Jing Fangxu, Alben Silas
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Feb;87(2):022711. doi: 10.1103/PhysRevE.87.022711. Epub 2013 Feb 19.
We analyze two- and three-link planar snakelike locomotion and optimize the motion for efficiency. The locomoting system consists of two or three identical inextensible links connected via hinge joints, and the angles between the links are actuated as prescribed periodic functions of time. An essential feature of snake locomotion is frictional anisotropy: The forward, backward, and transverse coefficients of friction differ. The dynamics are studied analytically and numerically for small and large amplitudes of the internal angles. Efficiency is defined as the ratio between distance traveled and the energy expended within one period, i.e., the inverse of the cost of locomotion. The optimal set of coefficients of friction to maximize efficiency consists of a large backward coefficient of friction and a small transverse coefficient of friction, compared to the forward coefficient of friction. For the two-link case with a symmetrical motion, efficiency is maximized when the internal angle amplitude is approximately π/2 for a sufficiently large transverse coefficient. For the three-link case, the efficiency-maximizing paths are triangles in the parameter space of internal angles.
我们分析了双连杆和三连杆平面类蛇形运动，并对运动进行了效率优化。运动系统由通过铰链接头连接的两个或三个相同的不可伸长连杆组成，连杆之间的角度作为规定的时间周期函数进行驱动。蛇形运动的一个基本特征是摩擦各向异性：向前、向后和横向的摩擦系数不同。针对内角的小幅度和大幅度情况，对动力学进行了分析和数值研究。效率定义为一个周期内行进距离与消耗能量的比值，即运动成本的倒数。与向前摩擦系数相比，使效率最大化的最佳摩擦系数集包括一个大的向后摩擦系数和一个小的横向摩擦系数。对于具有对称运动的双连杆情况，当横向系数足够大时，内角幅度约为π/2时效率最大化。对于三连杆情况，在内角参数空间中，使效率最大化的路径是三角形。
