## The Hui Machine

Oliver Knill, 8/08/2010

 This summer (2010), I played with a Hui machine at my parents house. It is fascinating. The very simple device is also known as the gee-haw whammy diddle,the mystery stick, hooey stick, the idiot stick, the magic windmill, the notched stick, the truth stick, or the stick-propeller device. Its physics is interesting. Rubbing a round wooden stick together produces a vibration whose elliptical excitation is transformed into rotational motion of a propeller. All the material as well as the rubbing appears to be symmetrical. Nevertheless, the user can change the direction of the wheel. Still today, the best explanations are from the 1980'ies. There are still many questions to be answered about the device. It is a pedagogical tool to illustrate what an experiment is, to see the process of hypothesis building and then to build an explanation. When does one really understand it? I add this to the pedagogy pages because concrete experiments and explanations illustrate a lot about what science is. Simple tools, which can be played by kids (and adults) are especially attractive As a first year mathematics student at the ETH, I had a nice general physics exposure. The lectures would always feature experiments. At one point, the Tippe top came up. (see Pauli and Bohr playing with such a top. Source: Nahin's book Mrs Perkins's Electric Quilt). Our physics professor Hans Joerg Leisi mentioned that the details of the mechanics of this device is not completely known which made me curious about it. Candel Water experiments are other examples for entertainment.

## Experiments

 The rotational motion does not depend on the position of the fingers which hold the device. The geometry of the device seems irrelevant. Not the frequency of the excitation nor the vigor and strength with which it is done matters. The position of an additional finger moving with the stick and damping the excitation is important. There is a side on which the propeller turns counter clockwise, and a side where it is clockwise. The distance of the damping finger to the excitation place matters.

## Explanation

The vibration of the solid stick is complicated. What kind of linear motion can happen?
• vibrations in the spacial directions
• bending vibrations
• torsion vibrations
The most convincing explanation tells that the stick starts to vibrate in a rotational manner. The friction of the nail with the wooden propeller will translate this rotational vibration into rotational motion. At first one might think that the Hui machine is impossible and that similarly than for the Feynmans Brownian ratchet it would violate the second law of thermodynamics, preventing vibrational motion energy to be transformed back into mechanical energy. Unlike Feynman's ratchet, the Hui machine works. Can one find an application of the device? Is there a practical way to gain vibrational energy back from vibrational motion?

## Real simulation

The ultimate explanation comes from a kinetic verification, in which the device is built with finitely many atoms and where macroscopic rotational motion should emerge from excitation triggered right. I did not yet have time to build it. Here is only an experiment rendered in Povray while heading back from vacation to the US. I still have to built this up within povray.