Kaleidoscopic Kaleidocycle Tessellations

A kaleidocycle is a linkage mechanism in which hinges in a skew position are connected in the shape of a ring. Its characteristic feature is a motion that keeps turning over, similar to a dolphin’s bubble ring or a ring of cigarette smoke. This paper proposes a representation method for describing the structure and motion of a kaleidocycle using a circle and two mirrors. Additionally, several linkage mechanisms that connect multiple kaleidocycles by the planar, spherical and space tessellation of circles and mirrors are introduced as applications of this method.