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Having non-singular assembly modes changing trajectories for the 3-RPSparallel robot is a well-known feature. The only known solution for definingsuch trajectory is to encircle a cusp point in the joint space. In this paper,the aspects and the characteristic surfaces are computed for each operationmode to define the uniqueness of the domains. Thus, we can easily see in theworkspace that at least three assembly modes can be reached for each operationmode. To validate this property, the mathematical analysis of the determinantof the Jacobian is done. The image of these trajectories in the joint space isdepicted with the curves associated with the cusp points.

Non-singular assembly mode changing trajectories in the workspace for the 3-RPS parallel robot