The spinor linkage – a mechanical implementation of the plate trick

@article{Holroyd2022TheSL,
  title={The spinor linkage – a mechanical implementation of the plate trick},
  author={Alexander E. Holroyd},
  journal={Journal of Mathematics and the Arts},
  year={2022},
  volume={16},
  pages={133 - 161}
}
  • A. Holroyd
  • Published 4 July 2021
  • Engineering
  • Journal of Mathematics and the Arts
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… 
The art of illustrating mathematics
Edmund viscerally remembers, during his PhD, Simon Donaldson describing the hopf fibration, sketching it on the board and discussing it. Those words and images triggered something, and a fundamental

References

SHOWING 1-9 OF 9 REFERENCES
Understanding quaternions and the Dirac belt trick
The Dirac belt trick is often employed in physics classrooms to show that a 2π rotation is not topologically equivalent to the absence of rotation whereas a 4π rotation is, mirroring a key property
How Efficiently Can One Untangle a Double-Twist? Waving is Believing!
It has long been known to mathematicians and physicists that while a full rotation in three-dimensional Euclidean space causes tangling, two rotations can be untangled. Formally, an untangling is a
Spinors and space-time
In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant
On a String Problem of Dirac
Visualizing quaternions
This intermediate-level tutorial provides a comprehensive approach to the visualization of quaternions and their relationships to computer graphics and scientific visualization. The introduction
Apparatus for providing energy communicating between a moving and a stationary terminal. United States Patent US 3586413
  • 1971
Apparatus for providing energy communicating between a moving and a stationary terminal
  • United States Patent US 3586413
  • 1971
Belt trick
    Spinors and space-time: Volume 1
    • Two-spinor calculus and relativistic fields, volume 1. Cambridge University Press
    • 1984