# Formal Design — Johannes Schönke and Michael Grunwald and Eliot Fried

We make moving objects that challenge human intuition. While everyone loves the continuous, unpredictable, natural flow of clouds, camp fires, or waves, our perception of manmade mechanisms is another story. It is easily recognized that the path of a child on a swing describes a circular arc, but the possible motions of a robot arm go way beyond the spatial imagination of most people. Our work illustrates kinematics, or the geometry of motion. By defining simple geometric rules between identical elements, we create objects which may undergo continuous and intriguing changes of configuration. Contemplating these motions illuminates that the underlying principles are the same as for clouds, camp fires, or waves.

The "Nine-Hinged Möbius Kaleidocycle I" (MK9-I) is a dynamic, self-propelled sculpture made from a nine-hinged linkage. The sculpture performs an everting motion, turning continuously inside out. Differently colored faces are shown in a periodic sequence of white, red, and black. "Möbius Kaleidocycles" were discovered last year and paper models were constructed at Bridges 2018. The sculpture, exhibited here for the first time, embodies many intriguing mathematical concepts. It is a singular configuration that, due to geometric constraints, can move in only one specific way. Its triangular faces form a nonorientable (Möbius) topology and it further represents a discrete precursor of a closed band with constant twist.