Higher-order continuation method for the rigid-body kinematic design of compliant mechanisms
Résumé
Compliant mechanisms are of great interest in precision engineering. In this paper we propose a higher-order contin- uation method to help their rigid-body kinematic design. Higher-order continuation method leads to direct accurate plotting of the input-output relationship of any mechanism using only its geometrical closed-loop equations, i.e. without complex derivation of any analytical model. These plots, called bifurcation diagrams, reveal essential information as joint velocity profile and the presence of singular configurations. Moreover, the continuous and accurate computation of the mechanism configuration in the vicinity of singularities provides detailed information about the kinematic behavior of the mechanism in its extreme positions. For the design of compliant mechanisms, the designer can ad- vantageously use the bifurcation diagrams to first evaluate the relevance of the selected mechanism, then identify a working configuration in order to obtain adequate kinematic properties without the derivation of the inverse kinematic model (IKM) or the direct kinematic model (DKM). The method is exemplified with a 3 universal-joint and 3 spherical-joint mechanism (3–US) mechanism, the IKM and DKM of which cannot be derived analytically. The latter has a large workspace and special kinematic behaviors consisting of a screw-like motion and platform gyration, which have not been studied before and could lead to interesting novel devices.
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