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.
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).
Overconstrained mechanisms can be obtained by connecting two or more cognate linkages together.
- ^ Roberts and Chebyshev (Springer) Retrieved 2012-10-12