The inverse kinematics problem for a serial-chain manipulator is to find the value of the joint positions given the position and orientation of the end-effector relative to the base and the values of all of the geometric link parameter. Once again, this is a simplified statement applying only to serial chains. A more general statement is: given the relative positions and orientations of two members of a mechanism, find the values of all of the joint positions. This amounts to finding all of the joint positions given the homogeneous transformation between the two members of interest