Evaluation of workspace of a spherical robotic wrist

In this paper, the problem of workspace analysis of spherical parallel manipulators (SPMs) is addressed with respect to a spherical robotic wrist. The wrist is designed following a modular approach and capable of a unlimited rotation of rolling. An equation dealing with singularity surfaces is derived and branches of the singularity surfaces are identified. By using the Euler parameters, the singularity surfaces are generated in a solid unit sphere, the workspace analysis and dexterity evaluation hence being able to be performed in the confined region of the sphere. Examples of workspace evaluation of the spherical wrist and general SPMs are included to demonstrate the application of the proposed method.