Universality theorems for linkages in the Minkowski plane

TL;DR

This paper characterizes the configuration spaces of mechanical linkages in the Minkowski plane and proves a universality theorem showing their ability to model various manifolds.

Contribution

It provides a complete characterization of linkage configuration spaces in the Minkowski plane and establishes a differential universality theorem for these linkages.

Findings

Characterization of partial configuration spaces in the Minkowski plane

Proof of a differential universality theorem for Minkowski linkages

Linkages can model a wide class of manifolds in the Minkowski setting

Abstract

A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a subset of the vertices. We characterize the possible partial configuration spaces of linkages in the Minkowski plane. We also give a proof of a differential universality theorem in the Minkowski plane: for any manifold M which is the interior of a compact manifold with boundary, there is a linkage which has a configuration space diffeomorphic to the disjoint union of a finite number of copies of M.