Mechanics of the serial kinematics machine can be represented as a multi-DOF kinematic chain combining some elastically connected links, and each link has 1-DOF in its nominal motion (translation or rotation) relative to the neighbor one. In this chapter, only the compliance of the most compliant elements of the mechanical systems – actuated joints along the directions of actuated motion – is taken into account. The purpose is to synthesize the compliance matrix connecting the external load with small displacements of the end-effector (EE). This process is started from formulation of the manipulator Jacobian matrix integrating geometric and kinematic data...