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

Focusing on the instantaneous velocities of passive joints, a formulation approach is proposed for the instantaneous kinematics and singularity analysis of a class of three-legged parallel robots. Since only four 3×3 matrices need to be analyzed, the complexity of singularity analysis is significantly, reduced. Using the product-of-exponentials (POE) formula, the kinematic equations possess well-defined algebraic structures so that the instantaneous kinematics and singularity analysis algorithms can be readily and systematically formulated. Three types of singularities, i.e. the forward, inverse, and combined singularities, have been identified. A unified condition for various singularities is proposed. Significant geometric conditions are also presented for identifying singularity configurations that require simple computations.