Bifurcation variation of a novel line-symmetric double-centered 6R metamorphic mechanism based on ellipses

This paper proposed a line-symmetric double-centered 6R metamorphic mechanism with bifurcation properties. The mechanism is constructed based on elliptical geometric properties, which is a comprehensive design method for constructing novel metamorphic mechanisms through intuitive geometric figures. Firstly, the geometric constraints of the 6R metamorphic mechanism are revealed, and the parameter constraints and closed-loop kinematic equations of the 6R metamorphic mechanism are deduced. Through the analysis of mechanism geometric constraints, four motion branches of the 6R metamorphic mechanism are obtained: collinear deployable motion branch MB1, spherical 4R motion branch MB2, spherical 4R motion branch MB3, and line-symmetrical Bricard motion branch MB4. Meanwhile, according to the screw theory, the analytical expressions and mobility of the constraint-screw systems under different motion branches are deduced. This led to the identification of the constraint and motion branch variations of the 6R metamorphic mechanism. Finally, the four serial link 4R singular configurations of the 6R metamorphic mechanism are specially studied, and the characteristics of the mutual reconfiguration of these four singular configurations are revealed.