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 pla tform mechanisms. The workspace boundary is characterized by the occur rence of manipulator singularity. The singularity locus is obtained bo th as a set of two implicit functions of the four Euler-Rodrigues para meters, which thus leads to a two-parameter manifold, and as a set of two-parameter explicit functions of joint variables that yield the fou r 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 ri ghts reserved.