Geometric Error Modeling of Parallel Manipulators Based on Conformal Geometric Algebra

Abstract

An approach for geometric error modeling of parallel manipulators (PMs) based on the visual representation and direct calculation of conformal geometric algebra is introduced in this paper. In this method, the finite motion of an open-loop chain is firstly formulated. Through linearization of the finite motion, error propagation of the open-loop chain is analyzed. Then the error sources are separated in terms of joint perturbations and geometric errors. Next, motions and constraints of PMs are analyzed visually by their reciprocal property. Finally geometric error model of PMs are formulated considering the actuations and constraints. The merits of this new approach are twofold: (1) complete and continuous geometric error modeling can be achieved since finite motions are considered, (2) visual and analytical computation of motions and constraints are applied for transferring geometric errors from the open-loop chain to the PM. A 2-DoF rotational PM is applied to demonstrate the geometric error modeling process. Comparisons between simulation and analytical models show that this approach is highly effective.