And yet it moves: Paradoxically moving linkages in kinematics

Schicho, Josef

doi:10.1090/bull/1721

And yet it moves: Paradoxically moving linkages in kinematics
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Bull. Amer. Math. Soc. 59 (2022), 59-95 Request permission

Abstract:

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.

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