Singularity analysis of three-legged, six-DOF platform manipulators with URS legs

A special class of platform manipulators is the subject of this paper. These manipulators comprise two platforms connected by three legs, each being composed of one universal (U), one revolute (R) and one spherical (S) joints, which gives the manipulator six degrees of freedom. Hence, two actuators are required per leg. Under the assumption that the two R joints proximal to the fixed platform, and making up the U-joint, are actuated, we derive the differential kinematic relations between actuator joint rates and mobile-platform twist. This model comprises two Jacobian matrices, the forward- and inverse-kinematics Jacobians. These relations are then applied to the singularity analysis of the parallel manipulator developed at Singapore Institute of Manufacturing Technology and Nanyang Technological University.