Stiffness Evaluation of Machines and Robots: Minimum Collinear Stiffness Value Approach

Abstract

New stiffness performance indices using the collinear stiffness value (CSV) associated with a given configuration in a working space of the machine are proposed. The CSV and its partial cases — a translational stiffness value (TSV), a rotational stiffness value (RSV), and a screw stiffness value (SSV) — have a simple and direct physical interpretation: the CSV is non-negative in singular configuration and positive in regular configurations. As a result, the minimal values of the CSV can be successfully applied to stiffness-related evaluations for all (i.e., both singular and regular) configurations. Similar to a determinant, the minimal CSV equals zero if and only if its associated configuration is singular. In regular configurations, the minimal CSV is applied to evaluation of local stiffness for a given configuration and global stiffness in the working space, wherein the established stiffness limitations are satisfied. Procedures for evaluation of the minimal CSV are developed. As an example, the absolute CSV of the Gough-Stewart platform and its relative stiffness in comparison with serial-type mechanisms are simulated. The proposed approach can be used as an effective design tool for evaluation and limitation of stiffness of machines and robots.