Modeling and Analysis of Beam Flexure Based Double Parallel Guiding Mechanisms: A Modified Pseudo-Rigid-Body Approach

In the present paper, we take the complaint double parallel guiding mechanism as a particular case study to investigate a modified pseudo-rigid-body (MPRB) modeling approach for beam flexure based mechanisms by considering the nonlinear effects of the center-shift and the load-stiffening. In particular, through incorporating the elastic stretch of the beam flexure into the linear Bernoulli-Euler equation, a more accurate model of the beam flexure is derived. Accordingly an MPRB model for a beam flexure is established, which consists of two rigid links joined at a revolute joint and a torsional spring along the beam. Different from traditional PRB model, the location of the torsion spring is not only determined by the characteristic radius factor, but also a purely elastic stretch under the action of the axial force. Meanwhile, both the characteristic radius factor and the equivalent stiffness of the beam flexure are no longer constant values, but affected by the applied general tip load, especially the axial force. Based on the analysis results of a beam flexure, we obtain a more accurate model of the double parallel guiding mechanisms, which is further verified by the finite element analysis (FEA) results. The proposed MPRB model provides a more parametric method to predict the performance characteristics such as deformation capability, stiffness variation, as well as error motions of the beam flexure based complaint mechanisms, and offers a new look into the design and optimization of beam-based compliant mechanisms.