Constraint and Dynamic Analysis of Compliant Mechanisms with a Flexible Multibody Modelling Approach

The models used in the conceptual phase of the mechatronic design should not be too complicated, yet they should capture the dominant system behaviour. Firstly, the awareness and possibly the avoidance of an overconstrained condition is important. Secondly, the models should reveal the system’s natural frequencies and mode shapes in a relevant frequency range. For the control system synthesis the low frequent behaviour up to the cross-over frequency needs to be known. Furthermore, the closed-loop system can be unstable due to parasitic modes at somewhat higher frequencies. In this chapter the applicability of a multibody modelling approach based on non-linear finite elements is demonstrated for the mechatronic design of a compliant six DOF manipulator. A kinematic analysis is applied to investigate the exact constrained design of the system. From dynamic models the natural frequencies and mode shapes are predicted and a state-space model is derived that describes the system’s input-output relations. The models have been verified with experimental identification and closed-loop motion experiments. The predicted lowest natural frequencies and closed-loop performance agree sufficiently well with the experimental data