Gyroscopic Precession In Motion Modelling Of Ball-Shaped Robots

Abstract In general, the curling stone is subject to mixed lubrication, resulting in the characteristic Stribeck -curve. As velocity increases, the friction force falls quadratically just to rise linearly yet almost flat after the minimum. In the case of a rotating curling stone this results in a torque. Due to isotropy , the lateral force arises as a delta of asymmetric friction forces opposite to the centripetal forces. \par This in turn allows a split friction model that splits up the quadratic curve into two rather constant values for the friction force on the advancing and the retreating side below a critical velocity difference of these sides: the flee force on the advancing side must not exceed the normal force of the retreating side. Only then a curl can happen. This explains why a stone curls towards the end of the throw. \par Following basic static considerations, the stone may theoretically rest on up to three points during a throw. Each single static case is investigated. These results are discussed with additional heuristic calculations that involve Scratch-Theory. Lastly, the influence of gyroscopic precession yields a graph that reflects established experimental observations: A desired flat curve within deviations ranging from 0.80 to 1.02 meter for up to 20 rotations just to rise linearly up to 2 meters for 80 rotations.

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Gyroscopic Precession

American Journal of Physics ◽

10.1119/1.1970998 ◽

1965 ◽

Vol 33 (10) ◽

pp. 847-847 ◽

Cited By ~ 5

Author(s):

J. L. Snider

Keyword(s):

Gyroscopic Precession

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A Three-Dimensional Diagram of Gyroscopic Precession

American Journal of Physics ◽

10.1119/1.1991480 ◽

1939 ◽

Vol 7 (5) ◽

pp. 342-345 ◽

Cited By ~ 1

Author(s):

Francis W. Sears

Keyword(s):

Three Dimensional ◽

Gyroscopic Precession

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Unicycle Robot Stabilized by the Effect of Gyroscopic Precession and Its Control Realization Based on Centrifugal Force Compensation

IEEE/ASME Transactions on Mechatronics ◽

10.1109/tmech.2016.2590020 ◽

2016 ◽

Vol 21 (6) ◽

pp. 2737-2745 ◽

Cited By ~ 11

Author(s):

Hongzhe Jin ◽

Tianlu Wang ◽

Fachuan Yu ◽

Yanhe Zhu ◽

Jie Zhao ◽

...

Keyword(s):

Centrifugal Force ◽

Gyroscopic Precession ◽

Force Compensation

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Analogies of Ocean/Atmosphere Rotating Fluid Dynamics with Gyroscopes: Teaching Opportunities

Bulletin of the American Meteorological Society ◽

10.1175/bams-d-12-00023.1 ◽

2013 ◽

Vol 94 (5) ◽

pp. 673-684 ◽

Cited By ~ 4

Author(s):

Thomas W. N. Haine ◽

Deepak A. Cherian

Keyword(s):

Fluid Dynamics ◽

Large Scale ◽

Rigid Bodies ◽

Adjustment Process ◽

Inertial Oscillation ◽

Rotating Fluids ◽

Gyroscopic Precession ◽

Rotating Shallow Water ◽

Potential Use

The dynamics of the rotating shallow-water (RSW) system include geostrophic f low and inertial oscillation. These classes of motion are ubiquitous in the ocean and atmosphere. They are often surprising to people at first because intuition about rotating f luids is uncommon, especially the counterintuitive effects of the Coriolis force. The gyroscope, or toy top, is a simple device whose dynamics are also surprising. It seems to defy gravity by not falling over, as long as it spins fast enough. The links and similarities between rotating rigid bodies, like gyroscopes, and rotating fluids are rarely considered or emphasized. In fact, the dynamics of the RSW system and the gyroscope are related in specific ways and they exhibit analogous motions. As such, gyroscopes provide important pedagogical opportunities for instruction, comparison, contrast, and demonstration. Gyroscopic precession is analogous to geostrophic flow and nutation is analogous to inertial oscillation. The geostrophic adjustment process in rotating fluids can be illustrated using a gyroscope that undergoes transient adjustment to steady precession from rest. The controlling role of the Rossby number on RSW dynamics is reflected in a corresponding nondimensional number for the gyroscope. The gyroscope can thus be used to illustrate RSW dynamics by providing a tangible system that behaves like rotating fluids do, such as the large-scale ocean and atmosphere. These relationships are explored for their potential use in educational settings to highlight the instruction, comparison, contrast, and demonstration of important fluid dynamics principles.

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