Mobile platform center shift in spherical parallel manipulators with flexible limbs

• A method for qualifying the MP center shift of SPMs was developed
• The stiffness matrix was developed with virtual-spring and Castigliano’s theorem
• The methodology is illustrated with case studies of SPMs with different designs
• The MP center shift and orientation error are visualized by means of isocontours
• Analytical solutions agree well with the FE simulated results

Spherical parallel manipulators (SPMs) with revolute joints work under the condition that all joint axes intersect at the manipulator center, where the mobile platform (MP) center is coincident with the center of the base platform. The center of each platform is the point of concurrence of the axes of the three revolute joints attached to the platform. When limb flexibility is considered, however, the MP center will shift away from the base platform center, which consequently influences the manipulator performance, e.g., its orientation accuracy. In this work, the stiffness of SPMs is analyzed, with focus on the MP center shift. The stiffness is modeled by adopting the virtual-spring method. Castigliano's theorem is used to calculate the limb deflection. The model is validated via FE analysis. Examples are included to show the center shift of SPMs with different designs.

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