Dynamics of a compliant transmission mechanism between parallel rotational axes

Compliant mechanisms have been applied successfully in many quasi-static applications. However, the dynamics of these mechanisms remain largely unexplored. In particular, dynamic problems hinder the implementation of compliant mechanisms in the field of power transmission systems. To realize this, here we present theoretical and experimental dynamics of a statically balanced compliant rotational power transmission mechanism, designed based on kinematics of the Oldham coupling. A fast and flexible generic model is proposed based on multi-body dynamics, which facilitates the design and implementation of this compliant transmission couplings in dynamic applications. In order to make the model applicable for the whole design family, the compliant embodiment is parametrized using a minimum set of design parameters. Furthermore, a case study is performed on an existing design and the method is validated experimentally. Predictions can be given of (i) the maximum attainable velocity before instability due to centrifugal forces, (ii) the lower resonance modes, and (iii) the characteristics of the resulting velocity transmission error. The proposed methodology is not only applicable to the compliant transmission couplings between parallel rotational axes but furthermore provides opportunities for the modeling of other compliant mechanisms applied in dynamic environments.