A unified method to find active forces and passive wrench of some parallel manipulators with n SPS active legs and a passive leg

Abstract A unified analysis approach is proposed for solving the active force and the passive wrench of some parallel manipulators with n SPS-type active legs and an unactuated passive leg. Firstly, some mathematical formulae for solving the force transformation matrix and active force and passive wrench are derived, and many possible types of the unactuated passive constrained legs are synthesized. Secondly, three parallel manipulators with three to five SPS-type active legs and a different passive leg are presented to illustrate as how to solve their inverse kinematics, force matrix, active forces, and passive wrench, and singularity by using the force matrix. Thirdly, some examples are given, and solving results have been verified by the simulation mechanism approach.

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