Kinematic and mechanical error analysis of serial spherical linkages using a modular approach

Abstract

Although spherical mechanisms have been widely implemented in medical and industrial fields, there still lacks a simple and systematic approach for analyzing their kinematics and mechanical errors. Therefore, the purpose of this paper is to provide a modular approach for kinematic and mechanical error analysis of serial spherical mechanisms that can be decomposed into predefined modules. Firstly, the forward and inverse kinematics, described by rotation matrices, of the spherical serial manipulator are derived. Besides, the error propagations of the spherical serial manipulator are formulated based on the derived kinematic equations. The derived algorithms are programed into subroutines to analyze the kinematics and mechanical error of a serial spherical linkage by analyzing each of its substructures as the illustrative examples have shown. Until now, the presented module in this paper is applicable to a variety of serial spherical mechanisms, and the feasibility of this method adopting high-class modules will be explored in the future.