7 / ~'!:('I DESIGN AND CONTROL OF A THREE DEGREE-OF-FREEDOM PLANAR PARALLEL ROBOT A Thesis Presented to The Faculty of the Fritz J. and Dolores H.Russ College of Engineering and Technology Ohio University In partial Fulfillment of the Requirements for the Degree Master of Science by Atul Ravindra Joshi August 2003 iii TABLE OF CONTENTS LIST OF FIGURES v CHAPTERl: INTRODUCTION 1 1.1 Introduction of Planar Parallel Robots 1 1.2 Literature Review 3 1.3 Objective of the thesis 5 CHAPTER2: PARALLEL ROBOT KINEMATICS 6 2.1 Pose Kinematics 6 2.1.1 Inverse Pose Kinematics 9 2.1.2 Forward Pose Kinematics 11 2.2 Rate Kinematics 15 2.3 Workspace Analysis 20 CHAPTER3: PARALLEL ROBOT HARDWARE IMPLEMENTATION 24 3.1 Design And Construction Of 3-RPR Planar Parallel Robot 24 3.2 Control Of3-RPR Planar Parallel Robot 34 CHAPTER4: EXPERIMENTATION AND RESULTS 41 CHAPTERS: CONCLUSIONS 50 S.1 Concluding Statement 50 5.2 Future Work 51 IV REFERENCES 53 APPENDIX A: LVDT CALLIBRATION 56 APPENDIX B: OPERATION PROCEDURE 61 APPENDIX C: INVERSE POSE KINEMATICS CODE 64 ABSTRACT v LIST OF FIGURES Figure Page 1.1 3-RPR Diagram 2 1.2 3-RPR Hardware 3 2.1 3-RPR Planar Parallel Manipulator Kinematics Diagram 7 2.2 3-RPR Manipulator Hardware 8 2.3 Inverse Pose Kinematics 10 2.4 Velocity Kinematics 16 2.5 Angle Nomenclatures 17 2.6 Example of the 3-RPR Reachable Workspace 21 2.3 Workspace analysis by geometrical method 22 3.1 Summary of the 3-RPR Hardware Configuration 28 3.2 3-RPR Planar Parallel Robot Hardware 29 3.3 External MultiQ Boards, Solenoid Valves, and Power Supply 30 3.4 Simulink/Wincon Interface to the 3-RPR Planar Parallel Robot 30 3.5 3-RPR Planar Parallel Robot Control Hardware 31 3.6 Power Supply For 3-RPR Planar Parallel Robot 32 3.7 Oil-Less Air Compressor For 3-RPR Planar Parallel Robot 32 3.8 External MultiQ Board 33 3.9 Solenoid Valve 33 vi 3.10 Cartesian Pose Control Mode for 3-RPR Planar Parallel Robot 35 3.11 Cartesian Rate Control Mode for 3-RPR Planar Parallel Robot 36 3.12 Prismatic link Leg Length Control Block Diagram 37 3.13 Simulink block diagram for implementing the coordinated Cartesian control for the 3-RPR planar parallel robot 39 4.1 Prismatic link length actual sensed (mm) versus Time (sec) for Case1 43 4.2 Prismatic link length actual sensed (mm) versus Time (sec) for Case2 45 4.3 Prismatic link length actual sensed (mm) versus Time (sec) for Case3 47 1 Chapter 1 : INTRODUCTION The design and control of a three degrees-of-freedom (dot) planar parallel robot is presented in this thesis. This chapter presents an introduction to the parallel manipulators, a literature review of the related research and the objective of the thesis. 1.1 Introduction of Planar Parallel Robot This section of the chapter deals with the introduction of planar parallel robots, especially the 3-RPR planar parallel robots. Parallel manipulators are robots that consist of separate serial chains that connect the fixed link to the end-effector link. The planar parallel robots refer to the class of manipulators, which are planar and actuated in parallel. The 3-RPR as shown in Figure 1.1, refers to the three serial chains, each having three dof. Each of these serial chains has a revolute joint (referred to as "R"), a prismatic joint (referred to as "P") and again a revolute joint (referred to as "R") connected in the respective order. These three serial chains of the configuration RPR with three dof each connect the fixed link (a triangular base in this thesis) to the end effector link (a moving triangular link in this thesis). Now with this configuration, one joint per chain is actuated (the prismatic joint is actuated in this thesis) and the remaining two joints are passive. Figure 1.2 shows the 3-RPR hardware developed in this thesis. 2 Regarding the potential advantages of parallel robots over serial robots it is found that parallel robots have a better stiffness and accuracy as compared to serial robots. Parallel robots are lighter in weight as compared with serial robots. In spite of having lower weights, parallel robots have a greater load bearing capacity than serial robots. Parallel robots have higher velocities and accelerations, and less powerful actuators as compared with serial robots. The only major drawback of the parallel robots over serial robots is that parallel robots have a reduced workspace as compared with serial robots. Figure 1.1 3-RPR Diagram 3 Figure 1.2 3-RPR Hardware 1.2 Literature Review This section presents the literature review for this thesis. Topics such as parallel robots; especially the three-dof planar parallel robots will be discussed in terms of how other authors have proceeded. The prominent subtopics, which will be covered, are the pose kinematics, the velocity kinematics, the workspace analysis and the control implementation of planar parallel robots. Parallel robotic devices were proposed by MacCallion and Pham (1979). Some configurations have been built and controlled (e.g. Sumpter and Soni, 1985). Numerous works analyze kinematics, dynamics, workspace and control of parallel manipulators (see Williams, 1988 and references therein). Hunt (1983) conducted preliminary studies 4 of various parallel robot configurations. Cox and Tesar (1981) compared the relative merits of serial and parallel robots. Aradyfio and Qiao (1985) examined the inverse kinematics solutions for three different three dof planar parallel robots. Williams and Reinholtz (1988a and 1988b) studied the dynamics and workspace for a number of parallel manipulators. Shirkhodaie and Soni (1987), Gosselin and Angeles (1988), and Pennock and Kassner (1990) each present a kinematic study of one planar parallel robot. Gosselin et al. (1996) presents the position, workspace, and velocity kinematics of one planar parallel robot. Recently, more general approaches have been presented. Daniali et al. (1995) present an in-depth study of actuation schemes, velocity relationships, and singular conditions for general planar parallel robots. Gosselin (1996) presents general parallel computation algorithms for kinematics and dynamics of planar and spatial parallel robots. Merlet (1996) solved the forward pose kinematics problem for a broad class of planar parallel robots. Williams and Shelley (1997) solved the inverse pose and velocity kinematics problem for all possible planar parallel manipulators. Williams and Joshi (1999) designed and built a three-dof planar parallel robot and proposed its control implementation scheme (the 3-RPR of this thesis). When the author was working on the research, much of the theory regarding the kinematics, workspace analysis, algorithms for the control architecture had been done 5 for planar parallel robots by various other authors. Therefore, the focus of the current work is hardware design, implementation and control. 1.3 Objective of the thesis This section of the chapter presents the objective of this thesis. The objective of this work is to implement in hardware a 3-RPR planar parallel robot design and to implement control using pneumatic actuators. The 3-RPR planar parallel robot has been built and has been controlled in real time using a personal computer. When the author started this research, the main emphasis was to make use of the available resources for designing, building and implementing control for the 3-RPR planar parallel robot. Thus when the author began working on the thesis the main emphasis was given on the following considerations: 1. Use of compressed air as an actuation medium. 2. To use the existing sensors, actuating devices, actuators and the power supply to form the electromechanical support system for the robot. 3. To implement the control using a personal computer with the MultiQ boards from the Quanser Consulting (1999); to develop and run the programs using Matlab/Simulink. 6 Chapter 2: PARALLEL ROBOT KINEMATICS This chapter presents the kinematics equations and solutions for the 3-RPR planar parallel manipulator. This chapter is divided into three sections: 1. The Pose Kinematics section, which deals with describing the inverse pose kinematics and forward pose kinematics. 2. The Rate Kinematics section, which describes the forward velocity kinematics, inverse velocity kinematics and the Jacobian matrix. 3. The Workspace analysis section, which discusses the computation of workspace for the 3-RPR planar parallel manipulator. 2.1 Pose Kinematics This section presents the symbolic inverse and forward pose kinematics solutions for the 3-RPR planar parallel manipulator. In order to pursue the kinematics analysis, abbreviations and symbols are used to define the geometry of the 3-RPR planar parallel manipulator. Most of the theoretical analysis in this section has been derived and presented by Dr Robert L. Williams II (Williams and Joshi, 1999). The kinematics diagram describing the geometry and configuration of the 3-RPR planar parallel manipulator is given in Fig. 2.1. There are three grounded passive revolute joints located on the base triangle at Ai' (i =1,2,3 ) and there are three moving passive revolute joints that are located on the moving triangular end effector link, at [.i' 7 (i = 1,2,3). The active prismatic joint variables indicate the total lengths Li, between the passive revolute joints. The frame {H} depicts the moving frame, positioned at the triangle centroid and the frame {B} depicts the fixed frame at the base. The Cartesian pose variables are described by the triangular end effector link pose array x ={x y f/JY. \ \ \ \ / \ C2 \ / -\------ / \ / L1 C1 y Al / I L2 e~l~ I {B} I.. X .. I '-----1~ X Figure 2.1 3-RPR Planar Parallel Manipulator Kinematics Diagram The intermediate joint angles B; (THETA i, where i=1,2,3) are passive and, are not required for hardware control, but which may be calculated for computer simulation and/or velocity and dynamics calculations (Williams and Joshi, 1999).