Kinematics, Singularity and Dexterity Analysis of Planar Parallel Manipulators Based on DH Method

Abstract

Parallel manipulators have separate serial kinematic chains that are linked to the ground and the moving platform at the same time. They have some potential advantages over serial robot manipulators such as high accuracy, greater load capacity, high mechanical rigidity, high velocity and acceleration (Kang et al., 2001; Kang & Mills, 2001). Planar Parallel Manipulators (PPMs), performing two translations along the x and y axes, and rotation through an angle of  around the z axis are a special group among the parallel robot manipulators. They have potential advantages for microminiaturization (Hubbard et al., 2001) and pick-and-place operations (Heerah et al., 2003). However, due to the complexity of the closed-loop chain mechanism, the kinematics analysis of parallel manipulators is more difficult than their serial counterparts. Therefore selection of an efficient mathematical model is very important for simplifying the complexity of the kinematics problems in parallel robots. In this book chapter, the forward and inverse kinematics problems of PPMs are solved based on D-H method (Denavit & Hartenberg, 1955) which is a common kinematic modelling convention using 4x4 homogenous transformation matrices. The easy physical interpretation of the robot mechanisms is the main advantage of this method. The Forward kinematics problem calculates the position and orientation of the end-effector if the set of joint angles are known. The inverse kinematics problem solves for the joint angles when the position and orientation of the end effector is given. In contrast to serial manipulators, the forward kinematics problem is much more difficult than the inverse kinematic problem for parallel manipulators. Afterwards very practical definitions are provided for Jacobian matrix and workspace determination of PPMs which are required for singularity and dexterity analyses. Rest of this book chapter is composed of the following sections. Some fundamental definitions about D-H method as a kinematics modelling convention, Jacobian matrix, condition number, global dexterity index, singularity and workspace determination are presented in Section 2. A two-degree-of-freedom (2-dof) PPM and a 3-dof Fully Planar Parallel Manipulator (FPPM) are given as examples to illustrate the methodology in the following Section. FPPMs are composed of a moving platform linked to 21