On the workspace determination of spherical serial and platform mechanisms

A technique based on the Euler-Rodrigues parameters of the rotation of a rigid body is developed to determine the workspace of spherical platform mechanisms. The workspace boundary is characterized by the occurrence of manipulator singularity. The singularity locus is obtained both as a set of two implicit functions of the four Euler-Rodrigues parameters, which thus leads to a two-parameter manifold, and as a set of two-parameter explicit functions of joint variables that yield the four Euler-Rodrigues parameters of the rotation of the moving platform at a singular posture. The technique is illustrated with various wrists and spherical platform examples. (C) 1998 Elsevier Science Ltd. All rights reserved.