Multibody systems that undergo a prescribed rotational motion arise in such engineered systems as robots, spacecraft, propulsion and power generation systems, and certain sensors and actuators. The sensitivity of the system's response to changes in the design variables is important for optimization and trade-off studies, as well as for understanding the implications of manufacturing tolerances. A general formulation is developed for analytically calculating the first-order design sensitivities of coordinate values for a multibody system's dynamic equilibrium state during prescribed rotational motions. The method is based upon the use of relative coordinates, and a velocity transformation technique, and it is applicable to multibody systems having open or closed loop configurations. To illustrate effectiveness, accuracy, and computational efficiency, the present method is applied in three examples, and the sensitivities obtained analytically are compared with those obtained by the standard finite difference method. The finite difference approach is particularly sensitive to the choice of step size near a critical speed, and its implementation is generally more costly that the present method. In particular, there is a zero-sensitivity point at which the equilibrium configuration is insensitive to small perturbations in the design parameter's value. That condition can be a useful design point to the extent that manufacturing tolerance and variation in design parameter's values have no effect on dynamic equilibrium positions.
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