Explorations in the History of Machines and Mechanisms

Volume 15 of the series History of Mechanism and Machine Science pp 505-519

Cognate Linkages the Roberts – Chebyshev Theorem

  • Egbert VerstratenAffiliated withDepartment of Mathematics, Faculty of Science, Vrije Universiteit Email author 


This article deals with investigations by Pafnuty Chebyshev and Samuel Roberts in the late 1800s, which led them independently to the conclusion that for each curve that can be drawn by four bar linkages, there are always three linkages describing the same curve. These different linkages resulting in the same curve can be called cognate linkages.

We will see that Chebyshev and Roberts had very different interests and motivations for studying four bar linkages. Despite of these differences, they came to a similar result concerning cognate linkages.