Measuring the global and directed propagation of several quality indicators in the optimal design of parallel robots through the evaluation of Lipschitz and GTI indices

Abstract

In the optimal design of multi-objective parallel robots, transmission ratios such as n_vmin and n_pmin are used to evaluate the extent to which velocity and force propagate from the joint space (q) to the robot's work space (x). Two pieces of information need to be measured in this evaluation: the degree of overlap between the drive and the actuator, and the amplification/attenuation of the drive when it becomes the actuator. Two methods are used to evaluate these factors: assessing the propagation across the entire space using the Lipschitz coefficient and evaluating in a specific direction of interest using the GTI (Geometric Transmission Index). In the improved Atlas algorithm proposed by the author, the Pareto boundary is defined as the intersection of convergent directional cones based on the propagation guidance atlases of the aforementioned design parameters. This paper introduces a method for evaluating these coefficients in the discrete design domain ri to automate the process of determining the Pareto boundary, thereby providing a basis for automating the entire design.