Harnessing elastic instability for power-amplification

虽然大型动物能够使用肌肉实时奔跑和跳跃，但肌肉在小尺度上的力量限制意味着昆虫等小型生物无法以同样的方式使用肌肉。尽管如此，跳蚤和蝗虫等昆虫令人印象深刻的跳跃能力是众所周知的。这些昆虫通过缓慢地使用它们的肌肉来储存能量，然后突然释放能量以快速运动来实现这一壮举。这类似于弓箭手使用弓箭的方式，也是“力量放大”的一个例子：如果能量储存缓慢但释放迅速，即使缓慢做功也能产生很大的力量。而且储存在弓弦中的弹性能量绝大部分转化为箭的动能。然而，对于昆虫，储存和释放机制并不那么清楚，提出了各种不同的机制。尽管如此，许多工程师正在开发利用类似的弹性机制来驱动快速运动的机器人，从而跳跃或抓住下落的物体。在本提案中，我们将使用数学建模来了解如何在一类昆虫启发的跳跃机器人中利用功率放大的潜力。这个模型系统的优点是，不同的组件可以直接由我们的合作者观察和控制，使我们能够了解它们是如何运作的。通过比较数学建模的结果与合作者进行的实验，我们试图了解是否机制的基础上“管理单元通过”在某种意义上是“更好”比简单的弹簧。我们还将了解跳跃的基底的几何形状对这些跳跃的有效性的关键作用。

While large animals are able to use muscles to run and jump in real-time, the power limitations of muscles at small scales mean that small creatures such as insects cannot use muscle in the same way. Despite this, the impressive jumping capabilities of insects such as the flea and locust are well known. These insects manage this feat by slowly using their muscles to store energy before releasing it suddenly to give rapid motion. This is analogous to how an archer uses a bow and arrow and is an example of 'power amplification': even doing work slowly can give rise to high power if the energy is stored slowly but released quickly.In the example of the archer it is clear that the energy is stored in the stretching of the bow string; moreover, the vast majority of the elastic energy stored in the bow string is converted to the kinetic energy of the arrow. For insects, however, the storage and release mechanisms are not so clear, with a variety of different mechanisms proposed. Nevertheless, many engineers are developing robots that exploit similar elastic mechanisms to actuate rapid motion and thereby jump or catch falling objects.In this proposal, we will use mathematical modelling to understand how the potential of power amplification can be harnessed in a class of insect-inspired, jumping robots. This model system has the advantage that the different components can be directly observed and controlled by our collaborators, allowing us to understand how they operate. By comparing the results of mathematical modelling with experiments performed by a collaborator, we seek to understand whether mechanisms based on 'snap-through' are in some senses 'better' than simple springs. We will also understand the key role that the geometry of the substrate that is jumped from plays with the effectiveness of these jumps.