New Approach for Rigid Body Guidance of Spherical Four-Bar Linkages

An approximate spherical circle-point of the moving rigid body in spherical motion is defined, and the approach of adaptive cone fitting is presented with respect to spherical curves. Then, the optimum synthesis of spherical four-bar linkages can be converted into an adaptive curve fitting. Thus, the mathematical model of saddle-point programming for this problem is established with the corresponding optimum algorithms proposed. Theoretically, it is provided that the existence of the best solution and the convergence of the optimum algorithms to optimum synthesis of spherical four-bar linkages. Finally, two numerical examples are given to show the feasibility and the validity for the approach.