Hypo-paradoxical Linkages: Linkages That Should Move-But Don't

TL;DR

This paper introduces hypo-paradoxical linkages, a class of mechanisms that appear mobile by classical criteria but are actually rigid, and explains their behavior and relation to other paradoxical linkages.

Contribution

It defines and analyzes hypo-paradoxical linkages, revealing mechanisms that defy traditional mobility criteria and expanding understanding of linkage behavior.

Findings

Identification of hypo-paradoxical linkages that are rigid despite appearing mobile

Analysis of the Bennet mechanism's unexpected positive mobility

Use of classical tools to explain paradoxical linkage behaviors

Abstract

While paradoxical linkages famously violate the Chebyshev-Grubler-Kutzbach criterion by exhibiting unexpected mobility, we identify an opposing phenomenon: a class of linkages that appear mobile according to the same criterion, yet are in fact rigid. We refer to these as hypo-paradoxical linkages, and proceed to analyze and illustrate their behavior. We use the same tools to further explain the unexpected positive mobility of Bennet mechanism.