中文摘要：

论文研究了一类含两个内部质量块的振动驱动系统在异性粘性摩擦下的平面运动，其中两个质量块在刚体内部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，验证了速度Verlet积分法的可靠性；然后，利用这种数值方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；最后，通过调节内部驱动的周期比和相位，得到了系统轨迹在直线和圆弧间相互切换的六种平面运动形式．

英文摘要：

With the rapid development of science and technology, the applications of mobile robots become increasingly widespread. Mobile robots can replace human workers in dangerous and harsh environment. However, in some narrow spaces such as pipes and intestinal tracts, traditional mobile robots like wheeled robots and legged robots can＇t play their roles effectively. Inspired by the motion of reptiles, some scholars began studying the worm-like robots, the mechanical models of which belong to the vibration-driven systems. Most studies on the planar motion of such systems concentrated on the translational motion and fixed-axis rotation, and the arc trajectories composed of folding lines lowering down the movement efficiency of vibration-driven systems. In this paper, the curvilinear motion and the switches among different trajectories of the system are studied. This study will not only improve the planar locomotion ability effectively, but also enrich the planar motion types of vibration-driven systems. In this paper, the planar locomotion is investigated for a class of vibration-driven systems with two internal masses. The internal masses, driven by the three-phase motion, move along two perpendicular slots. The planar locomotion of the system is produced by the two moving internal masses. The friction between the system and the supporting plane is supposed to be viscous and anisotropic. The mechanical system is modeled by Lagrange＇s equations of the second kind. The velocity-Verier algorithm 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, which verifies the velocity-Verier algorithm. Through numerical analysis, the influences of internal drives＇ period ratio and internal masses＇ relative accelerations on planar locomotion of the system are obtained. When the period ratio is 1, the trajectory of the system is a circle; otherwise, it is a straight line. The result is verified using the Runge