Kinematic Modeling of a Rigid-flexible coupling Flexure-jointed Linkage with Two Closed Loops

Combination flexible beams (CFB) can provide diverse mechanical behaviors for designing flexure-jointed linkages (FJLs). However, the kinematic analysis of FJLs with CFBs is more complicated due to the coupling between the large deflection of CFBs and the displacement of rigid links. Therefore, taking an FJL with two loops as an example, this paper deals with the kinematic modeling of rigid-flexible coupling FJLs to provide fundamental guidelines for their designs. Based on force analysis, the FJL is divided into two serial chains. Then, the kinematics of this FJL is derived by the deflection analysis of two chains utilizing the elliptic integral solution. The accuracy of the derived model is verified by the numerical comparison study.