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

Alexander E. Holroyd

Home/Archive/arXiv

arXiv · 2107.01681

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

Alexander E. Holroyd

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

physics.pop-ph physics.ed-ph

Keep this discovery

BibTeX RIS

Alexander E. Holroyd. 2021-07-04. The spinor linkage -- a mechanical implementation of the plate trick. https://arxiv.org/abs/2107.01681

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Epistemic Risk of the 31st Spore: If Planets Aren't Fine Tuned, We're Doing Life Detection Wrong

Exploration of planetary bodies within our solar system will be essential for understanding the origin of life on Earth and the distribution of life in the universe. Planetary protection policy is concerned with balancing this desire for exploration against the risks of contaminating alien planets with Earth life, and contaminating Earth with alien life. However, at present, we have no fundamental scientific understanding of life's emergence or its nature beyond Earth. Given this nearly complete ignorance about the possibility of alien life, or Earth life's capacity to expand beyond our planet, it is difficult to reason about the real risks of space exploration. Here we contend that contemporary understandings of the risks of forward contamination are based on arguments which inconsistently apply our incomplete knowledge to the problem. We reason that a more assertive posture towards space exploration, focused on determining whether other planets in the solar system are inhabited, is warranted and explain why such a posture may not increase the epistemic risks of planetary contamination. Finally, we explore the consequences of our arguments for planetary protection protocols, and life detection efforts.

physics.pop-ph↗

arXiv2026

Project Setu: 3D Multi-Physics Design and Scaled Structural Analysis for a Relativistic Lightsail Architecture

Deep-space exploration beyond the solar system requires eliminating chemical propellant mass penalties to achieve relativistic flight velocities (0.166c at 180 s, reaching the mission target of 0.20c at 227 s). This study presents a 3D multi-physics numerical framework for a 4.0-meter circular lightsail propelled by a 100 GW ground laser array, coupling 3D Maxwell FDTD wave optics, non-linear membrane mechanics, and Stefan-Boltzmann thermal radiation in ANSYS Mechanical APDL and Ansys Lumerical. A four-level grid convergence study establishes numerical independence with an ASME GCI_21 of 0.13%, resolving peak membrane stresses of 530.88 MPa with a 3.77x safety factor against stoichiometric Si3N4 tensile failure. With optical absorption constrained to 10 ppm (A = 1.0 x 10^-5), the steady-state core temperature stabilizes at 923.02 K (0.44% deviation from radiation theory), maintaining a +1,247 K margin below sublimation, while fundamental drumhead modal resonance (7.92 Hz) provides a 7.92x safety buffer against laser jitter. The electrodynamic radiation pressure formulation is cross-verified against published flight telemetry from JAXA IKAROS and NASA LightSail 2 within 0.12% and 2.13%, confirming classical momentum transfer modeling across solar and beamed propulsion regimes.

physics.pop-ph↗

arXiv2026

"It's getting away from us!" - Black Hole Horizons and Relative Speed

Black holes hold considerable fascination for the general public and students alike, and are commonly included in general-science courses on astronomy or modern physics. But teaching about the basics of black holes poses a considerable challenge: Any rigorous description requires concepts and techniques from general relativity, Einstein's theory of geometry and gravitation. And any half-way rigorous introduction to that theory, including the required mathematical tools, is significantly beyond the level of general-science courses. Inevitably, accounts of relativistic physics at the introductory undergraduate level make use of analogies, approximations and simplified models to teach about topics like black holes, gravitational waves, gravitational lensing, or cosmology. The purpose of this article is to given an account of one particular set of analogies for teaching about black holes, all of which are based on modelling the motions of observers in the vicinity of the black hole and rely on the concept of (relative) speed to describe properties of the black hole. While most elements of what I am about to describe can be found in the existing literature, I am not aware of any text that attempts to pull them together into a unified picture at a suitable level of presentation for undergraduate-level teaching; that is the goal of the present text.

physics.pop-ph↗