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Cognate linkage
Linkages of different dimensions with the same output motion / From Wikipedia, the free encyclopedia
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In kinematics, cognate linkages are linkages that ensure the same coupler curve geometry or input-output relationship, while being dimensionally dissimilar. In case of four-bar linkage coupler cognates, the Roberts–Chebyshev Theorem, after Samuel Roberts and Pafnuty Chebyshev,[1] states that each coupler curve can be generated by three different four-bar linkages. These four-bar linkages can be constructed using similar triangles and parallelograms, and the Cayley diagram (named after Arthur Cayley).
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Cognate_Linkages_-_Showcase.gif/640px-Cognate_Linkages_-_Showcase.gif)
Top row: Four-bar cognate linkages.
Middle row: Geared five-bar cognate linkages, derived from top row.
Bottom row: Closely related six-bar cognate linkages, derived from middle row.
Overconstrained mechanisms can be obtained by connecting two or more cognate linkages together.