"Möbius Kaleidocycles --- A New Family of Ring Mechanisms" by Dr. Johannes Schönke

A classical kaleidocycle is a ring made from six tetrahedra which are connected by hinges. This mechanism has fascinated engineers for many decades because of its intriguing cyclic motion based on a single internal degree of freedom preserving a threefold rotational symmetry. We will present work motivated by a deceptively simple question: Is it possible to make a kaleidocycle with a single degree of freedom with a number of tetrahedra different from six? We find that the answer to this question is yes and, moreover, that a mechanism of the desired type can be made with any number of tetrahedra. Our newly found objects can be viewed as closed twisted ribbons with a nonorientable topology equivalent to that of a 3-pi Möbius band. For this reason, we call them Möbius Kaleidocycles. Besides many mathematical properties and questions, we will also discuss interesting mechanical and energetic features of these mechanisms.