Synthesis of Spherical Four-Bar Function Generators to Match Two Prescribed Velocity Ratios

The present problem is a variation of synthesizing spherical four-bar function generators to coordinate three pairs of finitely separated crank-angle displacements. It is to be stressed here that, since the technique is on the basis of equations of three relative poles, the characteristic equation is simply a quadratic equation in the unknown tan ψ_o (initial output crank angle). It is not necessary, as in the case of a characteristic equation derived from displacement equations, to resort to techniques such as iterative methods for solving nonlinear equations. Equations are so presented as to facilitate computer programing. The synthesis of spherical crank-rockers is a special case of the present problem.