Two generalized models for planar compliant mechanisms based on tree structure method

Compliant mechanisms depend on elastic deformations to provide smooth and precise motions. It is essential to develop an accurate model to quantify the deformation for kinetic analysis and parameter optimization. This paper presents a tree structure method to characterize the structure of the mechanism, based on which, two generalized models are proposed for planar compliant mechanisms. Linear Tree Model aims at constructing the flexibility matrix of the whole mechanism. Not only the deformations of the mechanism can be calculated, but also the unknown forces/moments can be obtained through inverse operation. Beam Constraint Tree Model focuses on the precise load condition and deformed shape of each beam, and a nonlinear model, which considers load-stiffening, kinematic and elastokinematic effects, is adopted for the beam governing equation. Beam Constraint Tree Model is computed on the basis of Linear Tree Model, and can achieve higher accuracy. Simulations have been done to show the accuracy of the two models on different load conditions, and experiments with a compliant amplifier have been performed to verify the effectiveness of the proposed models. Furthermore, some examples are presented to show the applications of the proposed model. Both models are parametric, generalized and easy for computation, so they are practical for compliant mechanism design.