The kinematic map between actuators and end-effector in parallel robot is one of the main constraints for its workspace. With a geometric analysis on the map, this paper reveals the internal characteristics of the central symmetric parallel robot workspace, and presents a series of topology based constraint conditions for the numerical calculation in singularity-free workspace optimization. We use homeomorphism theorems and finite distortion principles to introduce these constraints, and explain how the singularity-free workspace can be considered as a simple connected set under these conditions. Finally, we determine the constraint conditions for two typical central symmetric parallel robots: the 3- RPR structure planar parallel robot and the 6-SPS structure Stewart parallel robot. And the constraint conditions are applied in the singularity-free workspace optimization respectively.
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