The Finite-Step-Integration Method for the Forward Kinematics of Parallel Manipulators

In this paper, the Finite-Step-Integration (FSI) method, based on differential geometry theory, is proposed for solving the forward kinematics (FK) of parallel manipulators (PMs). To regard the PM's configuration intended to solve as the final-form after executing a continuous motion, and the initial-form is known absolutely. The process of the motion is segmented into finite steps, and the system of constraint equations which can be applied on any step is established and linearized according to the invariable geometric characteristics of several differential elements of the PM. Finally, the linear system can be solved via finite iterations and calculations, and the final-form can be obtained completely. The example based on 6-UPS PMs is provided to illustrated the process further, and the method is validated on correctness and accuracy by ADAMS simulation. The research results show that the FSI method is an effective tool for the PM's FK analysis. The FSI method can be applied to the majority of PMs theoretically, as well as provide references for the analyses of velocity and acceleration.