Dynamic Modeling And Performance Analysis Of Compliant Mechanism Based On Transfer Matrix Method For Multibody System

Compliant mechanism is a new type of mechanism which uses the elastic deformation of the hinge to transfer the motion and force.It has high resolution and precision,and is mainly used in precision engineering,robotics,intelligent structures and other cutting-edge fields.At present,most scholars focus on the kinematics,statics and structural design of compliant mechanisms,but and there are few studies on the dynamics of compliant mechanisms.In this paper,the transfer matrix method for multibody systems(MSTMM)is used to establish the dynamic model of the compliant mechanism and analyze its related performance.The main research contents are as follows:MSTMM is mainly used to study the dynamics of multi-rigid-flexible body system,which needs to divides the complex multi-body system into several characteristic elements.The mechanical transfer relationship between the two ends of the unit is expressed in transfer matrix,and the dynamic model of the whole system is obtained by combining the mechanical transfer relations of each element.The dynamic model of the whole system can be obtained by combining the mechanical transfer relations of each element.Based on the basic idea of MSTMM analyzing the dynamics of multi-rigid-flexible system,the compliant mechanism is regarded as a multi-body system composed of many characteristic elements such as flexible hinges and rigid bars.Flexure hinges can be divided into straight-beam flexible flexure hinge and arc-shaped flexible flexure hinge,which are equivalent to equal section and variable section massless flexure beam respectively,and the transfer matrices can be derived by applying the theory of mechanics of materials.Compared with the flexible element,the rigid element in the compliant mechanism has large rigidity and small deformation,which is equivalent to a vibrating rigid body.Based on the theory of theoretical mechanics,the transfer matrix of the rigid element with single-input single-output and the rigid element with multiple-input single-output in the compliant mechanism were derived respectively.The compliant branch chain is an indispensable part of the compliant mechanism.Different branch chains will form compliant mechanisms with different forms and functions.Branched chain is regarded as a simple compliant mechanism composed of several characteristic elements such as flexure hinges and members.According to the connection form of each element in the branch chain,the transfer equation of the compliant branch chain can be obtained by combining the transfer matrix and transfer equation of each element under the global coordinate.The transfer equation of the compliant branch chain is a complex matrix equation with the natural frequency as the unknown quantity.It is reduced to a relatively simple homogeneous equation group by using the boundary conditions.The natural frequency and mode shape of the compliant branch can be obtained by solving the unknown variables of the homogeneous equation group.In order to analyze the dynamic response of the compliant branch chain under external excitation,the external force is substituted into the transfer equation to obtain the dynamic response equation of the compliant branch chain.The dynamic response equation is a matrix equation whose unknown variable is excitation frequency,the simple harmonic displacement response of any point in the compliant branch chain can be solved by substituting the boundary condition into the dynamic response equation.Based on the above-mentioned ideas,the transfer equation and dynamic response equation of chain-type compliant branch chain,lever displacement amplification branch chain and bridge-type displacement amplification branch chain in the compliant mechanism were established by using MSTMM,and analyzed the relevant dynamic characteristics of the compliant branch with the aid of boundary conditions.It is verified that the model can accurately reflect the performance of the three kinds of flexible branch chains by comparison with the finite element simulation.The compliant parallel mechanism is a common compliant mechanism connected by multiple compliant branch chains and an output platform through a certain form.According to the basic idea analyzing the dynamics of compliant mechanisms by using MSTMM,the compliant parallel mechanism can be divided into compliant branch chain and moving platform unit,and the moving platform is regarded as a vibration rigid body with multiple inputs and single outputs.The transfer equation of the compliant parallel mechanism can be obtained by combining the transfer equation of the compliant,the transfer equation of branch chain as well as the displacement relationship of the moving platform between the input points,and the natural vibration characteristics of the compliant parallel mechanism can be solved with the help of boundary conditions.The dynamic response equation of the whole mechanism is obtained by adding the external force into the transfer equation of the compliant parallel mechanism,and the dynamic response of any point in the compliant parallel mechanism can be solved by using the boundary conditions.In the light of the above ideas,the dynamic models of compliant parallel mechanism based on chain compliant branch,bridge displacement amplification branch and lever displacement amplification branch were established,and the dynamic characteristics of three types of compliant parallel mechanism are analyzed by using boundary conditions.Compared with finite element simulation,it is verified that the established models can accurately reflect the dynamic performance of compliant parallel mechanisms.