AND YET IT MOVES: PARADOXICALLY MOVING LINKAGES IN KINEMATICS

The possible configurations of a mechanical linkage correspond to the solutions of a system of algebraic equations. We can estimate the dimension of the solution set by counting free parameters and equational constraints. But this estimate does not always give the correct answer: sometimes the linkage moves although it should not. In this paper, we give mathematical explanations for this unexpected mobility.

Automated summary

This paper investigates the configurations of mechanical linkages and provides mathematical explanations for unexpected mobility in some cases.