Three-Link Mechanism as a Model of a Person on a Swing

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.