Classification of higher Mobility closed-loop Linkages

TL;DR

This paper offers a comprehensive classification of complex closed-loop linkages with high mobility, introducing new geometric methods to relate and analyze different linkage configurations.

Contribution

It presents a complete classification of paradoxical high-mobility closed-loop linkages and introduces a geometric relation to extend known results to more complex linkages.

Findings

Classified all paradoxical closed-loop $n$-linkages with $n extgreater=6$ and high mobility.

Derived necessary conditions for $nR$-linkages of mobility $n-5$.

Introduced a geometric relation linking different linkage configurations.

Abstract

We provide a complete classification of paradoxical closed-loop $n$-linkages, where $n\geq6$, of mobility $n-4$ or higher, containing revolute, prismatic or helical joints. We also explicitly write down strong necessary conditions for $nR$-linkages of mobility $n-5$. Our main new tool is a geometric relation between a linkage $L$ and another linkage $L'$ resulting from adding equations to the configuration space of $L$. We then lift known classification results for $L'$ to $L$ using this relation.