Rolling 4R linkages

In this paper, a family of mobile 4R linkages is proposed to complete the rolling gait. They are derived from the general 4R four-bar linkage. The first subgroup of this family consists of three planar straight rolling 4R linkages: (1) the linkage driven by four active revolute joints, (2) the linkage driven by an arbitrary active revolute joint, and (3) the overconstrained linkage driven by a motor mounted at the intersection of two additional links. The spherical 4R linkage which rolls along a circle belongs to the second subgroup. The third subgroup includes the spatial Bennett mechanism which rolls along a polygonal line. These rolling 4R linkages have alterable fixed links and are proved to roll successfully by simulations and experiments after the analyses of dynamics, stability and the strategy of motor acts. They can be used to develop new spatial four-bar or multi-bar linkages which could move straight and take a turn.