Motion-dependent modal analysis of flexible-joint mechanisms

Conventional modal analysis of flexible-joint mechanisms often overlooks motion-induced inertial and Coriolis effects. These effects inherently render the system non-self-adjoint, resulting in dynamic characteristics that differ from those of stationary states. To address this, motion-dependent modal analysis is proposed for flexible-joint mechanisms, where modal parameters are parameterized instantaneously by the states of rigid-body motion. First, a generalized dynamic equation of 2n dimensions is formulated, which incorporates both motor dynamics and feedforward-feedback control. Then, the vibration model is derived through Taylor expansion around arbitrary dynamic equilibrium states. Based on this motion-dependent vibration model with time-varying matrices, state space formulations are developed to define instantaneous modal parameters under arbitrary motion conditions. Subsequently, the influence of rigid-body motion on the vibrational characteristics is analyzed and verified with a 2-DOF mechanism. Finally, the model is applied to calculate the instantaneous modal parameters of a 6-DOF mechanism, verifying that the effect of rigid–flexible coupling is non-negligible under high-speed motion. The results show that the first-order frequency of the system can be reduced by 15.4% under high-speed motion, and Coriolis effects may induce instantaneous negative damping.