A Geometric and Analytical Approach for the Error Modeling of a Pointing Parallel Mechanism

Abstract This article explores a geometric and analytical approach to error modeling for a 3-DOF parallel pointing mechanism, designed for high-precision applications such as the orientation of spacecraft antennas and space telescopes. The method innovatively represents the clearances of spherical and universal joints using three-dimensional geometries. Following this, the propagation and accumulation of these clearances are modeled through a series of geometric operations. A clear expression of the complete error boundaries of the manipulator is derived. Additionally, an analytical algorithm is introduced for the first time to calculate the maximum orientation errors given a specified rotation axis. Although the simplification operation in the analytical method might result in overestimated maximums, as verified by the case studies, the method is nonetheless valuable. The reason is that a modest overestimation yields a conservative design margin, which is beneficial for engineering applications. Furthermore, it offers an effective and novel alternative for error analysis, contributing to the field’s body of knowledge.