NOVEL DESIGN AND ANALYSIS OF PARALLEL ROBOTIC MECHANISMS ZHONGXING YANG A DISSERTATION SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN MECHANICAL ENGINEERING YORK UNIVERSITY TORONTO, ONTARIO AUGUST 2019 © ZHONGXING YANG, 2019 ABSTRACT A parallel manipulator has several limbs that connect and actuate an end effector from the base. The design of parallel manipulators usually follows the process of prescribed task, design evaluation, and optimization. This dissertation focuses on interference-free designs of dynamically balanced manipulators and deployable manipulators of various degrees of freedom (DOFs). 1) Dynamic balancing is an approach to reduce shaking loads in motion by including balancing components. The shaking loads could cause noise and vibration. The balancing components may cause link interference and take more actuation energy. The 2-DOF (2-RR)R or 3-DOF (2-RR)R planar manipulator, and 3-DOF 3-RRS spatial manipulator are designed interference-free and with structural adaptive features. The structural adaptions and motion planning are discussed for energy minimization. A balanced 3-DOF (2-RR)R and a balanced 3-DOF 3-RRS could be combined for balanced 6-DOF motion. 2) Deployable feature in design allows a structure to be folded. The research in deployable parallel structures of non-configurable platform is rare. This feature is demanded, for example the outdoor solar tracking stand has non-configurable platform and may need to lie-flat on floor at stormy weathers to protect the structure. The 3-DOF 3-PRS and 3-DOF 3-RPS are re-designed to have deployable feature. The 6-DOF 3-[(2-RR)UU] and 5-DOF PRPU/2-[(2-RR)UU] are designed for deployable feature in higher DOFs. Several novel methods are developed for rapid workspace evaluation, link interference detection and stiffness evaluation. The above robotic manipulators could be grouped as a robotic system that operates in a green way and works harmoniously with nature. ii ACKNOWLEDGEMENT “I will extol the LORD at all times; His praise will always be on my lips.” -Psalm 34:1 NIV. I would like to thank my supervisor, Dr. Dan Zhang for all the supports that guide me to discover the beauty of robotics. His bountiful knowledge and state-of-the-art teaching shine the light on my road to research. I would like to thank my supervisory committee members, Dr. Alex Czekanski and Dr. George Zhu, the external examiner, Dr. Siyuan He, and internal examiner, Dr. Jinjun Shan, for their inspiring questions and constructive advices that bless me and help me grow precious fruits from my PhD studies. I would like to thank all the colleagues of the Advanced Robotics and Mechatronics Lab for peer support in exploring the marvelous world of robotics. A warm thanks to my family and friends for their hugs and a relationship of love. iii TABLE OF CONTENTS ABSTRACT ................................................................................................................................... ii ACKNOWLEDGEMENT ........................................................................................................... iii TABLE OF CONTENTS ............................................................................................................ iv LIST OF TABLES ....................................................................................................................... ix LIST OF FIGURES ..................................................................................................................... xi Chapter 1 Introduction................................................................................................................. 1 1.1 Robotics ................................................................................................................................. 1 1.2 Parallel Robots ...................................................................................................................... 2 1.3 Objectives of the Study ......................................................................................................... 4 1.4 Organization of the Dissertation ........................................................................................... 5 Chapter 2 Literature Review ....................................................................................................... 7 2.1 Synthesis Methodology ......................................................................................................... 7 2.2 Family of 2R1T Manipulators ............................................................................................. 10 2.3 Hybrid Structures ................................................................................................................ 12 2.4 Redundancy and Adaption .................................................................................................. 14 2.5 Kinematics and Dynamics ................................................................................................... 15 2.6 Trajectory and Interpolation ................................................................................................ 17 2.7 Optimization ........................................................................................................................ 18 iv 2.8 Chapter Conclusion ............................................................................................................. 19 Chapter 3 Research Motivation and Methods ......................................................................... 20 3.1 Research Motivations .......................................................................................................... 20 3.1.1 Dynamic Balancing ...................................................................................................... 20 3.1.2 Deployable Structures................................................................................................... 24 3.1.3 Link Interference .......................................................................................................... 25 3.2 Design Methods................................................................................................................... 27 3.3 Evaluation Methods............................................................................................................. 29 3.4 Applications and Optimizations .......................................................................................... 30 3.5 Chapter Conclusion ............................................................................................................. 31 Chapter 4 Dynamic Balancing for Various DOF Motions ...................................................... 32 4.1 Chapter Introduction ........................................................................................................... 32 4.2 Theories and Methodologies ............................................................................................... 33 4.3 Planar Dynamic Balancing .................................................................................................. 34 4.3.1 Planar (2-RR)R Mechanism Design ............................................................................. 35 4.3.2 Inverse Kinematics and Dynamics ............................................................................... 36 4.3.3 Operation Optimization of Energy Consumption Index ............................................... 41 4.3.4 Re-design to be (2-RR)R for Planar 3-DOF Operation ................................................ 49 4.3.5 Section Conclusion ....................................................................................................... 49 4.4 Spatial P*U* Dynamic Balancing ....................................................................................... 49 v 4.4.1 A 3-RRS Mechanism Design ....................................................................................... 50 4.4.2 Inverse Kinematics and Dynamics ............................................................................... 52 4.4.3 Design Optimization ..................................................................................................... 59 4.4.4 Operation Optimization of Energy Consumption Index ............................................... 61 4.4.5 Theory Verification ...................................................................................................... 67 4.4.6 Section Conclusion ....................................................................................................... 72 4.5 Combination for High DOF Mechanism ............................................................................. 72 4.6 Chapter Conclusion ............................................................................................................. 74 Chapter 5 Deployable 3-DOF P*U* Parallel Manipulators ................................................... 76 5.1 Chapter Introduction ........................................................................................................... 76 5.2 Theories and Methodologies ............................................................................................... 78 5.3 Adaptive 3-PRS Parallel Manipulator ................................................................................. 78 5.3.1 The 3-PRS Mechanism Design..................................................................................... 79 5.3.2 Inverse Kinematics and Stiffness ................................................................................