Discontinuous Mobility of One Family of Spatial 6R Mechanisms Through the Group Algebraic Structure of Displacement Set

Based on group theory and group algebraic structure of the displacement set, one family of single-loop spatial six-revolute mechanisms is offered to illustrate the discontinuous mobility of mechanism. Some properties of discontinuous mobility can be considered as those of the generalised kinematotropy. However, the former seems to be more general than the latter. In general, the discontinuously movable configuration of single-loop spatial 6R mechanism occurs as two or more independent manifolds or subgroups are involved in the same kinematic loop. There are totally three 6R mechanisms provided in this work. The first one is actually a famous Sarrus 6R mechanism, the second one is a hybrid 6R mechanism formed by the combination of one planar and one spherical 4R chains with one pair of collinear axes, and the last one belongs to the well-known generalised double-Hooke-joint mechanism. Their local or permanent mobility will depend on the various positions of joints during the movement.