Multi-degree Of Freedom Pseudo-rigid-body Model Of Compliant Mechanisms With Axial Deformation

The compliant mechanism is a new kind of mechanism which can transform force, movement and energy through the elastic deformation of its member. Compared with conventional rigid-body mechanisms, compliant mechanisms have many advantages such as reduced assembly time and friction of kinematic pairs. Therefore, compliant mechanisms became the new hot research fields in worldwide mechanism.Compliant mechanisms have particular function and broad prospect of application. compliant links often under large deflections which introduce geometry nonlinearities make the analysis of compliant mechanisms much too complex. The Pseudo-Rigid-Body Model(PRBM) is proposed by Howell, it makes nonlinear problem of compliant mechanism transformed into linear problem which can be solved by equivalent rigid body, laid the foundation for the research of compliant mechanism. 2R and PR pseudo-rigid-body model is proposed by later scholars, but the DOF(degrees of freedom) of this pseudo-rigid-body models is insufficient, lead to the simulation accuracy and scope is limited, limiting its further application. Focused on the deficiency of the PRBMs existed, a new multi-DOF PRBM is proposed by increasing the DOF of the PRBM. Considering various complex loads condition, their corresponding PRBM is established for the related research. The main content is summarized as follows:Firstly, aimed at compliant link with end torque load, the PRR PRBM of large deformation mechanism is established. Applying torque load at the end of the model, the three dimensional search process for the optimal of characteristic radius factors is presented by using parametric approximation method, and analyzing proportion of axial movement caused by prismatic pair of PRBM in the whole axial movement. Studies have shown that the prismatic pair almost doesn’t produce axial movement, in this case PRR PRBM same the 2R PRBM.Secondly, aimed at compliant link with end force load, the PRR PRBM of large deformation mechanism is presented. Through the positive kinematics obtain numerical expression of model characteristic parameters, using parametric approximation method to establish the program block diagram, using the method of linear regression to fit the stiffness coefficient of the model. According to numerical analysis software, analyzing the tip track character of the PRBM existed and compliant link, show that simulation precision of the PRR PRBM has been further improved.Thirdly, aimed at compliant link with end combined load, the PRR PRBM of large deformation mechanism is established. Dealing with the load ratio with extreme ways, mathematical expressions of PRBM is derived under two extreme load form. The characteristic parameters of the model are obtained by establishing three dimensional search procedures and linear fitting method. Compared with others PRBM, the result shows superiority of the PRR model with combined load.Finally, PRR PRBMs subject to different tip loads are applied to planar compliant mechanisms, the PRR PRBM of compliant four-bar linkage and compliant crank slider mechanism are established. Through analysis the relationship between crank link and displacement of slider, the result shows the validity of the pseudo-rigid-body model in analyzing compliant mechanism.