Buckling analysis of a 2-DOF parallel mechanism composed of right-angle-notch flexure universal hinges

With respect to the great ratio of the length to the thickness of right-angle-notch flexure hinge, the necessity of the study on the buckling characteristics of the right-angle-notch flexure universal hinges and the compliant parallel mechanism composed of them, was presented. The mathematical model, for calculating the buckling critical force of the right-angle-notch flexure universal hinge, was established on the approximate differential equation of deflection curve of the material bending theory. With this, the conception of equivalent section inertial moment was put forward. Finally, based on the former theoretical research on the compliant parallel multi-bar mechanism composed of the right-angle-notch flexure hinges, the mathematical formula for calculating the buckling critical force of the compliant parallel mechanism was proposed. The buckling critical force of the sample has been measured by experiment and by FEA (finite element analysis) with the commercial software ANSYS 8.0. The values from the mathematical model, from experiment and from FEA separately all met well, which indicated the correctness of the mathematical model. In summary, the mathematical model proposed above can be used in the optimization of the design of the right-angle-notch flexure hinge and it's compliant parallel mechanism in buckling characteristic.