On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution

2022 ◽  
Vol 420 ◽  
pp. 126906
Author(s):  
Aleksandar Obradović ◽  
Zoran Mitrović ◽  
Slaviša Šalinić
Keyword(s):  
Surface Of Revolution ◽  
Ball Rolling ◽  
Homogeneous Ball ◽  
Rolling Without Slipping

Theory of a Ball Rolling on a 1/ρ Surface of Revolution

1970 ◽  
Vol 38 (2) ◽  
pp. 140-145
Author(s):  
C. M. Andersen ◽  
Hans C. von Baeyer
Keyword(s):  
Surface Of Revolution ◽  
Ball Rolling

Dynamics of Golf Ball-Hole Interactions: Rolling Around the Rim

1999 ◽  
Vol 121 (1) ◽  
pp. 88-95 ◽  
Author(s):  
Mont Hubbard ◽  
Tait Smith
Keyword(s):  
Initial Conditions ◽  
Golf Ball ◽  
Capture Process ◽  
Velocity Impact ◽  
Ball Rolling ◽  
Pure Rolling ◽  
Rolling Without Slipping ◽  
Impact Parameter Space ◽  
Roll Out ◽  
Perturbation Solutions

A previous study of a golf ball rolling on the rim of a cup neglected the spin of the ball about a line perpendicular to the plane of contact. The capture process is studied here by numerically solving the equations for rolling without slipping on the rim. The boundary in the velocity-impact parameter space separating roll-in and roll-out trajectories corresponds to initial conditions for a set of near guasi-equilibrium trajectories. Stability of the equilibrium trajectories is investigated using symbolic linearization of perturbation solutions from them. Although the locally unstable equilibrium trajectories themselves are not attainable from the two-space of pure rolling initial conditions, the boundary is nevertheless a “barrier” in that it corresponds to long contact times and large roll around angles.

scholarly journals Note on a ball rolling over a sphere: Integrable Chaplygin system with an invariant measure without Chaplygin hamiltonization

2019 ◽  
Vol 46 (1) ◽  
pp. 97-108 ◽  
Author(s):  
Bozidar Jovanovic
Keyword(s):  
Invariant Measure ◽  
Rigid Body ◽  
Cotangent Bundle ◽  
Multiplier Method ◽  
Ball Rolling ◽  
Chaplygin System ◽  
Rolling Without Slipping ◽  
Body Inertia

In this note we consider the nonholonomic problem of rolling without slipping and twisting of an ??-dimensional balanced ball over a fixed sphere. This is a ????(??)?Chaplygin system with an invariant measure that reduces to the cotangent bundle ??*?????1. For the rigid body inertia operator r I? = I? + ?I, I = diag(I1,...,In) with a symmetry I1 = I2 = ... =Ir ? Ir+1 = Ir+2 = ... = In, we prove that the reduced system is integrable, general trajectories are quasi-periodic, while for ?? ? 1, ?? ? 1 the Chaplygin reducing multiplier method does not apply.

Real-time CAD-level surface of revolution reconstruction on visual slam

2020 ◽  
Author(s):  
Feng Li ◽  
Bin He ◽  
Gang Li ◽  
Ming Ma ◽  
Jian Li ◽  
...  
Keyword(s):  
Real Time ◽  
Level Surface ◽  
Visual Slam ◽  
Surface Of Revolution

Investigation of Synchronous Accuracy of Dual Arm Motion of Industrial Robot

2012 ◽  
Vol 516 ◽  
pp. 234-239 ◽  
Author(s):  
Wei Wu ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Rotational Motion ◽  
Manufacturing Systems ◽  
Industrial Robot ◽  
Circular Path ◽  
Stable Operation ◽  
Motion Error ◽  
Ball Rolling ◽  
Arm Motion ◽  
Five Axis ◽  
Dual Arm

Recently, new needs have emerged to control not only linear motion but also rotational motion in high-accuracy manufacturing fields. Many five-axis-controlled machining centres are therefore in use. However, one problem has been the difficulty of creating flexible manufacturing systems with methods based on the use of these machine tools. On the other hand, the industrial dual-arm robot has gained attention as a new way to achieve accurate linear and rotational motion in an attempt to control a working plate like a machine tool table. In the present report, a cooperating dual-arm motion is demonstrated to make it feasible to perform stable operation control, such as controlling the working plate to keep a ball rolling around a circular path on it. As a result, we investigated the influence of each axis motion error on a ball-rolling path.

scholarly journals Darboux Transforms of a Harmonic Inverse Mean Curvature Surface

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Katsuhiro Moriya
Keyword(s):  
Mean Curvature ◽  
Curvature Surface ◽  
Surface Of Revolution ◽  
Darboux Transforms

The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward Bäcklund transform. For a given isothermic harmonic inverse mean curvature surface, its classical Darboux transform is a harmonic inverse mean curvature surface. Then a transform of a solution to the Painlevé III equation in trigonometric form is defined by a classical Darboux transform of a harmonic inverse mean curvature surface of revolution.

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