and the relationship between the flexor tendon forces and the externally applied forces to the handles and the fingers. In terms of handle sizes, the average internal tendon force of the smallest handle size (30mm) was, for external grip force F, 4.2F and the largest handle showed 7.0F. Also, the mean efficiency of the internal forces to the external forces was 5.3F (See Table 5.5). In other words, the force efficiency decreased significantly as the cylinder diameter increased. These finding supported Hypothesis 3 by showing the efficiency of flexor tendon-to-grip force ratios on different handle sizes.

More description about handle size effects will be discussed in the following section 6.4.

In terms of the tendon force ratio between FDP and FDS, the efficiency of external forces to internal forces was improved as the %FDS increased (10% to 40%), but it dropped at 50% FDS (i.e. FDP:FDS = 1:1). The efficiency at the 40% FDS force (i.e. 116

FDP:FDS = 3:2) was significantly better (4.1F) and it was worst for the 10% FDS force

(7.9F) in power grip. Consequently, the efficiency of the external to internal forces was optimal at 40% FDS force (3:2 FDP to FDS force ratio) with the smallest diameter handle.

These findings can be compared with the results from previous studies. Although researchers generally agreed on the proportion of muscle and tendon forces required for the externally applied forces, they presented various ranges of these ratios for the external force to internal tendon force. In the result of biomechanical model, Kong (2001) showed the average ratios were, for an external force of F, 9.05F for FDP and 2.83F for FDS in power grip motion. Chao et al. (1989) also reported 3.17 and 1.51 for FDP and FDS in grasp motion, respectively. In terms of validation experiment, Schuind et al. (1992) reported that 7.92 for FDP and 1.73 for FDS in tip pinch motion. The variability of these results may be expected because all researchers did not use the same finger characteristics: moment arm, finger configurations, and angles of the applied forces to the finger tip regarding the function of intrinsic vs. extrinsic muscles during power grip motion.

6.4. Hypothesis 4: The handle size effect

Grip force was measured using five different diameter split cylindrical handles with a force transducer inserted. These grip force data presented the effect of handle diameter on grip strength. There was a negative relationship between handle diameter and grip force, which showed that the grip force increased from 38.3 to 23.0 N, as the cylindrical handle diameter increased from 30 to 60 mm. Thus, the highest grip force was generated on the smallest handle size (30mm), and the lowest grip force was on the 117 largest diameter handle (60mm). This finding supporting Hypothesis 4 is straightforward and consistant with other studies (Edgren et al., 2004; Seo and Amstrong, 2008)(see

Figure 6.1). Edgren et al. (2004) also found the inverse relationship of handle size and grip force measured by a cylindrical gauge dynamometer like a split handle with a force transducer used in this study. Seo and Amstrong (2008) measured split cylinder grip strength decreased with increasing ratio of handle diameter to hand length and hand size.

Kong and Lowe (2005) presented that the total finger force, which was defined as the sum of all phalangeal segments showed a significant inverse relationship with handle diameter as the fingers were more extended to grasp larger handles, but they measured the finger force distribution with FSR film sensors on each phalange instead of using a split handle dynamometer.

Previous investigators have suggested that the grip force decrease with large handle diameters may be due to muscle length-strength relationship and the locations of the fingertip on the handle. Also, the smaller handles created a biomechanical configuration that was described by Replogle (1983) in which the fingers more completely encircle the handle and the phalanges can generate forces that effectively counter act one another. In other hands, when a handle diameter increases, the finger becomes less flexed. Accordingly, the index finger, the ring finger and the little finger

(which are all shorter than the middle finger) may lose some of their mechanical advantage and may thus lose the ability to exert more force (Chen, 1991). 118

30 Mean of Grip Force Grip of Mean

1 2 3 4 5 handle

Figure 6.1. The main effect of handle with mean grip force

The average actual grip forces measured in this study were considerably less than general grip forces exerted by a human subject, although the trends of handle effect were consistent with previous studies. This may be attributable in part to the characteristic of the specimen: the grip force was entirely generated by finger flexoor tendons only. Thus, intrinsic muscles and other supplemental muscle were not applied in the grip motion.

Exclusion of intrinsic muscle action is a limitation of this cadaver study, though this study is a valid approach to investigate the mechanism of forearm flexor tendons in a human hand. Moreover, most previous studies measured grip forces produced by maximum voluntary contraction (MVC) while grasping a handle, but the result in this study was derived from limited tendon forces generated by the motion deliver unit. Thus, the magnitude of grip force could be different, but the patterns of grip force depending on different handle diameters could be comparable with previous studies. In terms of the 119 way data were collected: Grip strength was measured by split cylindrical handles, whereas typical use of usually considers the one directional force only. There might be grip force losses due to shear forces and uncoordinated force direction, some previously discussed.

The current data, like previous studies, demonstrate that there is an ‘optimal’ handle diameter to produce the highest magnitude grip force. It’s hard to define the optimal handle size due to the diversity of human hand length and span. Thus, the optimal handle can be defined by qualitative measuring. Pheasant and O’Neill (1975) indicated that grip force was highest when the thumb tip was aligned with the four fingertips. Seo et al. (2007) speculated that maximum grip force can be achieved when the fingertips and thumb tip work together against the palm, thus resulting in great reaction force on the palm. In the captured pictures in Figure 5.15, the power grip motion with the smallest handle (30mm) shows that the thumb tip aligned with the four fingertips and fingertips worked against the palm. As shown in Figure 5.15, when handle diameter increased from the optimal diameter (smallest handle), fingers opened more and moment arms for finger flexors decreased. Consequently, the grip force may decrease as the moment arms decrease (An, 1983). Based on the specimen hand size, the 30mm handle was optimal in producing maximum grip force in this experiment. To find out the optimal handle size in detail, we need to normalize the handle size compared with hand sizes. To get normalized data, more specimen and iterations are required with diverse anthropometric hand data. 120

6.5. Hypothesis 5: Finger Force Distribution

A method for measuring the hand-handle contact force was proposed and evaluated to assess the finger force distribution in power grip motion. The contact force applied at the hand-handle interface was measured using a thin-film FSR under different combinations of the tendon force ratio (FDP vs. FDS). On average, the forces produced by the middle finger and distal phalange were always significantly larger than those produced by the other fingers and phalanges. These patterns for the magnitudes and percentage contributions of individual finger and phalange forces to the total force in the finger force distribution are similar with the findings in previous studies of the grip force tasks (Amis 1987; Kong and Lowe 2005) and also supported Hypothesis 5 by showing finger and phalange forces.

Figure 6.2 shows the main effect of finger force distribution and each phalange forces. Also, Kong (2001)’s result measured by a human subject was plotted in the same graph to compare the trend of force distributions. In both plots, middle finger had significantly highest contact force followed by index finger force and little finger was lowest. However, finger forces were notably less than the previous study, but overall force patern of each finger was quite similar. In terms of phalange forces, middle and 121

FINGER Phalange 7 Kong, 2001 6 HMS 5

3 Mean of Force (N) Force of Mean 2

0 1 2 3 4 1 2 3 4

Figure 6.2. Mean contact force of each finger and phalange

proximal phhalange forces were much less than in the previous study, though the contact force of distal phalange was significatly highest in both studies. Also, the average actual finger forces measured in this study were considerably less than finger forces exerted by a human subject. As described in previous section, this may be attributable in part to the difference between a cadaver and a human subject. Moreover, intrinsic muscle was required for fine-tuning to get uniform phalange contact forces.

Low contact forces of index, ring and little finger cab be explained by that three fingers shorter than the middle finger may loose some of their mechanical advantage and thus unable to generate more pressure (Chen, 1991). Although the magnitude of applied contact force was lower than other study, the efficiency of internal force to external force shown in Table 5.10 was consistent with previous studies. 122

6.6. Hypothesis 6: Finger Joint Angles

The simulated contraction of extrinsic muscles generated concurrent flexion at the interphalangeal (IP) joints, i.e. the joints were rotated in one direction only. High proportion of FDP force with less FDS force made PIP joint angle decrease and DIP joint angle increase. In contrast, the same proportion of FDP and FDS force, i.e. 1:1 FDP to

FDS, produced flexed PIP joint and flatten DIP joint. Therefore, 3:2 FDP to FDS tendon force ratio that already described in previous sections showed most identical curvature motion and this finding supported Hypothesis 6. Furthermore, the finger motions produced with a 3:2 tendon force ratio was applied to validate the biomechanical hand model in section 5.6. Through the index finger motion captured by lateral view camera, the handle size effect could be explained.

In terms of the metacarpophalangeal (MCP) joints, it was hard to control the MCP joint by pulling the extrinsic flexor muscles (FDP and FDS). The MCP joints of specimen were extended in rest condition due to high flexibility of the MCP joints. Thus, we had to hold up MCP joints until PIP and DIP joints were fully flexed during activating the grip motion. The role of the extrinsic finger flexor muscles (FDP and FDS) in initiating rotation of the MCP joint and in coordinating flexion at the MCP, PIP and DIP joints remains a matter of some debate (Kamper 2002). A previous study reported that the intrinsic muscles (Lumbrical and Ulnar/Radious interosseous) were seen as the primary

MCP flexors, especially in regard to initiation of MCP flexion (Moore and Dalley, 1999).

Also, a cadaver study utilizing static loading of the FDS tendon found that significant PIP flexion occurred before the loads become sufficient to initiate MCP flexion (Delattre et 123 al., 1983). Furthermore, Kampler et al. speculated that intrinsic muscles may assist MCP flexion indirectly by increasing the resistance to the interphalangeal flexion.

Therefore, these previous studies support that the variation of MCP joint angle in

Figure 5.16 was quite small and did not have any effect from the different tendon force ratio. It was a limitation of the cadaver experiment that MCP joint could not be well controlled by pulling extrinsic flexor tendon forces.

6.7. Mathematical Model Validation

In the comparison of the biomechanical prediction model and this study, actual data (phalange length, finger force distribution and finger joint angle) were input to the prediction model. The predicted flexor tendon forces were, on average 44% higher than the actual tendon forces. Also, the predicted FDP force was 61% higher than the actual

FDP force, but the FDS force was 38% less in the predicted FDS force. The reason that the predicted FDP was higher than the actual FDP and the smaller predicted FDS than the actual can be expected under the assumption of the prediction model. The model assumed the tendon force ratio of the FDP to FDS as 3:1. However, the result of the model always shows more FDP force and less FDS force than 3:1 due to the α constant value (0.3) in the model. Consequently, to get more identical results, the α parameter (tendon force ratio) should be predetermined depending on the PIP and DIP joint angles in power grip motion. The actual tendon forces were compared with the results from other biomechanical finger models. Average ratios were, for an external force of F, 2.27F-

3.47F for the FDP and 1.51-4.23F for the FDS in power grip motion (An et al., 1985;

Chao et al., 1976; Chao and An, 1978). These ratios were smaller than the result of 124 predicted tendon force ratio but quite similar with the ratio of actual tendon force

(internal force) and grip force (external force) measured in this study.

125

Chapter 7

SUGGESTION FOR FUTURE RESEARCH

The contribution of this study was to validate the mathematical model and analyze the mechanism of hand flexor tendons in power grip function. Thus, tendon force ratio and efficiency of grip force were analyzed by measuring grip force with split cylindrical handles. Also, those results were compared with finger joint angle and the prediction model. Though it provides novel insights into the functional manifestation of the power grip motion with cylindrical handles and assess excessive internal tendon loads to prevent musculo-skeletal disorders (MSDs), there are several improvements required.

7.1. Handle Design

The grip force measured with a split cylinder depends on the handle at which the force transducer is placed in the hand (Edgren et al., 2004). Therefore, grip force measured with a split cylinder in this study may have some limitation to reflect the true grip forces on these cylindrical handles. Consequently, instead of a one directional force transducer, a three directional force transducer inserted in a split handle may increase the sensitivity for measuring different directional phalange forces to a cylindrical handle and three dimensional force directions can be calculated to get the vector grip force.

Moreover, the handle design could be modified to other shapes like a trigger. Repetitive and forceful triggering is a risk factor in general work environments as well as grasping. 126

To investigate the triggering mechanism, this cadaver model can be modified with the triggering handle.

7.2. Finger Force Distribution

Finger force distribution measurement has the several advantages. First, finger force distribution measurement is not affected by device or hand orientation. Second, it is proportional to friction that is applied during object manipulation, such as lifting, twisting, and pushing. However, it has a disadvantage as well. The finger force measurement does not include direct measurement of shear force. Accordingly, a finger force measurement need to be accompanied with a grip force measurement on a cylindrical handle. In cadaver model, it was hard to measure each phalange force with film FSRs. A FSR force sensor usually provided an accurate contact force in a human subject, but attaching FSRs on a cadaver hand was difficult to contact the small spot of sensor on a handle surface. If a large flexible pressure pad is covered around a cylindrical handle, contact forces on each phalange could be measured more accurately.

7.3. Intrinsic Muscles

Future studies delineating the motion contribution of the intrinsic muscles would be useful in drawing concrete conclusions about their role in phalangeal joint motion. It was assumed that the effect of intrinsic muscles on the finger flexion can be neglected.

However, metacarpal joint was not controlled without the tension of intrinsic muscles in cadaver model. Kamper et. al. (2006) also stated that the intrinsic muscle is necessary to 127 produce MCP flexion, especially to initiate the flexion. Hence, although the muscle may not be controlled by the motion unit, it should be pulled by cables or weights to keep proper tensions for more realistic power grip motion.

7.4. Passive Force-Length Relationship

Although acknowledged by most researchers, passive muscle force in the antagonist muscles have been neglected and assumed to be dependent on the external force applied to the fingers (An et al., 1985; Chao et al., 1976, Schuind et al., 1992). By definition, passive force cannot be dependent on the external force applied on activation level, as implied by relating it to external force, but must be dependent on muscle length alone. Since the cadaver model developed in this study could conduct the test for passive force-length relationship, the quantification of the relationship would provide important factors in post-surgical rehabilitation, splinting, and tool design as well.

128

REFERENCES

Aldien, Y., Welcome, D., Rakheja, S., Dong, R., and Boileau, P.E., 2005. Contact pressure distribution at hand–handle interface: role of hand forces and handle size. International Journal of Industrial Ergonomics. 35: 267–286.

Amis, A.A., 1987. Variation of finger forces in maximal isometric grasp tests on a range of cylinder diameters. Journal of Biomechanical Engineering. 9: 313-320.

An, K. M., Chao, E.Y., Cooney, W.P., and Linscheid, R.L., 1979. Normative model of human hand for biomechanical analysis. Journal of Biomechanics. 12: 775-788.

An, K. N., Chao, E.Y., Cooney, W.P., and Linscheid, R.L., 1985. Forces in the normal and abnormal hand. Journal of orthopedic research. 3: 202-211.

Armstrong, T. J., 1994. Cumulative trauma disorders of the hand and wrist: Ergonomics guide. American Industrial Hygiene Association.

Armstrong, T. J., 1999. Cumulative trauma disorders of the hand and wrist: Ergonomics guide. American Industrial Hygiene Association.

Armstrong, T.J. and Chaffin, D.B., 1978. An investigation of the relationship between displacements of the finger and wrist joints and the extrinsic finger flexor tendons. Journal of biomechanics. 11: 119-128.

Armstrong, T. J. and Chaffin, D.B., 1979. Carpal tunnel syndrome and selected personal attributes. Journal of Occupational Medicine. 21(7): 481-486.

Ayoub, M.M. and Lo Presti, P., 1971. The determination of an optimum size cylindrical handle by use of electromyography. Ergonomics. 14 (4): 509-518.

Bendz, P., 1980. The motor balance of the Wngers of the open hand. Scandinavian Journal of Rehabilitation Medicine. 12, 115–121.

Brand, P.W., Beach, R.B., and Thompson, D.E., 1981. Relative tension and potential excursion of muscles in the forearm and hand. Journal of Hand Surgery. 6:209- 218. 129

Brand, P.W. and Hollister, A., 1993. Clinical mechanics of the hand. St. Louis, MO, Mosby-Year Book. Inc.

Bright, D.S. and Urbaniak, J.S., 1976. Direct measurements of flexor tendon tension during active and passive digit motion and its application to flexor tendon surgery. Transactions. 22nd annual orthopedic research society, 240.

Bureau of Labor Statistics (BLS), 2001. Reports on survey of occupational injuries and illnesses in 1977–2001. Bureau of Labor Statistics. US Department of Labor, Washington, DC.

Cannon, L. J., Bernacki, E.J. and Walter, S.D., 1981. Personal and occupational factors associated with carpal tunnel syndrome. Journal of Occupational Medicine. 23(4): 255-258.

Chaffin D.B., 1973. Localized muscle fatigue--definiton and measurement. J. Occupational Med. 15(4):346-54.

Chang, S.R., Park, S, and Freivalds, A., 1999. Ergonomic evaluation of the effects of handle types on garden tools. International Journal of Industrial Ergonomics. 24: 99-105.

Chao, E. Y., An, K.N., Cooney, W.P., and Linscheid, R.L., 1989. Biomechanics of the Hand: A Basic Research Study, World Scientific, Singapore.

Chao, E.Y.S. and An, K.N., 1978. Determination of internal forces in human hand. Journal of engineering mechanics division ASCE 104: 255-272.

Chao, E.Y.S., Opgrande, J.D., and Axmear, F.E., 1976. Three-dimensional force analysis of finger joints in selected isometric hand functions. Journal of biomechanics. 9: 387-396.

Chen, Y., 1991. An evaluation of hand pressure distribution for a power grasp and forearm flexor muscle contribution for a power grasp on cylindrical handles. Lincoln, Nebraska, University of Nebraska. Ph.D.

Cooney, W. P. and Chao, E.Y.S., 1977. Biomechanical analysis of static forces in the thumb during hand function. The journal of bone and joint surgery. 59(1): 27-36. 130

Darling, W. G., & Cole, K. J., 1990. Muscle activation patterns and kinetics of human index finger movements, Journal of Neurophysiology. 63, 1098–1108.

Darling, W. G., Cole, K. J., & Miller, G. F., 1994. Coordination of index Finger movements. Journal of Biomechanics. 27, 479–491.

Delattre, J.F., Ducasse, A., Flament, J.B., and Kenesi, C., 1983. The mechanical role of the digital fibrous sheath: application to reconstructive sugery of the flexor tendon. Anatomia Chinica. 5: 187-197.

Dennerlein, J.T., Miller, J., Mote, C.D. Jr., and Rempel, D.M., 1997. A low profile human tendon force transducer: the influence of tendon thickness on calibration. Journal of biomechanics. 30(4): 395-397.

Dennerlein, J.T., Diao, E., Mote Jr., C.D., and Rempel, D.M., 1998. Tensions of the flexor digitorum superficialis are higher than a current model predicts. Journal of Biomechanics. 31(4): 295-301.

Dong, R.G., Schopper, A.W., McDowell, T.W., Welcome, D.E., Wu, J.Z., and Smutz, W.P., 2004. Vibration energy absorption (VEA) in human ﬁngers-hand-arm system. Medical Engineering and Physics. 26:483–492.

Doyle, J.R., 1989. Anatomy of the ﬂexor tendon sheath and pulley system: a current review. Journal of Hand Surgery. 14A: 349–351.

Dul, J., 1983. Development of a minimum-fatigue optimization technique for predicting individual muscle forces during human posture. Biomechanical Engineering, Vanderbilt University. Ph.D Dissertation.

Edgren,C.S., Radwin, R.G., and Irwin, C.B., 2004. Grip force vectors for varying handle diameters and hand sizes. Human Factors. 46 (2): 244-251.

Feldman, R.G., Goldman, R. and Keyserling, W.M., 1983. Peripheral nerve entrapment syndromes and ergonomic factors. American Journal of Industrial Medicine. 4: 661-681.

Fellows, G.L. and Freivalds, A., 1991. Ergonomics evaluation of a foam rubber grip for tool handles. Applied Ergonomics. 22: 225–230. 131

Higgins, I.R. and Mandiberg, J.J., 2000. The World's Best Anatomical Charts Collection Book I - Systems and Structure. Skokie, Illinois, Anatomical Chart Company.

Hirsch, D., Pagy, D., Miller, D., Dumbletion, J.H., and Miller, E.H., 1974. A biomechanical analysis of the metacarpophalangeal joint of the thumb. Journal of biomechanics. 7:343-348.

Idler, R. S. and S., J.W., 1986. The effects of pulley resection on the biomechanics of the proximal interphalangeal joint. The university of pennsylvania orthopaedic Journal. 2: 20-23.

Idler, R.S., 1985. Anatomy and biomechanics of the digital flexor tendons. Hand Clin 1:3-11.

Irwin, C. B. and Radwin, R.G., 2008. A new method for estimating hand internal loads from external force measurements. Ergonomics. 51:156–167.

Kamper, D.G., Hornby, T.H., and Rymer, W.Z., 2002. Extrinsic flexor muscles generate concurrent flexion of all three finger joints, Journal of Biomechanics, 35:1581- 1589.

Kamper, D.G., Fischer, H.C., and Cruz, E.G., 2006. Impact of finger posture on mapping from muscle activation to joint torque. Clinical biomechanics. 21 (4): 361-369.

Keir, P.J. and Wells, R.P., 1999. Changes in geometry of the finger flexor tendons in the carpal tunnel with wrist posture and tendon load: an MRI study on normal wrists. J. Clinical biomechanics. 14 (9): 635-645.

Ketchum, L.D., Brand, P.W., Thompson, G., Pocock, G.S., 1978. The determination of moments for extension of the wrist generated by muscles of the forearm, Journal of Hand Surgery. 3, 205–210.

Keyserling, W. M., Stetson, D., Silverstein, B., and Brouwer, M., 1993. A checklist for evaluating ergonomic risk factors associated with upper extremity cumulative trauma disorders. Ergonomics. 36(7): 807-831. 132

Kong, Y.K., 2001. Optimum Design of Handle Shape through Biomechanical Modeling of Hand Tendon Forces. Ph.D. dissertation, University Park, PA: Pennsylvania State University

Kong, Y.K. and Freivalds, A., 2003. Evaluation of meat-hook handle shapes. International Journal of Industrial Ergonomics. 32: 13-23.

Kong, Y.K., Freivalds, A., and Kim, S.E., 2004. Evaluation of handles in a maximum gripping task. Ergonomics. 47(12): 1350-1364.

Kong, Y.K., Lowe, B.D., 2005. Evaluation of handle diameters and orientations in a maximum torque task. International Journal of Industrial Ergonomics. 35:1073- 1084.

Kuehl, R.O., 2000. Design of Experiments: Statistical Principles of Research Design and Analysis. New York: Duxbury.

Kursaa, K., Diaob, E., Lattanzab, L., and Rempel, D., 2005. In vivo forces generated by finger flexor muscles do not depend on the rate of fingertip loading during an isometric task. Journal of Biomechanics. 38:2288-2293.

Landsmeer, J., 1961. Study in the anatomy of articulation 1. The equilibrium of the intercalated bone. Acta Morphologica Neerlando-Scandinavica. 3:287–303.

Li, Z.M., Zatsiorsky, V.M., and Latash, M.L.,2001. The effect of finger extensor mechanism on the flexor force during isometric tasks. Journal of Biomechanics. 34:1097–1102.

Lin, G. T., Cooney, W.P., Amadio, P.C. and An, K.N., 1990. Mechanical properties of human pulleys. Journal of Hand Surgery (American). 15(B): 429-434.

Lipscomb, P.R., 1995. Tenosynovitis of the hand and the wrist: Carpal tunnel syndrome, DeQuervain's desease, triger digit. Clinical orthopaedics. 13:164-181.

Long, C., Conrad, P.W., Hall, E.A. and Furler, S.L., 1970. Intrinsic-extrinsic muscle control of the hand in power grip and precision handling: an electromyographic study. Journal of bone and joint surgery. 52A: 853-867. 133

Marco, R.A.W., Sharkey, N.A. and Smith, T.S., 1998. Pathomechanics of closed rupture of the flexor tendon pulleys in rock climbers. The journal of bone and joint surgery. 80A(7):1012-1019.

McComas, A. J. and Thomas, H.C., 1968. Fast and slow twitch muscles in man. Journal of the Neurological Sciences. 7(2):301-307.

McGorry, R.W., 2001. A system for the measurement of grip forces and applied moments during hand tool use. Applied Ergonomics. 32:271-279.

Moore, J. S., 1992. Carpal tunnel syndrome. Occupational Medicine. State of the Art Reviews. 7: 741-763.

Moore, K.L. and Dalley II, A.F., 1999. Clinically Oriented Anatomy. Lippincott Williams & Wilkins, Philadelphia, PA.

Nathan, P. A., Keniston, R.C., Myers, L.D. and Meadows, K.D., 1992. Longitudinal study of median nerve sensory conduction in industry - relationship to age, gender, hand dominance occupational hand use and clinical diagnosis. Journal of Hand Surgery. 17A(5): 850-857.

National Research Council & Institute of Medicine, 2001. Musculoskeletal disorders and the workplace: low back and upper extremities. Washington. DC, National Academy Press.

Netter, F.H., 1989. Atlas of human anatomy. Aummit, NJ, CIBA-GEIGY Corporation.

NIOSH, 1997. Musculoskeletal Disorders and Workplace Factors. Report 97-141. Cincinnati, OH, National Institute for Occupational Safety and Health.

NIOSH, 2001. National Occupational Research Agenda for Musculoskeletal Disorders. Cincinnati, OH, National Institute for Occupational Safety and Health.

Nordin, M. and Frankel, V.H., 1989. Basic biomechanics of the musculoskeletal system. Williams & Wilkins.

OSHA, 2001. Table of non-fatal occupational injuries and illnesses with days away from work involving musculoskeletal disorders by selected worker and case characteristics. 134

Phalen, G.S., 1972. The carpal tunnel syndrome, clinical evaluation of 598 hands. Clin. Orthop. 83: 29-40.

Phesant, S. and O’Neill, D., 1975. Performance in gripping and turning – A study in hand/handle effectiveness. Applied Ergonomics. 6:205-208.

Putz-Anderson, V., 1988. Cumulative trauma disorders: A manual for musculoskeletal diseases of the upper limbs. Taylor and Francis.

Rempel, D. and Horie, S., 1994. Effect of wrist posture during typing on carpal tunnel pressure. Working with Display Units: 4th International Scientific Conference.

Replogle, J. O., 1983. Hand torque strength with cylindrical handles. In Proceedings of the Human Factors Society 27th Annual Meeting, Santa Monica. 412-416.

Schuind, F., Garcia-Elias, M., Cooney III., W.P., and An, K.N., 1992. Flexor tendon forces: in vivo measurements. Journal of Hand Surgery (American). 17(2): 291- 298.

Seo, N.J. and Amstrong, T.J., 2008. Investigation of grip force, normal force, contact area, hand size, and handle size for cylindrical handles. Human Factors. 50(5):734-744.

Seo, N.J., Amstrong, T.J., Ashton-Miller, J.A., and Chaffin D.B., 2007. The effect of torque direction and cylindrical handle diameter on the coupling between the hand and a cylindrical handle. Journal of biomechanics. 40 (14): 3236-3243.

Sharkey, N.A., Smith T.S., and Lundmark D.C., 1995. Freeze clamping musculotendinous junctions for in vitro simulation of joint mechanics. Journal of biomechanics. 28(5): 631-635.

Silverstein, B.A., Fine, L.G., and Armstrong, T.J., 1986. Hand wrist cumulative trauma disorders in industry. British journal of industrial medicine. 43: 779-784.

Silverstein, B.A., Fine, L.J., and Armstrong, T.J., 1987. Occupational factors and carpal tunnel syndrome. American Journal of Industrial Medicine. 11: 343-358.

Smith, E.M., Juvinall, R.C., Bender, L.F., and Pearson, J.R., 1964. Role of the finger flexors in rheumatoid deformities of the metacarpophalangeal joints. Arthritis and rheumatism. 7:467-480. 135

Spence, A.P., 1990. Basic human anatomy. The Benjamin/Cumming Publishing Company, Inc.

Spoor, C.W., 1983. Balancing a force on the fingertip of a two-dimensional finger model without intrinsic muscles. Journal of Biomechanics. 16:497–504.

Steinberg, D.R., 1992. Acute flexor tendon injuries. Orthopedic clinics of north America. 23(1): 125-140.

Steindler, A., 1955. Kinesiology of the human body. Charles Thomas Publisher.

Tanaka, S., Wild, D.K., Seligman, P.J., Halperin, W.E., Thun, M., Timbrook, C. and Wasil, J., 1988. Use of worker's compensation claims data for surveillance of cumulative trauma disorders. Journal of Occupational Medicine. 30: 488-492.

Valero-Cuevas, F.J., Zajac, F.E., and Burgar, C.G., 1998. Large index-fingertip forces are produced by subject-independent patterns of muscle excitation. Journal of Biomechanics. 31:693–703.

Vallbo, A. B., & Wessberg, J., 1993. Organization of motor output in slow finger movements in man, Journal of Physiology. 469, 673–691.

VanWely, P., 1970. Design and disease. Applied Ergonomics. 1(5): 262-269.

Waters, T. R., 2004. National efforts to identify research issues related to prevention of work-related musculoskeletal disorders. Journal of Electromyography and Kinesiology. 14: 7-12.

Webb Associates, 1978. Anthropometric Source Book, NASA Ref. 1024. Vol. I.

Weightman, B. and Amis, A.A., 1982. Finger joint force predictions related to design of joint replacements. Journal of biomedical engineering. 4: 197-205.

Welcome, D., Rakheja, S., Dong, R., Wu, J., and Schopper, A., 2004. An investigation on the relationship between grip, push and contact forces applied to a tool handle. International Journal of Industrial Ergonomics. 34: 507–518

Werner, R. A., Albers, J.W., Franzblau, A. and Armstrong, T.J., 1994. The relationship between body mass index and the diagnosis of carpal tunnel syndrome. Muscle and Nerve. 17(6): 632-636. 136

Wimer, B., Dong, R., Welcome, D., and Warren, C., 2009. Development of a new dynamometer for measuring grip strength applied on a cylindrical handle. J. Medical Engineering & Physics. article in press.

137

APPENDIX A: Hand Motion Simulator control block diagram

A.1. Force Feedback Motion Control

138

A.2. Manual Motion Control 139

A.3. Velocity Control

140

A.4. Data Saving

141

APPENDIX B: Calibration of Force Transducer (FSRs)

B.1. Regression plots of actual forces and force units for 16 channels

1200 1000 y = 455.0ln(x) ‐ 853.8 y = 452.0ln(x) ‐ 893.3 1000 R² = 0.987 800 R² = 0.978 800 600 600 400 400 200 200 0 0 ‐200 0 204060 ‐200 0204060 ‐400 ‐400 ‐600 ‐600 CH 1 CH 2 ‐800 ‐800 Log. (CH 1) Log. (CH 2) ‐1000 ‐1000

1200.00 1000.00 y = 451.5ln(x) ‐ 796 y = 459.9ln(x) ‐ 897.2 1000.00 800.00 R² = 0.994 R² = 0.975 800.00 600.00 600.00 400.00 400.00 200.00 200.00 0.00 0.00 ‐200.00 0 204060 ‐200.00 0204060 ‐400.00 ‐400.00 ‐600.00 ‐600.00 CH 3 CH 4 ‐800.00 ‐800.00 Log. (CH 3) Log. (CH 4) ‐1000.00 ‐1000.00

1200.00 1200.00 y = 453.7ln(x) ‐ 834.7 y = 455.2ln(x) ‐ 869.5 1000.00 1000.00 R² = 0.988 R² = 0.983 800.00 800.00 600.00 600.00 400.00 400.00 200.00 200.00 0.00 0.00 ‐200.00 0 204060‐200.00 0 204060 ‐400.00 ‐400.00 ‐600.00 ‐600.00 CH 5 CH 6 ‐800.00 ‐800.00 Log. (CH 5) Log. (CH 6) ‐1000.00 ‐1000.00 142

1200.00 1200.00 y = 452.0ln(x) ‐ 860.9 1000.00 y = 482.6ln(x) ‐ 865.8 1000.00 R² = 0.982 R² = 0.985 800.00 800.00 600.00 600.00 400.00 400.00 200.00 200.00 0.00 0.00 ‐200.00 0 204060‐200.00 0 204060 ‐400.00 ‐400.00 ‐600.00 CH 7 ‐600.00 CH 8 ‐800.00 Log. (CH 7) ‐800.00 Log. (CH 8) ‐1000.00 ‐1000.00

1000.00 1000.00 y = 436.4ln(x) ‐ 824.4 y = 436.7ln(x) ‐ 816.2 800.00 800.00 R² = 0.991 R² = 0.994 600.00 600.00 400.00 400.00 200.00 200.00 0.00 0.00 ‐200.00 0 204060‐200.00 0 204060 ‐400.00 ‐400.00 ‐600.00 ‐600.00 CH 9 CH 10 ‐800.00 ‐800.00 Log. (CH 9) Log. (CH 10) ‐1000.00 ‐1000.00

1000.00 1200.00 y = 415.5ln(x) ‐ 805.3 y = 439.3ln(x) ‐ 791.3 800.00 1000.00 R² = 0.988 R² = 0.990 600.00 800.00 400.00 600.00 400.00 200.00 200.00 0.00 0.00 ‐200.00 0204060 ‐200.00 0 204060 ‐400.00 ‐400.00 ‐600.00 CH 11 ‐600.00 CH 12 ‐800.00 ‐800.00 Log. (CH 11) Log. (CH 12) ‐1000.00 ‐1000.00

143

1200.00 1000.00 y = 441.9ln(x) ‐ 680.5 y = 413.3ln(x) ‐ 881.6 1000.00 800.00 R² = 0.997 R² = 0.959 800.00 600.00 600.00 400.00 400.00 200.00 200.00 0.00 0.00 ‐200.00 0204060 ‐200.00 0 204060‐400.00 ‐400.00 ‐600.00 CH 14 CH 13 ‐600.00 ‐800.00 Log. (CH 13) Log. (CH 14) ‐800.00 ‐1000.00

144

APPENDIX C: Result of Statistical Analysis

C.1. Residual Plots for the normality

(Top: for ANCOVA Bottom: for ANOVA)

Residual Plots for Grip Force Normal Probabilit y Plot of t he Residuals Residuals Versus t he Fit t ed Values

99.9 5 99

90 0 50 Percent 10 Residual -5

1 0.1 -10 -10 -5 0 5 10 20 30 40 Residual Fitted Value

Histogram of the Residuals Residuals Versus the Order of the Data 16 5

12 0 8

Residual -5 Frequency 4

0 -10 -8 -6 -4 -2 0 2 4 1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Residual Observation Order

Residual Plots for Grip Force Normal Probabilit y Plot of t he Residuals Residuals Versus t he Fit t ed Values 99.9 5 99

90 0 50 Percent 10 Residual -5

1 0.1 -10 -10 -5 0 5 10 20 30 40 Residual Fitted Value

Histogram of the Residuals Residuals Versus the Order of the Data 16 5

12 0 8 Residual

Frequency -5 4

0 -10 -8 -6 -4 -2 0 2 4 1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Residual Observation Order

145

C.2. Grip Force Experiment

C.2.1. Analysis of Variance (ANOVA): General Linear Model

Analysis of Variance for Grip Force, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P Int. Force 4 1784.05 1784.05 446.01 46.28 0.000** handle 4 1846.00 1846.00 461.50 47.89 0.000** Int. Force*handle 16 192.88 192.88 12.05 1.25 0.265 Error 50 481.88 481.88 9.64 Total 74 4304.81

S = 3.10445 R-Sq = 88.81% R-Sq(adj) = 83.43%

C.2.2. Pair-wise comparison of tendon force ratios

Tukey Simultaneous Tests Response Variable Grip Force All Pairwise Comparisons among Levels of Int. Force Int. Force = 120 subtracted from:

Int. Difference SE of Adjusted Force of Means Difference T-Value P-Value 140 3.329 2.191 1.519 0.5537 160 7.361 2.191 3.359 0.0108 180 9.736 2.191 4.443 0.0003 200 13.994 2.191 6.386 0.0000

Int. Force = 140 subtracted from:

Int. Difference SE of Adjusted Force of Means Difference T-Value P-Value 160 4.032 2.191 1.840 0.3594 180 6.407 2.191 2.924 0.0364 200 10.665 2.191 4.867 0.0001

Int. Force = 160 subtracted from:

Int. Difference SE of Adjusted Force of Means Difference T-Value P-Value 180 2.375 2.191 1.084 0.8141 200 6.633 2.191 3.027 0.0276

Int. Force = 180 subtracted from:

Int. Difference SE of Adjusted Force of Means Difference T-Value P-Value 200 4.258 2.191 1.943 0.3048

146

C.2.2. Pair-wise comparison of handle

Tukey 95.0% Simultaneous Confidence Intervals Response Variable Grip Force All Pairwise Comparisons among Levels of handle

Tukey Simultaneous Tests Response Variable Grip Force All Pairwise Comparisons among Levels of handle handle = 1 subtracted from:

Difference SE of Adjusted handle of Means Difference T-Value P-Value 2 -9.05 1.134 -7.98 0.0000 3 -8.62 1.134 -7.60 0.0000 4 -9.35 1.134 -8.25 0.0000 5 -15.56 1.134 -13.72 0.0000

handle = 2 subtracted from:

Difference SE of Adjusted handle of Means Difference T-Value P-Value 3 0.429 1.134 0.378 0.9955 4 -0.298 1.134 -0.263 0.9989 5 -6.506 1.134 -5.740 0.0000

handle = 3 subtracted from:

Difference SE of Adjusted handle of Means Difference T-Value P-Value 4 -0.727 1.134 -0.641 0.9675 5 -6.935 1.134 -6.118 0.0000

handle = 4 subtracted from:

Difference SE of Adjusted handle of Means Difference T-Value P-Value 5 -6.209 1.134 -5.477 0.0000 147

C.2.3. Regression of Grip Force on Relative FDS% for 5 handles

Regression Analysis: Grip Force versus Relative FDS% (Handle = 1) The regression equation is Grip Force = 22.5 + 0.450 Relative FDS%

Predictor Coef SE Coef T P Constant 22.468 2.553 8.80 0.000 Relative FDS% 0.45012 0.06865 6.56 0.000

S = 3.17975 R-Sq = 76.8% R-Sq(adj) = 75.0%

Regression Analysis: Grip Force versus Relative FDS% (Handle = 2) The regression equation is Grip Force = 20.6 + 0.246 Relative FDS%

Predictor Coef SE Coef T P Constant 20.630 2.367 8.71 0.000 Relative FDS% 0.24588 0.06366 3.86 0.002

S = 2.99563 R-Sq = 53.4% R-Sq(adj) = 49.9%

Regression Analysis: Grip Force versus Relative FDS% (Handle = 3) The regression equation is Grip Force = 13.3 + 0.465 Relative FDS%

Predictor Coef SE Coef T P Constant 13.327 1.571 8.49 0.000 Relative FDS% 0.46505 0.04222 11.01 0.000

S = 1.96472 R-Sq = 90.3% R-Sq(adj) = 89.6%

Regression Analysis: Grip Force versus Relative FDS% (Handle = 4) The regression equation is Grip Force = 9.83 + 0.542 Relative FDS%

Predictor Coef SE Coef T P Constant 9.825 3.109 3.16 0.008 Relative FDS% 0.54245 0.08348 6.50 0.000

S = 3.84066 R-Sq = 76.5% R-Sq(adj) = 74.6%

Regression Analysis: Grip Force versus Relative FDS% (Handle = 5) The regression equation is Grip Force = 11.9 + 0.306 Relative FDS%

Predictor Coef SE Coef T P Constant 11.947 2.341 5.10 0.000 Relative FDS% 0.30603 0.06275 4.88 0.000

S = 2.89860 R-Sq = 64.7% R-Sq(adj) = 61.9% 148

C.3. Finger Force Distribution Experiment

C.3.1. ANOVA for phalange forces on different finger and %FDS

Analysis of Variance for Total, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P FINGER 3 2438.67 2438.67 812.89 53.58 0.000** %FDS 4 251.32 251.32 62.83 4.14 0.007** FINGER*%FDS 12 168.13 168.13 14.01 0.92 0.533 Error 40 606.88 606.88 15.17 Total 59 3465.00

S = 3.89513 R-Sq = 82.49% R-Sq(adj) = 74.17%

Analysis of Variance for Distal, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P FINGER 3 1387.76 1387.76 462.59 36.79 0.000** %FDS 4 171.86 171.86 42.96 3.42 0.017* FINGER*%FDS 12 175.13 175.13 14.59 1.16 0.343 Error 40 502.88 502.88 12.57 Total 59 2237.63

S = 3.54571 R-Sq = 77.53% R-Sq(adj) = 66.85%

Analysis of Variance for Middle, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P FINGER 3 19.0049 19.0049 6.3350 395.70 0.000** %FDS 4 0.0895 0.0895 0.0224 1.40 0.252 FINGER*%FDS 12 0.1576 0.1576 0.0131 0.82 0.629 Error 40 0.6404 0.6404 0.0160 Total 59 19.8924

S = 0.126529 R-Sq = 96.78% R-Sq(adj) = 95.25%

Analysis of Variance for Proximal, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P FINGER 3 20.0554 20.0554 6.6851 58.29 0.000** %FDS 4 0.9367 0.9367 0.2342 2.04 0.107 FINGER*%FDS 12 2.3771 2.3771 0.1981 1.73 0.097 Error 40 4.5878 4.5878 0.1147 Total 59 27.9570

S = 0.338665 R-Sq = 83.59% R-Sq(adj) = 75.80%

Analysis of Variance for Metacarp, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P FINGER 3 35.7824 35.7824 11.9275 22.48 0.000** %FDS 4 9.0516 9.0516 2.2629 4.27 0.006** FINGER*%FDS 12 7.2044 7.2044 0.6004 1.13 0.363 Error 40 21.2199 21.2199 0.5305 Total 59 73.2582

S = 0.728352 R-Sq = 71.03% R-Sq(adj) = 57.28%

149

C.3.2. Pair-wise comparison of fingers

Tukey Simultaneous Tests Response Variable Total All Pairwise Comparisons among Levels of FINGER FINGER = 1 subtracted from:

Difference SE of Adjusted FINGER of Means Difference T-Value P-Value 2 9.761 1.563 6.244 0.0000 3 -4.833 1.563 -3.092 0.0159 4 -6.687 1.563 -4.278 0.0004

FINGER = 2 subtracted from:

Difference SE of Adjusted FINGER of Means Difference T-Value P-Value 3 -14.59 1.563 -9.34 0.0000 4 -16.45 1.563 -10.52 0.0000

FINGER = 3 subtracted from:

Difference SE of Adjusted FINGER of Means Difference T-Value P-Value 4 -1.854 1.563 -1.186 0.6381

C.3.3. Pair-wise comparison of phalange

Tukey Simultaneous Tests Response Variable Force All Pairwise Comparisons among Levels of Phalange Phalange = 1 subtracted from:

Difference SE of Adjusted Phalange of Means Difference T-Value P-Value 2 -5.950 0.5770 -10.31 0.0000 3 -5.898 0.5770 -10.22 0.0000 4 -4.957 0.5770 -8.59 0.0000

Phalange = 2 subtracted from:

Difference SE of Adjusted Phalange of Means Difference T-Value P-Value 3 0.05200 0.5770 0.09011 0.9997 4 0.99317 0.5770 1.72114 0.3150

Phalange = 3 subtracted from:

Difference SE of Adjusted Phalange of Means Difference T-Value P-Value 4 0.9412 0.5770 1.631 0.3632

VITA

SHIHYUN PARK

Shihyun Park was born in November 30, 1974 in Busan, the Republic of Korea.

He received a B.S. in Industrial Engineering from the Dong-Eui University in 1997. After finishing his undergraduate degree, Shihyun took three years hiatus from formal education and served as a military officer in ROK Army. In August 2000, he entered the

Graduate School of the Dong-Eui University in the department of Industrial Engineering.

He was a research assistant and focused on the ergonomics studies during MS degree.

Shihyun Park completed his Master’s degree in February of 2002 and moved to

State College, PA, where he began working on his doctorate in Industrial and

Manufacturing Engineering at Pennsylvania State University. As a research assistant,

Shihyun worked at the Center for Cumulative Trauma Disorder Research where he concentrated primarily on the ergonomic program for manufacturing companies and the biomechanics of the hand and a cadaver model of the power grip motion. He is a member of the Human Factors and Ergonomics Society (HFES) and the American Society of

Biomechanics (ASB).