Performing Nonsingular Transitions Between Assembly Modes in Analytic Parallel Manipulators by Enclosing Quadruple Solutions

Abstract

This paper analyzes the multiplicity of the solutions to forward kinematics of two classes of analytic robots: 2RPRPR robots with a passive leg and 3RPR robots with nonsimilar flat platform and base. Since their characteristic polynomials cannot have more than two valid roots, one may think that triple solutions, and hence nonsingular transitions between different assembly modes, are impossible for them. However, the authors show that the forward kinematic problems of these robots always admit quadruple solutions and obtain analytically the loci of points of the joint space where these solutions occur. Then, it is shown that performing trajectories in the joint space that enclose these points can produce nonsingular transitions, demonstrating that it is possible to design simple analytic parallel robots with two and three degreesoffreedom (DOF) and the ability to execute these transitions.