Abstract

Background: Rigidity is a crucial index for the flexible micro-motion mechanism design and research. Most of the researchers studied the correlated characteristics by a selected rigidity analysis method. The rigidity models based on Lagrange equation and work-energy theorem can both fulfill the requirements for common usage. Unfortunately, there is no sufficient contrastive analysis between the two broadly used methods and definite applicable fields for a given method, leading to an ambiguous selection for the rigidity analysis method.

Methods: Taking micro displacement amplifier module (MDAM) as example, the relationship of all components' elastic deformations is built up to obtain the accurate motion equation based on pseudo-rigid-body method. In view of energy conversion relationship, two kinds of rigidity model are established separately by Lagrange equation and work-energy theorem. Differences between the two methods are compared.

Results: The input displacement and the output displacement are non-linear for MDAM. The changing curves of needed input force according to the output displacement by work-energy theorem and Lagrange equation based methods are almost completely parallel to each other. But there still exist a certain difference, which becomes greater as the input displacement increases.

Conclusion: For MDAM, the theoretical rigidity modeling method based on Lagrange equation has taken the components' micro displacement into consideration and it has a higher precision compared with work-energy theorem method.

Keywords: Flexible mechanism, kinematics, lagrange equation, micro-motion, rigidity, work-energy theorem.