The mathematical model of the human arm as a switched linear system

The article presents the process of designing a mathematical model of the human arm. Modelling arm consists of two joints connected by the rotational link. Each of them is represented as a rectangular prism which changes shape during the movement. The moment of shape change depends on the two-state coordinates: the angular displacement q₁ and q₂. Based on the analysis of the arm movement, a mathematical model has been proposed. The design process was made on the basis of switched systems theory. In the first step, we present the transition from the general equation of the two-link arm dynamics to the state equation for stationary linear models. In the second step, a mathematical model has been shown as a switched linear system. The article also shows that the switching rule depends on the two components of the state vector. A switching method was presented in the schematic drawings.