Geometric analysis of coupler-link mobility and circuits for planar four-bar linkages

The problem of mobility analysis of planar four-bar linkages is revisited. The mobility is analyzed in terms of the range of coupler angle by a geometric approach, with a special interest on its full rotatability when the linkage is driven by the coupler link. A constraint triangle which characterizes the movement of the coupler link is constructed. By virtue of the constraint triangle, a new formulation on the couple curve rotation is derived, upon which the ranges of coupler angle are determined and the turning points are identified. Moreover, with the range of coupler angle, the number of circuits is determined. Examples are included to demonstrate the mobility analysis with the new approach.