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And Power-Velocity Relationships in a Multi-Joint Movement

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The Pennsylvania State University The Graduate School College of Health and Human Development FORCE- AND POWER-VELOCITY RELATIONSHIPS IN A MULTI-JOINT MOVEMENT A Thesis in Exercise and Sport Science by Andrew Timothy Todd Hardyk 2000 Andrew Timothy Todd Hardyk Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2000 We approve the thesis of Andrew Timothy Todd Hardyk Date of Signature _____________________________ _______________ Vladimir M. Zatsiorsky Professor of Kinesiology Thesis Advisor Chair of Committee _____________________________ _______________ Richard C. Nelson Professor Emeritus of Biomechanics _____________________________ _______________ William J. Kraemer Professor of Applied Physiology _____________________________ _______________ H. Joseph Sommer III Professor of Mechanical Engineering _____________________________ _______________ Mark L. Latash Professor of Kinesiology Graduate Program Director, Department of Kinesiology Abstract Force-velocity characteristics in multi-joint movements, specifically the vertical jump, have been relatively unexplored in the literature. There were five main goals in this study: 1) to accurately define the force-velocity relationships for a multi-joint movement and compare them to Hill’s classic force-velocity curve, 2) to compare several options for presenting force-velocity curves in a multi-joint movement, 3) to accurately define the power-load and power-velocity relationships in a multi-joint movement for the ranges of force and velocity that were obtainable, 4) since the entire theoretical power- velocity curve was not obtainable because of physical limitations, to determine whether the data in this experiment lies in the ascending or descending portion of the theoretical power-velocity curve, and 5) to determine the load and velocity at which maximum power was produced. Ten well-trained subjects were asked to perform maximum effort, noncountermovement vertical jumps with a range (80% of bodyweight unloading to 125% of bodyweight additional loading) of external loads applied. Each subject performed 28-34 trials with two trials at each condition. The instant of the maximum levels of the various velocity measures was used as the time to measure all of the other variables and the trial with the highest maximum center of mass velocity was selected for analysis. Relationships were identified as ‘Hill-like’ if they were descending, had upward concavity, and 0<a/Fo<1. All of the variables studied in this investigation (maximum velocity of the center of mass, maximum knee angular velocity, maximum leg extension velocity, ground reaction force, and knee moment) were plotted against load. None of these relationships compared well with Hill’s curve. Various logical combinations of these variables were compared to each other and to Hill’s curve. Only ground reaction force vs. maximum center of mass velocity (video), vs. maximum knee angular velocity, and vs. maximum leg extension velocity were Hill-like. The best fit was the ground reaction force vs. maximum center of mass velocity (video) relationship, mathematically fit with Hill’s curve. iii Power, calculated by multiplying ground reaction force and maximum center of mass velocity, varied as expected with maximum center of mass velocity and was on the descending part of the theoretical power-velocity curve. Maximum power corresponded to approximately 37-61% of the maximum squat lift of the subjects and 56% of maximum velocity. This was higher than predicted from theoretical models, but was similar to weightlifting studies. This study successfully determined the force-velocity and power-velocity relationships for a multi-joint movement. Theoretical reasons why there was limited agreement with Hill’s curve were discussed. No other study known by the author covers as wide a range of forces and velocities in vertical jumping. iv Table of Contents List of Figures ...............................................................................................vii List of Tables .................................................................................................. x Acknowledgements........................................................................................ xi Chapter 1 Introduction .................................................................................... 1 Chapter 2 Review of Literature ...................................................................... 8 2.1 Force-Velocity Relationships ..........................................................................9 2.1.1 Single-Trial Force-Velocity Experiments ........................................................... 9 2.1.2 Multi-Trial Force-Velocity Experiments........................................................... 10 2.1.3 Types of Multi-Trial Force-Velocity Experiments............................................ 12 2.1.3.1 Classical Force-Velocity Studies ................................................................ 13 2.1.3.2 Isolated Fiber/Single Muscle Force-Velocity Studies................................. 15 2.1.3.3 Single-Joint Force-Velocity Studies ........................................................... 20 2.1.3.4 Multi-Joint Force-Velocity Studies............................................................. 24 2.2 Power-Velocity and Power-Force Relationships...........................................30 2.3 Conclusion .....................................................................................................31 Chapter 3 Methods........................................................................................ 32 3.1 Subjects..........................................................................................................33 3.2 Experiment.....................................................................................................34 3.3 Experimental Protocol ...................................................................................37 3.4 Data Collection ..............................................................................................38 3.5 Data Analysis.................................................................................................40 3.6 Parameter Combinations................................................................................43 3.7 Statistics.........................................................................................................45 3.8 Delimitations of the Study.............................................................................46 Chapter 4 Results .......................................................................................... 49 4.1 Results of Individual Variables with Changes in Load .................................50 4.2 Parameter Combinations for Exploring Force-Velocity Relationships.........56 4.3 Force-Velocity Comparison Between Force Plate and Video Analysis........59 4.4 Force-Velocity Relationships and Hill’s Curve ............................................61 4.5 Power-Velocity and Power-Force Relationships...........................................65 Chapter 5 Discussion .................................................................................... 68 5.1 General Considerations..................................................................................69 5.2 Individual Variables and Load ......................................................................71 5.2.1 Time and Distance Moved................................................................................. 71 Center of Mass Velocity............................................................................................. 72 5.2.3 Ground Reaction Force...................................................................................... 73 5.2.4 Knee Angular Velocity and Leg Extension Velocity ........................................ 74 5.2.5 Knee Moment .................................................................................................... 75 5.2.6 EMG .................................................................................................................. 75 5.3 Parameter Combinations for Studying Force-Velocity Relationships ..........76 v 5.3.1 Ground Reaction Force vs. Center of Mass Velocity........................................ 77 5.3.2 Ground Reaction Force vs. Knee Angular Velocity and Leg Extension Velocity .................................................................................................................................... 77 5.4 Force Plate and Video Method Comparison..................................................78 5.5 Comparisons to Hill’s Curve .........................................................................79 5.6 Theoretical Mechanical and Physiological Explanations..............................80 5.6.1 Muscular Factors ............................................................................................... 81 5.6.1.1 Muscle Length............................................................................................. 82 5.6.1.2 Muscle Prestretch ........................................................................................ 82 5.6.1.3 Quick Release vs. No Quick Release Methods........................................... 83 5.6.1.4 Instantaneous Muscle Force and Velocity .................................................. 84 5.6.2 Individual and Multiple Joint Factors................................................................ 84 5.6.2.1 Joint Geometry and Joint Configuration .....................................................85
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