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
Author(s):  
Feng Li ◽  
Bin He ◽  
Gang Li ◽  
Ming Ma ◽  
Jian Li ◽  
...  

2012 ◽  
Vol 516 ◽  
pp. 234-239 ◽  
Author(s):  
Wei Wu ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama

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.


Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Katsuhiro Moriya

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.


2021 ◽  
Author(s):  
Zhanyuan Yin ◽  
Leif Zinn-Brooks

Abstract Ball-rolling dung beetles shape a portion of dung into a ball and roll it away from the dung pile for later burial and consumption. These beetles perform dances (rotations and pauses) atop their dung balls in order to choose an initial rolling direction and to correct their rolling direction (reorient). Previous mathematical modeling showed that dung beetles can use reorientation to move away from the dung pile more efficiently. In this work, we study if reorientation can help beetles avoid competition (i.e., avoid having their dung balls captured), and if so, under what circumstances? This is investigated by implementing a model with two different type of beetles, a roller with a dung ball and a searcher which seeks to capture that dung ball. We show that reorientation can help rollers avoid searchers in a wide range of conditions, but that there are some circumstances in which rolling without reorienting can be a beetle's optimal strategy. We also show that rollers can minimize the probability that their dung ball is captured without making precise measurements of the time interval between dances or the angular deviation for dances.


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