We study a general form of gears known as non‐circular gears that can transfer periodic motion with variable speed through their irregular shapes and eccentric rotation centers. To design functional non‐circular gears is nontrivial, since the gear pair must have compatible shape to keep in contact during motion, so the driver gear can push the follower to rotate via a bounded torque that the motor can exert. To address the challenge, we model the geometry, kinematics, and dynamics of non‐circular gears, formulate the design problem as a shape optimization, and identify necessary independent variables in the optimization search. Taking a pair of 2D shapes as inputs, our method optimizes them into gears by locating the rotation center on each shape, minimally modifying each shape to form the gear's boundary, and constructing appropriate teeth for gear meshing. Our optimized gears not only resemble the inputs but can also drive the motion with relatively small torque. We demonstrate our method's usability by generating a rich variety of non‐circular gears from various inputs and 3D printing several of them.

中文翻译：

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非圆齿轮的计算设计与优化

我们研究了一种称为非圆形齿轮的齿轮的一般形式，它可以通过其不规则形状和偏心旋转中心以可变速度传递周期性运动。设计功能性非圆形齿轮并非易事，因为齿轮副必须具有兼容的形状才能在运动过程中保持接触，因此驱动齿轮可以通过电机可以施加的有界扭矩推动从动件旋转。为了应对这一挑战，我们对非圆齿轮的几何、运动学和动力学进行建模，将设计问题表述为形状优化，并在优化搜索中确定必要的自变量。以一对 2D 形状作为输入，我们的方法通过在每个形状上定位旋转中心将它们优化为齿轮，最小化修改每个形状以形成齿轮的边界，并为齿轮啮合构造合适的齿。我们优化的齿轮不仅类似于输入，而且还可以以相对较小的扭矩驱动运动。我们通过从各种输入生成丰富多样的非圆形齿轮并 3D 打印其中几个来证明我们方法的可用性。