Parameter Optimization Of Pseudo-rigid-body Model Based On Strain Energy Matching

In a compliant mechanism,the motion,force,and energy transfer and conversion of the mechanism are primarily achieved by deformation of the flexible members of the mechanism.Compared with the rigid mechanism realized by the traditional sports pair,the compliant mechanism has great advantages in both performance improvement and cost reduction.However,the geometric nonlinearity caused by the large deformation of the flexible member not only complicates the analysis and design of the compliant mechanism,but also affects the wide application of the compliant mechanism.Therefore,research on the compliant mechanism is necessary.The purpose of the PRBM(Pseudo-Rigid-Body Model)is to provide a simple method for analyzing nonlinear large deformation systems,so that the theoretical method of the rigid mechanism can be used to analyze the compliance mechanism.At present,the parameters of PRBM are generally selected by parameter approximation method,and the error is relatively large.This paper proposes a parameter optimization design method for PRBM based on strain energy matching.The main accomplishments are the following three aspects:(1)Based on the existing 2R PRBM,the 2R-1P PRBM of fixed guide beam is proposed.The geometric relationship analysis and mechanical relationship analysis are carried out on the model,and the force balance equation is listed.The model parameters,namely the characteristic radius coefficient and the torsion spring constant,are optimized by an optimization algorithm based on strain energy matching.The optimized model is used to analyze the internal and external LET,which is simplified into a fixed-oriented 2R-1P PRBM.The relationship between force and displacement is calculated,and the internal and external LET are modeled and analyzed in ANSYS software.The error of the two is analyzed to prove the accuracy of the optimization model based on strain energy matching.Further attempts to apply this method to the parameter optimization of other pseudo rigid body models are presented.(2)Analyze the existing optimization method of 3R PRBM.Based on this,the strain energy optimization method is used to optimize the 3R PRBM.Compared with the existing kinematically optimized model,the tip locus and the tip slope angel error are analyzed.It is found that the strain energy optimized 3R PRBM can accurately simulate the deformationof the compliant beam.Applying it to the example calculation and analysis,the 3R PRBM of the partially compliant four-bar mechanism is established,and the deformation is calculated by the parameters of strain energy optimization.The results are in good agreement with the actual deformation,and the strain energy optimization is also verified.(3)Based on the static analysis,consider the dynamic characteristics of the PRBM,analyze the dynamic equations of the three pseudo-rigid models of the 1R,2R,3R PRBM,calculate the kinetic energy and deformation potential energy,and substitute In the Lagrangian equation,the dynamic equations are derived and the dynamic response curves of three pseudo-rigid models are drawn.The 3R PRBM can more accurately reflect the dynamic characteristics of the compliant mechanism,and it is applied to the parallel guiding mechanism to establish The 3R PRBM of the parallel guiding mechanism is analyzed for its dynamic characteristics.The strain-energy optimization method is used to optimize the 2R-1P model and 3R PRBM of the fixed guide beam,and the force-displacement analysis is performed on the model with the strain energy optimization,and the two pseudo-rigid bodies are applied in some compliance mechanisms.The model is calculated by example,which verifies the feasibility and accuracy of strain energy optimization.