The present paper intends to report a discovery of geometric invariant in finite synthesis of space mechanism called “the duality of R-R link.” The duality itself is first proven here by using the screw geometry to give it a simple and intuitive form. Second, proving the 4-bar mechanism made by the dual R-R links is a Bennett mechanism it is made possible to synthesize the Bennett mechanisms for rigid-body guidance and function generation. Synthesizing the Bennett mechanisms the first time, for these practical uses, is important in itself. However, from the point of view of “the duality” it is only one special application.

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