双连杆机构的间歇滑动运动
Intermittent sliding locomotion of a two-link body
摘要：
我们研究的可能性，有效的间歇性运动的两个链接机构，通过改变他们的互连角周期性地在时间上滑动。我们发现，各向异性比的滑动摩擦系数是一个关键参数，而解决方案有一个简单的尺度依赖于摩擦系数的大小。由于摩擦力各向异性很大，有效的运动包括低阻力状态下的滑行，以及快速和不对称的动力和恢复冲程。随着各向异性的减小，爆发-滑行运动变为长动力冲程和短恢复冲程的运动，并且每个冲程上的互链角速度大致恒定。这些运动被认为是在空间中的正弦曲线和幂律运动所描述的两个和五个参数，分别。与对称功率和恢复冲程的情况相比，允许占空比变化大大增加了运动的效率。只有当摩擦力非常各向异性时，允许动力冲程和恢复冲程的振幅的进一步变化才能进一步提高效率。近各向同性摩擦，各种最佳有效的运动被发现与更复杂的波形。许多最佳正弦和幂律运动类似于我们在更一般的周期函数（截断傅立叶级数）空间中进行优化搜索所发现的运动。当我们增加阻力对速度的幂律依赖时，最佳运动变得更平滑，更慢，效率更低，特别是在各向同性摩擦附近。
英文摘要：
We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. We find that the anisotropy ratio of the sliding friction coefficients is a key parameter, while solutions have a simple scaling dependence on the friction coefficients' magnitudes. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes. As the anisotropy decreases, burst-and-coast motions change to motions with long power strokes and short recovery strokes, and roughly constant interlink angle velocity on each. These motions are seen in the spaces of sinusoidal and power-law motions described by two and five parameters, respectively. Allowing the duty cycle to vary greatly increases the motions' efficiency compared to the case of symmetric power and recovery strokes. Allowing further variations in the concavity of the power and recovery strokes improves the efficiency further only when friction is very anisotropic. Near isotropic friction, a variety of optimally efficient motions are found with more complex waveforms. Many of the optimal sinusoidal and power-law motions are similar to those that we find with an optimization search in the space of more general periodic functions (truncated Fourier series). When we increase the resistive force's power-law dependence on velocity, the optimal motions become smoother, slower, and less efficient, particularly near isotropic friction.
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