三相驱动下含两质量块刚体的平面运动

本文研究了一类含两个质量块的振动驱动系统在粘性摩擦下的平面运动，其中两个内部质量在相互垂直的水平槽道上作三相运动。利用第二类拉格朗日方程，建立了系统的动力学方程；其次，利用系统直线运动时的理论解，验证速度Verlet积分法的可靠性；利用这种算法分析了系统的平面运动，得到了内部驱动参数与系统运动轨迹、运动速度的关系；然后，基于数值分析结果，通过调节内部驱动参数，得到了系统在不同轨迹间的六种转换形式；最后，通过组合不同的转换形式，得到了曲率连续变化的平面运动路径。

Planar locomotion of a rigid body driven by three-phase motion of two internal masses

In this paper, planar locomotion is investigated for a class of vibration-driven system with two internal masses. The internal masses, driven by three-phase motion, move on two perpendicular slots. Planar locomotion of the system is derived from the two moving internal masses. The friction between the system and supporting plane is supposed to be viscous and anisotropic. First, the mechanical system is modeled by using the second kind Lagrange’s equation. Secondly, the velocity-Verlet is employed to analyze the planar locomotion of the system. For the rectilinear locomotion, the analytical solution and the numerical simulation are in good agreement and it implies the reliability of the velocity algorithm. Thus, the planar locomotion of the system can be obtained. Moreover, we establish the relations among the internal driven parameters, the trajectory and velocity of the vibration-driven system. It follows from the numerical results that the six types of the switching trajectory can arise by choosing the driven parameters. Integrating the different switching trajectories, one can obtain any continuous-curvature paths.