Architecture Singularity Distance Computations for Linear Pentapods

TL;DR

This paper introduces a geometric index to measure how far linear pentapods are from being architecturally singular, aiding in design optimization by quantifying structural singularities.

Contribution

It presents a method to compute the closest architecture singular design for linear pentapods using numerical algebraic geometry algorithms.

Findings

The index effectively measures architectural singularity distance.

Algorithms successfully identify nearest singular configurations.

The approach enhances design robustness and analysis.

Abstract

The kinematic/robotic community is not only interested in measuring the closeness of a given robot configuration to its next singular one but also in a geometric meaningful index evaluating how far the robot design is away from being architecturally singular. Such an architecture singularity distance, which can be used by engineers as a criterion within the design process, is presented for a certain class of parallel manipulators of Stewart-Gough type; namely so-called linear pentapods. Geometrically the architecture singular designs are well-understood and can be subclassified into several cases, which allows to solve the optimization problem of computing the closest architecture singular design to a given linear pentapod with algorithms from numerical algebraic geometry.