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Mechanism Theory

3D overconstrained linkages

The minimum number of links to construct a mobile loop with revolute joints is four as a loop with three links and three revolute joints is either a rigid structure or an infinitesimal mechanism when all three revolute axes are coplanar and intersect at a single point. So 3D overconstrained linkages can have four, five or six links. When these linkages consist of only revolute joints, they are called 4R, 5R or 6R linkages.

The first overconstrained mechanism which appeared in the literature was proposed by Sarrus (1853). Since then, other overconstrained mechanisms have been proposed by various researchers. Of special interest are those proposed by Bennett (1903), Delassus (1922), Bricard (1927), Myard (1931), Goldberg (1943), Waldron (1967, 1968 and 1969), Wohlhart (1987, 1991 and 1993) and Dietmaier (1995).

Bennett linkage

Current work is carried out on the kinematics of existing 3D overconstrained linkages. And a number of new linkages have been found.

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