A Single-Loop 8R Linkage with Plane-Symmetry and Bifurcation Property

This paper for the first time presents a novel single-loop 8R linkage with plane-symmetry and bifurcation property. By integrating two equilateral Bennett loops, structure and geometric parameters of the proposed 8R linkage are introduced. In the light of screw theory, three types of configurations of this 8R linkage are analyzed carefully in accordance with the geometric characteristics of joint axes. The bifurcation associated with diverse transitory positions is consequently identified based on the constraint singularity. Meanwhile, this analysis simplifies the independent geometric constraint equations in view of the plane-symmetry. Further, with the evolved regular octahedron and tetragonal trapezohedron, a particular 8R linkage with specific parameters sets up the interrelationship between mechanisms and polyhedra, and exhibits geometric symmetry and artistic beauty. Also, through properly designing the parameters, the kaleidocycle motion of this linkage are revealed and the foldability is verified in virtue of the alternative form of Bennett linkage.

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