A Survey on the Theory of Bonds

TL;DR

This paper provides a comprehensive introduction to bond theory, an algebraic approach for understanding paradoxical mobility in mechanical linkages, especially those with revolute or prismatic joints.

Contribution

It offers a self-contained overview of bond theory and discusses its application to closed linkages, highlighting its role in explaining unexpected mobility.

Findings

Bond theory explains paradoxical mobility algebraically.

Application to closed linkages with revolute or prismatic joints.

Provides foundational understanding for future research.

Abstract

Many researchers tried to understand/explain the geometric reasons for paradoxical mobility of a mechanical linkage, i.e. the situation when a linkage allows more motions than expected from counting parameters and constraints. Bond theory is a method that aims at understanding paradoxical mobility from an algebraic point of view. Here we give a self-contained introduction of this theory and discuss its results on closed linkages with revolute or prismatic joints.