Error analysis of stiffness in double parallel four-bar mechanism

Traditionally, based on the pseudo rigid body model method, the ideal stiffness of double parallel four-bar mechanism is obtained by virtual work principle while support arm bar is regard as a rigid rod. However, a terrible error between ideal and real stiffness will be caused in practice as a result of the bending deformation of support arm bar. Therefore, it is urgent to analyze the error of stiffness in double parallel four-bar mechanism and to explore the condition in which the support arm bar could be equivalent to rigid rod. In the paper, an accurate expression of stiffness in the double parallel four-bar mechanism is derived by integral method while the support arm bar is studied as a variable cross section beam through force analysis and deformation analysis. The error between stiffness derived from virtual work principle and integral method is obtained, and whose changing trend with the structural parameters of the right-angle flexure hinge and the support arm bar is analyzed. The result demonstrates that the error is less than 1% when the thickness ratio is larger than 6 and the length ratio is between 6 and 25, that is, the support arm bar can be equivalent to rigid rod, and whose bend deformation can be neglected.