A Generalized and Analytical Method to Solve Inverse Kinematics of Serial and Parallel Mechanisms Using Finite Screw Theory

Abstract

Inverse kinematics is a very important issue in the field of mechanisms and robotics, which is the fundamental problem in kinematical analysis, design and synthesis for both serial mechanisms (SMs) and parallel mechanisms (PMs). The objective of inverse kinematics is to formulate computable kinematic equation at the given pose of end-effector of a SM or moving platform of a PM and then solve all the joint parameters (variables). Solving analytical solution of inverse kinematics is the prerequisite for trajectory planning, precise control and manipulation of mechanisms. This paper presents a generalized method to analytically do inverse kinematics of PMs using finite screw theory. Firstly, the kinematic equation of PM is algebraically formulated through describing finite motions generated by the PM, its limbs and joints employing finite screws. Then, the general procedures to analytically solve the finite screw based kinematic equation are given. Finally, a PM with three translational and one rotational Schoenflies motion is taken as an example to verify the validity of the proposed method.