Experimental Investigation of the Painlevé Paradox in a Robotic System
Experimental Investigation of the Painlevé Paradox in a Robotic System
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DOI：
10.1115/1.2910825
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发表时间：
2008-07
期刊：
影响因子：
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通讯作者：
Zhen Zhao;Caishan Liu;Wei-Gang Ma;Bin Chen
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文献类型：
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作者：
Zhen Zhao;Caishan Liu;Wei-Gang Ma;Bin Chen
本文旨在通过实验研究刚体系统在所谓的悖论情形下的动力学行为。实验设置对应于我们先前的工作Liu等人[2007，“The Bouncing Motion Appearing in a Robotic System With Unilateral Constraint，“Nonlinear Dyn.，49（1-2），217-232]，其中双连杆机器人系统与移动轨道接触。实验结果表明，在接触点处存在切向冲击，并且具有与Moreau [1988年，“有限自由度动力学中的单侧接触和干摩擦”，非光滑力学和应用，Springer-Verlag，维也纳，pp. 1-82]的接触点的相对切向速度必须立即接近零，一旦潘列夫悖论发生。在切向冲击之后，可以激发弹跳运动，并且弹跳运动受到移动轨道的速度的影响。我们采用刘等提出的切向碰撞规则来确定系统的碰撞后速度，并使用事件驱动算法进行数值模拟。数值计算和实验结果之间的定性比较进行，并显示出良好的协议。这项研究不仅提供了一个实验支持的冲击假设有关的问题的Painleve悖论，但也可以找到它的应用程序在更好地理解出现在机器人系统中的不稳定现象。
This paper aims at experimentally investigating the dynamical behaviors when a system of rigid bodies undergoes so-called paradoxical situations. An experimental setup corresponding to the analytical model presented in our prior work Liu et al. [2007, "The Bouncing Motion Appearing in a Robotic System With Unilateral Constraint, " Nonlinear Dyn., 49(1-2), 217-232] is developed, in which a two-link robotic system comes into contact with a moving rail. The experimental results show that a tangential impact exists at the contact point and takes a peculiar property that well coincides with the maximum dissipation principle stated in the work of Moreau [1988, "Unilateral Contact and Dry Friction in Finite Freedom Dynamics," Nonsmooth Mechanics and Applications, Springer-Verlag, Vienna, pp. 1-82] the relative tangential velocity of the contact point must immediately approach zero once a Painleve paradox occurs. After the tangential impact, a bouncing motion may be excited and is influenced by the speed of the moving rail. We adopt the tangential impact rule presented by Liu et al. to determine the postimpact velocities of the system, and use an event-driven algorithm to perform numerical simulations. The qualitative comparisons between the numerical and experimental results are carried out and show good agreements. This study not only presents an experimental support for the shock assumption related to the problem of the Painleve paradox, but can also find its applications in better understanding the instability phenomena appearing in robotic systems.