Motions of a rimless spoked wheel: A simple three-dimensional system with impacts
Motions of a rimless spoked wheel: A simple three-dimensional system with impacts
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DOI：
10.1080/02681119708806242
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发表时间：
1997-09-01
期刊：
影响因子：
--
通讯作者：
Ruina, A
中科院分区：
文献类型：
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作者：
Coleman, MJ;Chatterjee, A;Ruina, A
本文讨论了刚性无轮缘轮毂的力学问题。正多边形，‘滚动’下坡。我们所说的“滚动”，指的是车轮在一个“支承”轮辐上转动，直到另一个轮辐与地面相撞，然后将支承转移到那个轮辐上，以此类推。我们对该系统的定常运动进行了三维(3D)数值和解析稳定性研究。在任何固定的、足够大的斜率下，系统都有一个稳定的稳定滚动运动族。对于多辐条、小坡度的情况，我们得到了在给定航向三维稳定横摇所需最小坡度的解析近似。无框轮子与被动-动力步行机械有一些共同的定性特征，它是一个间歇性碰撞和周期性运动的被动式三维系统。就复杂性而言，它介于一维撞击振荡器和3D行走机器之间。与在拍面上滚动的圆盘相比，圆盘的稳定滚动运动充其量只能是中性稳定的，而无框车轮可以具有渐近稳定性。当辐条数目接近无穷大时，在极限范围内，无轮缘车轮的行为在平均意义上接近于滚动盘的行为，并且变得中性稳定。同样，在这个平均意义上，分段完整系统(无框车轮)接近于非完整系统(圆盘)。
This paper discusses the mechanics of a rigid rimless spoked wheel, or. regular polygon, 'rolling' downhill. By 'rolling', we mean motions in which the wheel pivots on one 'support' spoke until another spoke collides with the ground, followed by transfer of support to that spoke, and so an. We carry out three-dimensional (3D) numerical and analytical stability studies of steady motions of this system. At any fixed, large enough slope, the system has a one-parameter family of stable steady rolling motions. We find analytic approximations for the minimum required slope at a given heading for stable rolling in three dimensions, for the case of many spokes and small slope. The rimless wheel shares some qualitative features with passive-dynamic walking machines; it is a passive 3D system with intermittent impacts and periodic motions. In terms of complexity, it lies between one-dimensional impact oscillators and 3D walking machines. In contrast to a rolling disk on a pat surface which has steady rolling motions that ave only neutrally stable at best, the rimless wheel can have asymptotic stability. In the limit as the number of spokes approaches infinity, the behavior of the rimless wheel approaches that of a rolling disk in an averaged sense and becomes neutrally stable. Also, in this averaged sense, the piecewise holonomic system (rimless wheel) approaches a non-holonomic system (disk).