Generalized kinematic mapping of constrained plane motions and its application to the accuracy analysis of general planar parallel robots

Accuracy analysis becomes one of the key issues of parallel robots when used as high-precision applications. However, the maximal output error index only presents a general evaluation of accuracy performance for robot manipulators. This paper presents a unified approach for the accuracy analysis of the general planar three-legged parallel robots based on the generalized kinematic mapping of constrained plane motions. A generalized form of the classical kinematic mapping is set up, which is applicable to any curve-constrained plane motions. Then, the constrained plane motions can be transformed to parametric surfaces in the three-dimensional projective space with intuitive interpretations. Using this technique, the motion constraints of all potential legs for planar parallel robots can be derived as spatial solids. And the exact output error bound, denoted by a small workspace, can be determined as the intersection of the error solids of the individual legs, which provides a more accurate and systematical description of robot accuracy. The proposed method is generic for accuracy analysis and can be applied to any planar parallel robot with a unified procedure.