Flexible multibody modelling for the mechatronic design of compliant mechanisms

In high precision equipment the use of compliant mechanisms is favourable as elastic joints offer the advantages of low friction and no backlash. To satisfy exact constraint design the mechanism should have exactly the required degrees of freedom and constraints so that the system is kinematically and statically determinate. For this purpose we propose the following kinematic analysis using a flexible multibody modelling approach. In compliant mechanisms the system’s degrees of freedom are presented clearly from the analysis of a system in which the compliant part are free to deform while the support is considered rigid. If the Jacobian matrix associated with the dependent coordinates is not full column or row rank, the system is underconstraint or overconstraint. The rank of this matrix is calculated from a singular value decomposition. For an underconstraint system any motion in the mechanism that is not accounted for by the current set of degrees of freedom is visualised using data from the left singular matrix. For an overconstraint system a statically indeterminate stress distribution is derived from the right singular matrix and is used to visualise the overconstraints. In the next step of the mechatronic design the system’s closed-loop stability and performance are considered. Valuable insight is obtained from a dynamic analysis in which the non-linear models are linearised in selected configurations to derive natural frequencies and mode shapes.