Discontinuous Mobility of a Folding Square-Block Toy: A Class of Single Loop Spatial 8-Bar Mechanism

Based on the group theory and group algebraic structure of the displacement set, an interesting playing toy of the magic folding square block belonging to one class of single-loop spatial eight-revolute mechanism is offered to illustrate the discontinuous mobility of mechanism. This folding toy’s mobility generally has two finite global dofs as a whole kinematic chain. Nevertheless, during the movement, the permanent finite mobility of mechanism depends on the various positions of joints. When the block profile-shape constraints are taken into account, one bifurcation between one 2-dimensional manifold and one 1-dimensional manifold occurs at an initial transition position and the other bifurcation between two 1-dimensional manifolds exists in another specified configuration. In addition, any motion of one working mode destroys the geometrical condition that is required for the other modes but a bifurcation toward a spatial mode with two finite dofs remains possible by ingoring the profile shape constraints. In fact, there is a discontinuous mobility with a trifurcation among three subsets. It is composed of a general spatial mode with 2-dimensional manifold, one part mobility chain of 2-dimensional manifold and another part mobility chain of 1-dimensional manifold.