Configuration spaces of spatial linkages: Taking Collisions Into Account

TL;DR

This paper develops a comprehensive model of the configuration space for spatial linkages in three-dimensional space, explicitly incorporating contact and collision scenarios, with detailed examples illustrating the approach.

Contribution

It introduces a completed configuration space C(Gamma) that accounts for link collisions and touches, advancing the understanding of linkage configurations in 3D.

Findings

Constructed a completed configuration space C(Gamma) considering collisions.

Provided a simplified blow-up version of the space of immersions.

Presented detailed examples demonstrating the model's application.

Abstract

We construct a completed version C(Gamma) of the configuration space of a linkage Gamma in R^3 which takes into account the ways one link can touch another. We also describe a simplified version of C(Gamma) which is a blow-up of the space of immersions of Gamma in R^3 A number of simple detailed examples are given.