The spinor linkage -- a mechanical implementation of the plate trick

TL;DR

This paper introduces a novel mechanical linkage that demonstrates the plate trick, allowing continuous rotation without twist accumulation, using a sequence of rigid bodies and hinge joints controlled by a handle.

Contribution

The paper presents a new mechanical implementation of the plate trick using a linkage with a single degree of freedom and a mechanical control mechanism.

Findings

Successfully demonstrates the plate trick mechanically

Operates with a single degree of freedom

Controlled by a simple handle mechanism

Abstract

The plate trick or belt trick is a striking physical demonstration of properties of the double cover of the three-dimensional rotation group by the sphere of unit quaternions or spinors. The two ends of a flexible object are continuously rotated with respect to each other. Surprisingly, the object can be manipulated so as to avoid accumulating twists. We present a new mechanical linkage that implements this task. It consists of a sequence of rigid bodies connected by hinge joints, together with a purely mechanical control mechanism. It has one degree of freedom, and the motion is generated by simply turning a handle.