Mechanical systems that undergo prescribed rotational motions arise in such engineered systems as robots, spacecraft, propulsion and power generation systems, and certain sensors and actuators. In order to avoid the resonance or the critical speed of the system and to keep the desired dynamic equilibrium state in the mechanical system undergoing rotational motions, the system’s design parameter values or driving angular speed should be tuned. In this work, a general formulation for the inverse dynamic equilibrium analysis is developed to directly calculate the driving angular speed or design parameter values which satisfy the condition of the desired dynamic equilibrium positions. The method is based upon the use of relative coordinates and a velocity transformation technique, and it is applicable to multibody systems having either open or closed loop configurations. To illustrate the method’s effectiveness, accuracy, and computational efficiency, two numerical examples are considered, and the results obtained analytically are compared with those obtained by using a commercial program’s transient analysis. In some cases, the equilibrium configuration is shown to have an operating condition for which the response has nearly zero standard deviations for small perturbations in a design parameter’s value. In that case, to verify the method’s effectiveness and usefulness, Monte-Carlo simulation results are shown.