The directional motion of a continuous worm induced by travelling the mass center of its body is studied in this paper. To this end, a new locomotion gait is constructed to derive the condition that the worm can move forward in one period. The interaction force between the worm body and environment is an anisotropic dry friction. The governing equation describing worm-like motion is firstly considered as a quasi-static case for a slow actuation history or for a larger friction. Then the solution of this equation is derived based on the specific form of the tension and its continuous distribution along the worm body. Furthermore, through the method of piecewise analysis of the motion, the expressions of the tension and the displacement along its body in each stage are specifically calculated. The net displacement over one period is further obtained. As a result, the condition that the directed motion of the worm can be effectively achieved. The results show that the worm can keep the body length unchanged by means of the given locomotion gait during the motion process.

中文翻译：

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通过改变各向异性环境中质心的位置实现蠕虫状运动

本文研究了蠕虫通过其质心运动引起的定向运动。为此，构造了一种新的运动步态，以得出蠕虫可以在一个周期内向前运动的条件。蜗杆体与环境之间的相互作用力是各向异性的干摩擦。首先，描述蠕虫状运动的控制方程式被认为是准静态情况，用于缓慢的驱动历史或较大的摩擦力。然后，根据张力的特定形式及其沿蜗杆主体的连续分布，得出该方程式的解。此外，通过对运动进行分段分析的方法，可以具体计算出每个阶段沿其主体的张力和位移的表达式。进一步获得一个时期的净位移。结果，可以有效地实现蜗杆的定向运动的条件。结果表明，蠕虫可以在运动过程中通过给定的运动步态保持体长不变。