A general formulation for the tolerance analysis of dynamic equilibria in multibody systems having prescribed rotational motion is developed. In a state of dynamic equilibrium, a subset of generalized coordinates assume constant values, while the remaining coordinates vary and respond in time. Applications in which multibody systems exhibit dynamic equilibria include robots, spacecraft, propulsion and power generation systems, and some sensor devices. In the derived approach, manufacturing tolerances are mathematically modeled by probabilistic and statistical variables, through an analytical approach and through Monte Carlo simulation. An efficient computational method based upon direct differentiation is developed to calculate the first order sensitivity of the equilibria with respect to the design and manufacturing variables. To verify the accuracy and effectiveness of the present method, the present analytical method and the companion Monte Carlo approach are applied in examples to a rotating pendulum, a mechanical speed governor, and a model of a rate gyroscope sensor.
