The Jacobian inverse technique is a simple yet effective way of implementing inverse kinematics. Let there be m variables that govern the forward-kinematics equation, i.e. the position function. These variables may be joint angles, lengths, or other arbitrary real values. If, for example, the IK system lives in a 3-dimensional space, the position function can be viewed as a mapping p ( x ) : R m → → R 3 . Let p 0 = p ( x 0 ) give the initial position of the system, and