An improved approach to the inverse dynamic analysis of parallel manipulators by a given virtual screw

This paper provides an improved approach to the inverse dynamic analysis of parallel manipulators (PMs) based on the screw theory and Jourdain's principle of virtual power. First, velocity and acceleration mappings from the Cartesian coordinate system to the screw system are established. Next, by introducing a novel concept of virtual screw that is formulated by a combination of virtual angular velocity and virtual linear velocity, four theorems are defined and proven to build the dynamic equations of PMs. Owing to the existing expression of acceleration screws and the introduced virtual screw, the proposed approach not only has the advantages of intuitive physical concepts and universal form but also avoids the difficult derivatives of time and the determination of generalized velocities, which is employed by conventional methods and is determined difficultly for some hybrid PMs. Finally, taking a 1PU+3UPS PM as an instance, the inverse dynamic analysis and numerical examples are presented to demonstrate the feasibility of the proposed approach.