Snappability and singularity-distance of pin-jointed body-bar frameworks

TL;DR

This paper introduces a geometric measure of a framework's ability to snap between configurations, based on elastic strain energy, and uses it to assess stability and proximity to singular configurations in mechanical design.

Contribution

It presents a novel intrinsic pseudometric for pin-jointed frameworks that quantifies snappability and singularity-distance, aiding design of multistable and stable mechanisms.

Findings

The proposed measure correlates with the framework's snap capability.

It provides a way to compute the distance to shaky configurations.

Application demonstrated on Stewart-Gough type manipulators.

Abstract

It is well-known that there exist rigid frameworks whose physical models can snap between different realizations due to non-destructive elastic deformations of material. We present a method to measure this snapping capability based on the total elastic strain energy density of the framework by using the physical concept of Green-Lagrange strain. As this so-called snappability only depends on the intrinsic framework geometry, it enables a fair comparison of pin-jointed body-bar frameworks, thus it can serve engineers as a criterion within the design process of multistable mechanisms. Moreover, it turns out that the value obtained from this intrinsic pseudometric also gives the distance to the closest shaky configuration in the case of isostatic frameworks. Therefore it is suited for the computation of these singularity-distances for diverse mechanical devices. In more detail we study this problem for parallel manipulators of Stewart-Gough type.