Virtual link-lengths approximating method for forward kinematics of multiple motion-coupled linkage mechanism

The forward kinematics of one kind of multiple motion-coupled linkages mechanisms were investigated, which were applied to the finger of one kind of under-actuated hand, when the finger was not touching any objects. By setting virtual link-lengths for multiple motion-coupled linkages, a numerical approximating method to solve the linkages forward kinematics was advanced. The objective was to improve the iterative speed slowed by the motion-couple of multiple linkages. In this method, these virtual link-lengths were used as several new variables in Newton Iteration to reduce the amount of derivation and computation for each differential iterative step and then the entire computing time. The operating speed had an obviously improvement in a numerical example.