Learning control provides an integrated approach for handling inverse kinematics and inverse dynamics of mechanisms, in the presence of parametric errors in system modeling. This technique is applied to reduce residual vibrations at the bonding cap of an electromechanical bonding machine for integrated circuits (ICs); a process of electrically linking silicon chips to the leads. The bonding cap trajectory for the bonding motion is actuated by high-speed cams driven by electric motors. The primary causes of residual vibrations are due to errors in the design model of the nonlinear electromechanical system, in camshaft speed control, as well as, in cam profile fabrication. This article demonstrates the capability of learning control to reduce the residual vibrations in such machines, by compensating for these sources of errors.