M`\ddot{o}`bius Kaleidocycles:
A New Class of Everting Ring Linkages

Eliot Fried

Mathematics, Mechanics, and Materials Unit

Okinawa Institute of Science and Technology Graduate University

eliot.fried@oist.jp

    Many mechanical devices from scissors to robotic arms are characterizable as 'linkages' or sets of rigid links connected by moving joints. Known linkages displaying a single degree-of-freedom, which facilitates control, have hitherto consisted of six or fewer links. In this talk, we will introduce a new class of one-degree-of-freedom ring linkages: 'M`\ddot{o}`bius kaleidocycles'. These objects consist of seven or more identical hinge-joined links and might thus serve as building blocks in positioning, extrusion, and pultrusion systems, to instance a few among many promising applications in engineering, architecture, robotics, and chemistry. They also pose a myriad of intriguing fundamental geometrical and topological questions, some of which will be touched upon in this talk. This is joint work with postdoctoral scholar Johannes Sch`\ddot{o}`nke.

Keyword: spatial mechanisms, nonorientability, single degree-of-freedom