Kinetostatic analysis and solution classification of a class of planar tensegrity mechanisms

TL;DR

This paper analyzes a specific class of planar tensegrity mechanisms with three springs, classifying their equilibrium configurations and stability under various conditions using advanced algebraic methods.

Contribution

It provides a systematic classification of solutions for a class of tensegrity mechanisms using discriminant varieties and algebraic elimination techniques.

Findings

Mechanisms can have up to six equilibrium configurations.

One or two configurations are stable depending on conditions.

Advanced algebraic methods effectively classify solutions.

Abstract

Tensegrity mechanisms are composed of rigid and tensile parts that are in equilibrium. They are interesting alternative designs for some applications, such as modelling musculo-skeleton systems. Tensegrity mechanisms are more difficult to analyze than classical mechanisms as the static equilibrium conditions that must be satisfied generally result in complex equations. A class of planar one-degree-of-freedom tensegrity mechanisms with three linear springs is analyzed in detail for the sake of systematic solution classifications. The kinetostatic equations are derived and solved under several loading and geometric conditions. It is shown that these mechanisms exhibit up to six equilibrium configurations, of which one or two are stable, depending on the geometric and loading conditions. Discriminant varieties and cylindrical algebraic decomposition combined with Groebner base elimination are used to classify solutions as a function of the geometric, loading and actuator input parameters.