A Thesis report on KINEMATIC STUDY OF A SPATIAL HYBRID MANIPULATOR FOR ROBOT-ASSISTED SURGERY Submitted in the partial fulfillment of requirement for the award of degree of MASTER OF ENGINEERING IN CAD/CAM Engineering Submitted by Amanpreet Singh Roll No. 801281004 Under the joint guidance of Dr. Ashish Singla Mr. Sanjeev Soni Assistant Professor, Senior Scientist, Biomedical Mechanical Engineering Department, Instrumentation Division, CSIR-CSIO, Thapar University, Patiala. Chandigarh. MECHANICAL ENGINEERING DEPARTMENT Thapar University, Patiala July, 2014 ii ACKNOWLEDGEMENT Through this, I would like to acknowledge those great people who have a significant influence on my professional life. It was seven-eight years back, when I was studying in Bachelors, I got an inspiration to pursue higher studies in the field of robotics from Mr. Deepak Bhandari. I am mainly influenced by his level of knowledge, way to present it, how to make the things easier. At that time, I thought of myself like him and decided to do research in the field of Robotics. Unfortunately, up-to June- 2012, I didn’t get any chance to fulfil my desire. However, in July 2012, I got admission in the same discipline in the most prestigious university (Thapar University, Patiala). Thereafter, one year of M.E has gone. I was seeking to work on robots analytically as well as experimentally. However, still i didn’t get any chance. Fortunately, in September 2013, I got that opportunity which I was looking for since long i.e to work in the field of robotics under the guidance of my mentor, who is a person with excellent knowledge, has the best way to present it, with excellent creativity and a great personality, which inspires lot of others in day-to-day life. Thereafter, I went to CSIR- CSIO Chandigarh and found myself fortune enough to meet another great personality, who let me to work on medical/surgical robots (also referred as future robots). Now, it’s my pleasure to acknowledge, Dr. Ashish Singla (Assistant Professor, Mechanical Engineering Department, Thapar University, Patiala) and Mr. Sanjeev Soni (Senior Scientist, Biomedical Instrumentation Division, CSIR-CSIO, Chandigarh), who fulfilled my all desires. I am greatly thankful for their valuable suggestions, motivation, guidance, encouragement, efforts, timely help and the attitude with which they resolved all of my queries. I would like to say thanks to Dr. Ekta Singla (Assistant Professor, SMMEE, IIT Ropar) for her support during my thesis. I would like to say thanks to Mr. Vipin Sharma for his kindness and support during my thesis. Also, I am deeply indebted to my family for their love, encouragement and ample support. Amanpreet Singh iii ABSTRACT The recent developments in the field of robotics lead to the replacement of conventional machines as well as human beings employed to a specific work. In the last three decades, a lot of research has been carried out in all the major domains of robotics like kinematics, dynamics and controls. The scope of this thesis is limited to kinematic study only. It has been found in the literature that the pioneer work done by Denavit and Hartenberg to develop the kinematic model of a serial manipulator, is limited to open-loop manipulators only. A couple of other ambiguities are also reported by different researchers in the past. The main focus of this work is to develop the kinematic model of a hybrid manipulator, which is a combination of open- and closed-loop chains containing planar and spatial links. The positional and orientational inconsistencies are observed, when such hybrid manipulators are modeled with the D-H parameter method. To overcome these inconsistencies, the concept of dummy frames is proposed in the present thesis and successfully implemented on the prototype of a hybrid manipulator, which is a 7-DOF manipulator being developed for medical/surgical applications at CSIR-CSIO lab, Chandigarh. Moreover, the analytical formulation of the spring design for gravity balancing of the hybrid manipulator is also presented in the current thesis. iv CONTENTS Declaration ii Acknowledgement iii Abstract iv Contents v List of Figures ix List of Symbols xiii List of Tables xvii 1 INTRODUCTION 1 1.1 Robots 1 1.2 Robot Classification 1 1.2.1 Serial Manipulators 2 1.2.2 Hybrid Manipulators 4 1.3 Motivation 5 1.4 Application of Work 5 1.5 Scope of the Thesis 7 1.6 Organization of the Thesis 8 2 LITERATURE REVIEW 9 2.1 Introduction 9 2.2 Different Methods for Describing Robot Kinematics 9 2.2.1 Denavit and Hartenberg Method 10 2.2.2 Sheth and Uicker Method 16 v 2.2.3 A New Geometric Method 19 2.2.4 A Unified Method 24 2.2.5 A Simple and Systematic Method 25 2.2.6 Quaternion Algebra Based Method 27 2.2.7 Screw Theory Based Displacement Method 28 2.2.8 Lie Algebra 29 2.3 Summary 29 3 KINEMATICS OF GENERAL SERIAL 31 MANIPULATORS 3.1 Introduction 31 3.2 Link Coordinate Transformations 32 3.2.1 Point Transformations 32 3.2.2 Line Transformations 32 3.3 Homogeneous Transformations 34 3.3.1 Homogeneous Rotation and Translation 35 3.3.2 Limitations of Homogeneous Transformations 36 3.4 Forward Kinematics 37 3.5 Open-Loop Robot 38 3.5.1 General Description 38 3.5.2 Examples 39 3.6 Closed-Loop Robot 46 3.6.1 General Description 46 3.6.2 Example 49 3.7 Observations 51 3.8 Summary 52 vi 4 KINEMATICS OF HYBRID MANIPULATORS 54 4.1 Introduction 54 4.2 Spatial Hybrid Manipulator 54 4.3 Manipulator for Medical Applications 55 4.4 Kinematic Study of MMA 56 4.5 Development of the Forward Kinematic Model of MMA 59 4.6 Ambiguity in D-H Parameter Method 63 4.7 Improvement in D-H Parameter Method 65 4.7.1 Concept of a Virtual-Link 65 4.7.2 Concept of a Dummy Frame 66 4.8 D-H Parameters of MMA Augmented with Dummy 67 Frames 4.9 Validation 73 4.9.1 Geometrical Validation 73 4.9.2 Validation with Physical Prototype 75 4.10 Case Study: Complete Kinematic Model of MMA 77 4.10.1 Development of the Closed-Loop Constraints 77 4.10.2 Inclusion of Parallelogram Linkage in the 84 Kinematic Model of MMA 4.10.3 Solution Proposed to Resolve the Orientation 88 Inconsistency 4.10.4 Development of Kinematic Model using Dummy 90 Frames 4.11 Geometrical Validation of Kinematic Model 95 4.12 Summary 95 vii 5 GRAVITY BALANCING OF ROBOTIC 96 MANIPULATORS 5.1 Introduction 96 5.2 Gravity Balancing 96 5.3 Literature Review 97 5.3.1 Passive Gravity Compensation Methods 98 5.4 Gravity Balancing of MMA 104 5.4.1 Spring Design for Gravity Balancing 105 5.5 Summary 112 6 CONCLUSIONS AND FUTURE DIRECTIONS 113 6.1 Conclusions 113 6.2 Future Directions 114 APPENDIX A 115 REFERENCES ONLINE REFERENCES viii LIST OF FIGURES 1.1-(a) : General mechanical structure of a robotic manipulator. 2 1.1-(b) : General mechanical structure of a mobile robot. 2 1.2-(a) : An open-loop Serial manipulator. 3 1.2-(b) : A closed-loop Serial manipulator. 3 1.3 : A parallel-serial hybrid manipulator. 4 1.4-(a) : Description of application of the MMA. 6 1.4-(b) : Real-time application of the MMA by surgeon. 6 1.5 : Real-time demonstration of “da Vinci surgical system”. 7 2.1 : Schematic representation of original D-H parameter 10 method [3]. 2.2 : Distal variant of original D-H parameter method. 12 2.3 : Schematic representation of proximal variant of D-H 14 parameters method [3]. 2.4 : Schematic representation of the S-U method. 17 2.5 : Khalil and Kleinfinger method for binary links. 21 2.6 : Khalil and Kleinfinger method for tree-like structured 22 robots. 2.7 : Khalil and Kleinfinger Method for links with more than 23 two joints. 3.1 : General description of kinematics of robotic 31 manipulators. 3.2 : Description of forward kinematics. 37 ix 3.3 : General description of an open-loop robotic 38 manipulator. 3.4 : Description of 4-axis SCARA robot according to distal 39 variant. 3.5 : Description of 5-axis articulated robot according to 40 distal variant. 3.6 : Description of 4-axis SCARA robot according to 41 proximal variant. 3.7 : Description of 5-axis articulated robot according to 42 proximal variant. 3.8 : Description of 6-axis Puma 560 robot according to 43 proximal variant. 3.9 : Description of 4-axis SCARA robot according to S-U 44 method. 3.10 : Description of 5-axis articulated robot according to S-U 45 method. 3.11 : Schematic representation of basic structure of closed- 47 loop robot. 3.12 : Transformations between frames ‘j’ and ‘k’. 48 3.13 : Parallelogram Linkage with, assigned link frames and 49 marked D-H parameters. 4.1 : General representation of kinematic structure of a 55 spatial hybrid manipulator. 4.2 : Basic kinematic structure of manipulator for medical 56 applications (MMA). x 4.3-(a) : Line diagram of the MMA in assumed home position 57 with assigned link-frames according to proximal variant of D-H parameter method. 4.3-(b) : Line diagram of MMA with marked D-H parameters. 58 4.4 : Four-axis SCARA robot with assigned link-frames and 64 marked D-H parameters. 4.5-(a) : Geometry of a solid spatial link 퐿4 64 4.5-(b) : Spatial link 퐿4 with parallel joint axes 64 4.5-(c) : Spatial link 퐿4 with perpendicular joint axes describing 64 the recognizable deficiency of proximal variant of original D-H parameter method.