Circuit and Branch Rectification of the Spatial 4c Mechanism

Spatial 4C mechanisms are two degree of freedom kinematic closed-chains consisting of four rigid links simply connected in series by cylindrical(C) joints. In this work we are concerned with the design of spatial 4C mechanisms which move a rigid body through a finite sequence of prescribed locations in space. This task is referred to as rigid-body guidance by Suh and Radcliffe (20) and as motion generation by Erdman and Sandor (6). When 4C mechanisms are synthesized for such a task, for example by utilizing Roth’s spatial generalization of Burmester’s planar methods (17; 18), the result is the physical dimensions which kinematically define the mechanism. However, the motion of the mechanism which takes the workpiece through the sequence of prescribed locations in space is not determined. In fact, it may be impossible for the mechanism to move the body through all of the desired locations without disassembling the mechanism. This condition is referred to as a circuit defect. Moreover, in some cases the mechanism may enter a configuration which requires an additional mechanical input to guide the moving body as desired. These are referred to as branch defects. This paper presents a methodology for analyzing spatial 4C mechanisms to eliminate circuit and branch defects in motion generation tasks.