A quick algorithm for finding mechanical singularity by stochastic approximation

Abstract

In this paper, we focus on a quick algorithm based on stochastic approximation (SA) which is used to seek mechanical singularity. Different from conventional methods, the proposed SA algorithm is quicker and much more effective. SA, also known as stochastic recursive algorithms, take many forms and have numerous applications. Integrated with mechanical kinematic Jacobian matrix, the SA algorithm is based on the strict and integrated illation process. During the illation process, the restrictive qualifications for this algorithm are also outlined. By the analysis of 3-PCR parallel mechanism, such a quick SA algorithm can find the singular points wherever the initial point starts to seek. The algorithm can be used for those mechanisms which satisfy the restrictive qualifications to seek out singular points near the initial working points in workspace quickly and effectively.