Abstract Dynamic balance eliminates the fluctuating reaction forces and moments induced by high-speed robots that would otherwise cause undesired base vibrations, noise and accuracy loss. Many balancing procedures, such as the addition of counter-rotating inertia wheels, increase the complexity and motor torques. There exist, however, a small set of closed-loop linkages that can be balanced by a specific design of the links' mass distribution, potentially leading to simpler and cost-effective solutions. Yet, the intricacy of the balance conditions hinder the extension of this set of linkages. Namely, these conditions contain complex closed-form kinematic models to express them in minimal coordinates. This paper presents an alternative approach by satisfying all higher-order derivatives of the balance conditions, thus avoiding finite closed-form kinematic models while providing a full solution for arbitrary linkages. The resulting dynamic balance conditions are linear in the inertia parameters such that a null space operation, either numeric or symbolic, yield the full design space. The concept of inertia transfer provides a graphical interpretation to retain intuition. A novel dynamically balanced 3-RSR spatially moving mechanism is presented together with known examples to illustrate the method.

中文翻译：

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刚体动力学的高阶导数应用于空间链接的动态平衡

摘要 动态平衡消除了高速机器人引起的波动反作用力和力矩，否则会导致不希望的底座振动、噪音和精度损失。许多平衡程序，例如添加反向旋转的惯性轮，增加了复杂性和电机扭矩。然而，存在一小组闭环链接，可以通过链接质量分布的特定设计进行平衡，从而可能导致更简单且具有成本效益的解决方案。然而，平衡条件的复杂性阻碍了这组联系的扩展。也就是说，这些条件包含复杂的封闭形式的运动学模型，以在最小坐标中表达它们。本文提出了一种通过满足平衡条件的所有高阶导数的替代方法，从而避免有限的封闭式运动学模型，同时为任意链接提供完整的解决方案。由此产生的动态平衡条件在惯性参数中是线性的，因此零空间操作，无论是数字还是符号，都会产生完整的设计空间。惯性传递的概念提供了一种图形解释来保持直觉。提出了一种新颖的动态平衡 3-RSR 空间移动机制，并结合已知示例来说明该方法。