Chebyshev inclusion function based interval kinetostatic modeling and parameter sensitivity analysis for Exechon-like parallel kinematic machines with parameter uncertainties

Abstract

This paper aims to investigate the effects of parameter uncertainties on kinetostatic behaviors of Exechon-like parallel kinematic machines (PKMs). A general interval kinetostatic model for Exechon-like PKMs is established by using Chebyshev inclusion function. The prediction accuracy and efficiency of the interval model are numerically verified. Based on the interval model, two indexes are formulated to quantify the effects of parameter uncertainties on kinetostatics of the PKM. The gravity-caused elastic displacements of the PKM are computed throughout its workspace when considering design parameters as interval variables. A sensitivity analysis is carried out to identify the most influential design variables when the PKM is under a condition of parameter uncertainties. Based on this, a cost-effective scheme of tolerance allocation is designed for the PKM in a convenient manner. The analyses reveal the interval kinetostatic response of the PKM is strongly position-dependent and nonlinear-related to multiple uncertain parameters. Hence, parameter uncertainties need to be fully considered during early design stage of such PKMs. The proposed interval model can be further applied to similar over-constrained parallel robots with minor modifications.