Singularity analysis of three-legged parallel robots based on passive-joint velocities

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace of the mobile platform. Singularity analysis become important in design, motion planning, and control of parallel robot s. Focusing on the instantaneous velocities of passive joints, a new formul ation approach is proposed for the instantaneous kinematics and singularity analysis of a class of three-legged parallel robots. Excluding the passive spherical joints at the leg ends, the number of I-dof passive joints in a three-legged, 6-dof, parallel robot is three, which is only half of the num ber of active joints (six). Consequently, the complexity, of the singularit y analysis is significantly reduced because only four 3 x 3 matrices need t o be analyzed. Using the product-of-exponential formula, the kinematic equa tions possess well-defined algebraic structures so that the instantaneous k inematics and singularity analysis algorithms can be readily and systematic ally formulated. Three types singularities, i.e., the forward, inverse, and combined singularities, have been identified. A unified condition for vari ous singularities is proposed. Significant geometric conditions are also pr esented for identifying singularity configurations that requires simple com putations.