Abstract

We model movements of a person swinging on a swing. We consider a flat three-link hinged mechanism as the main mechanical model of the person sitting on the swing. The first, second, and third links model the human body, two hips that are rigidly connected to the swing, and two shins, respectively. The hinge between the first and second links models two hip joints, while the hinge between the second and third links models two knee joints. In each of the interlink hinges, a control moment, limited in magnitude, is applied. At the point of the support of the swing, the moment of viscous friction acts. A mathematical model of a controlled three-link mechanism is built. In solving the problem of synthesizing the control of a three-link model, the law of the control of a simpler (auxiliary) two-link swing model is preconstructed. Then this law is used to control the three-link model. Motion equations with the control built in the form of feedback, have periodic orbitally asymptotically stable solutions. Depending on the parameters of the model, such solutions describe the oscillations of a swing with a constant amplitude or rotation. The control that damps the swing is also built.

中文翻译：

---

三连杆机构作为秋千上的人的模型

摘要

我们模拟一个人在秋千上的运动。我们将扁平的三连杆铰链机构视为坐在秋千上的人的主要机械模型。第一个，第二个和第三个链接分别模拟人体，刚性连接到秋千的两个臀部和两个胫骨。第一连杆和第二连杆之间的铰链可模拟两个髋关节，而第二连杆和第三连杆之间的铰链可模拟两个膝关节。在每个互连铰链中，施加一个大小受限制的控制力矩。在摆动的支撑点，粘性摩擦的时刻起作用。建立了受控三连杆机构的数学模型。在解决综合三连杆模型的控制问题时，预先构造了一个简单（辅助）两连杆摆动模型的控制规律。然后使用该定律控制三链路模型。具有以反馈形式构建的控制的运动方程具有周期轨道渐近稳定解。根据模型的参数，此类解决方案描述了振幅恒定或旋转的摆动的振荡。还建立了抑制摆动的控制装置。