A stiffness modeling approach for multi-leaf spring mechanism supporting coupling error analysis of nano-stages

In the present paper, we take the multi-leaf spring mechanism as a particular element to develop a modeling approach for the stiffness by considering the coupling effects of the cross axis force. With this, a more accurate model of the multi-leaf spring based nano-stage is derived by incorporating the effect of cross axis input force, which can better predict the coupling error. The new analytical model indicates that the total axial stiffness is an inverse-quadratic function of the cross axis input load instead of a constant value, which can be used to analyze the cross axis coupling error of multi-leaf spring based nano-stages. The proposed analysis method is then verified by FEA and experiments, where excellent results are demonstrated in predicting the cross axis coupling effects of nano-stages such as stiffness variation and coupling error. The proposed approach offers a new look into the design and manipulation of multileaf spring based nano-stages.

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