Dynamic Modeling And Characteristic Analysis Of Beams With Inflection Points In Compliant Mechanisms

Compliant mechanism can use the deformation of flexible components to accomplish the transmission of motion and force.Compared with the conventional rigid body mechanism,compliant mechanism has many advantages such as freeto-assembly,simplifying the manufacturing process,reducing friction and wear,etc.As a result,compliant mechanism has received deep attention in the past decades particularly in the field of micro-electromechanical systems(MEMS)and optical institutions.Though a great deal of research publications have been reported on various areas of compliant mechanisms,most of these papers are focused on the kinematics analysis or topology optimization design of compliant mechanisms and few has reported advances on the dynamic issues,particularly,the dynamics regarding the flexible beams featuring with inflection points.Motivated by these,in this paper,two pseudo-rigid body dynamics models of four degrees of freedom and a pseudo-rigid body dynamics model of five degrees of freedom are established for the flexible beams with inflection points,and dynamic characteristics of the three models are analyzed and compared.Then the dynamic characteristics of the parallel guide mechanism are analyzed by the pseudo-rigid body dynamic model of five degrees of freedom.Firstly,the RRHR pseudo-rigid body dynamic model with four degree-of-freedom of the compliant beam is proposed,where " R " denotes a rotation pair with torsion spring and " H " denotes a rotation pair without torsion spring to simulate the inflection point of the flexural beam.For the compliant beam with inflection point,the RRHR dynamic model is established,and the kinetic energy and potential energy is obtained based on the new model.The dynamic equation is derived applying the Lagrange equation and the dynamic response curves have been obtained using MATLAB software,and the dynamic characteristics of the model are analyzed.The results show that the pseudo-rigid-body dynamic model not only reflects the wide range of oscillations as a whole,but also reflects the large deformation at the inflection point of the flexural beam.Secondly,for compliant beam with a large moment load,the RHRR pseudo-rigid-body dynamic model is developed further.The dynamic equation is derived applying the Lagrange equation and the dynamic response curves have been obtained.Compared with the results of ADAMS software simulation,the maximum amplitude,minimum amplitude,maximum and minimum amplitude difference and mean square error of the four corner curves are calculated respectively,As well as the four joint angle errors under the same position.The results show the validity of the theoretical calculation and the validity of the pseudo-rigid body dynamic model.Then,in order to be able to adapt to the larger range of load,RRHRR pseudo-rigid-body dynamic model with load independence is established and the dynamic response is studied.Comparing RRHRR dynamic model with RRHR dynamics model and RHRR dynamics model from two aspects of dynamic equation and dynamic characteristics,the results show that RRHRR dynamic model has higher superiority.In order to verify the validity of the model,the dynamic modeling and characteristic analysis of the parallel guided compliant mechanism is carried out on the basis of the RRHRR dynamic model,and the displacement of the horizontal link is analyzed.Finally,the dynamic characteristics of the parallel-oriented compliant mechanism are studied by using the RRHRR pseudo-rigid body dynamics model,and the displacement,velocity and acceleration of the horizontal link are analyzed to verify the effectiveness of the model.