About: Cognate linkage

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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, 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.

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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, 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. (en)
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  • Animation showing the construction of two four-bar cognate linkages from an initial four-bar cognate. (en)
  • Animation showing the construction of a six-bar cognate linkages from an initial four-bar cognate. (en)
  • The pink link indicates the former ground link that has become a rectilinear link. (en)
  • Animation showing the construction of Chebyshev's table linkage using the two cognate linkages Chebyshev linkage and Chebyshev lambda linkage. (en)
  • Cayley diagram for generating 4-bar coupler cognates. (en)
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  • Note (en)
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  • Cognate Linkages - Cheybshev Table Linkage Construction.gif (en)
  • CaleyDiagram.gif (en)
  • Cognate Linkages - 6-bar geared linkages.gif (en)
  • Cognate Linkages - Construction.gif (en)
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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, 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. (en)
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  • Cognate linkage (en)
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