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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 needed for transformation of the machine joint rates into the angular and linear velocity of the EE [1-4].