Extended Dynamics of the Remarkable Dynabee:
The gyroscopic wrist exercising device originally known as the Dynabee[i], also called the Force Ball, or the Roller Ball, utilizes a unique mechanism to accelerate an enclosed, roughly spherical rotor to high rotation rates – each end of the rotor’s axle slides while rolling along opposing insides of an enclosed track (Fig.1) , accelerated by the friction torques supplied at these contacts.[ii] Dr. Ojakangas has studied this amazing device for several years, and has recently (October, 2020) submitted an extensive new work describing the dynamics of the dynabee for publication in the American Journal of Physics. Unlike previous works in the literature, this paper includes the critically important effects of gravity and sliding friction on the motion of the rotor. Interestingly, an important angle describing the orientation of the axle relative to the housing behaves as a damped pendulum, and is closely related, mathematically, to the physics required to explain the synchronous rotation states of nearly all moons in the solar system.
[i] Mishler, A. L., 1973, ‘‘Gyroscopic Device,’’ U.S. Patent 3726146.
[ii] In theoretical mechanics, this is known as a nonholonomic constraint. cf. Lanczos, C, 1970, The Variational Principles of Mechanics, University of Toronto press, Toronto, Canada.
click here to download PDF of preprint: The Extended Dynamics of the Remarkable Dynabee
In the last few years, armed with the department’s 3D printer and various electronic components, Dr. Ojakangas has made many devices based on the principle of the dynabee. On the left is a slow-motion video of one such device, fitted with measuring tools for analysis of the motion. Dr. Ojakangas has chosen to call this a hurricane ball, because the acceleration of the rotor is caused by the Coriolis force, which also drives hurricanes and typhoons. Shadows from a vertical light source on the small dial indicate the orientation of the housing, while the angular position of the axle relative to the housing can be read from the large circular scale. Students Jaxon Adams, Jose Alcantara, and Holly Harrison worked hard to digitize data from such videos, in order to compare motion with theory in the work described above. The hurricane ball prototype seen on the right, however, contains electronics allowing rapid automatic measurement and storage of kinematic data. It weighs 6.5lb and has reached rotation rates of 26 revs/sec, giving it a kinetic energy similar to a bowling ball moving at 40mph. It contains a Teensy microprocessor, 9DOF MEMs motion measurement unit, and is fitted with three rows of 96 RGB independently addressable LEDs. The LEDs are to generate a Persistence of Vision display presenting exercise performance data and other visuals to the user.
The video on the left shows a hurricane ball designed for fun. It lights up in beautiful patterns that change as the rotor accelerates. On the right is an example of another (very different) human-powered gyroscopic device, for which Dr. Ojakangas has a patent pending.
Left: an early prototype of Dr. Ojakangas’ “hurricane ball” invention. This one is a bit like a dynabee turned inside out.
Right: A unique gyroscopic invention that generates different “Persistence of Vision” graphic displays as an enclosed rotor reaches various speeds of rotation. The toy generates different musical sequences as the speed increases. Patent pending.