Some Remarks on the RRR Linkage
The variety of rigid-body displacements of the final link of a 3\(R\) kinematic chain are investigated. In most cases the variety generated is a Segre manifold; the Cartesian product of three projective lines. The homology of this variety as a subvariety of the Study quadric is found and simple applications to some enumerative problems in kinematics are given. The conditions for the variety to fail to be a Segre variety are investigated in full and the case where the linkage forms the first three joints of a Bennett mechanism is examined.
Keywords3\(R\) linkages Segre variety Homology
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