Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model, also easily generalisable to 2D to 3D folding. A Turning Machine starts out as a line of connected monomers in the discrete plane, each with an associated turning number. A monomer turns relative to its neighbours, executing a unit-distance translation that drags other monomers along with it, and through collective motion the initial set of monomers eventually folds into a programmed shape. We fully characterise the ability of Turning Machines to execute line rotations, and to do so efficiently: computing an almost-full line rotation of $5\pi/3$ radians is possible, yet a full $2\pi$ rotation is impossible. We show that such line-rotations represent a fundamental primitive in the model, by using them to efficiently and asynchronously fold arbitrarily large zig-zag-rastered squares and $y$-monotone shapes.

中文翻译：

---

车床

分子机器人具有挑战性，因此最好保持简单。我们考虑基于异步执行的简单折叠指令的抽象分子机器人模型。车床是一个简单的 1D 到 2D 折叠模型，也很容易推广到 2D 到 3D 折叠。车床以离散平面中的一系列连接单体开始，每个单体都有相关的车削编号。一个单体相对于它的邻居转动，执行单位距离平移，将其他单体拖动到一起，通过集体运动，初始单体组最终折叠成程序化的形状。我们充分描述了车床执行线旋转的能力，并有效地执行此操作：计算几乎完整的线旋转 $5\pi/3$ 弧度是可能的，但完整的 $2\pi$ 旋转是不可能的。