Constructing equations of rigid body systems dynamics and algorithms for solving control problems of biomechanical systems

The article proposes two new approaches to studying the biomechanics of anthropoid structures. The first method involves constructing systems of differential equations of motion using functions of a complex variable, which simplifies the determination of link coordinates defined by a single complex function in exponential form. This approach facilitates the calculation of the squares of the velocities of the links' centers of mass and accelerates the process of computing the system's kinetic energy. Two models of a mechanism with five movable links are considered, differing only in the method of measuring the angles that determine the positions of the links. The description of the method is illustrated using the example of a more intuitive mechanism model, with angles measured from the horizontal axis of the fixed reference frame. For the mechanism model with angles measured from the axes of local coordinate systems, the procedure for constructing the system of differential equations of motion is similar but significantly more cumbersome. The second method pertains to solving the problem of controlling the motion of an anthropoid mechanism and involves the application of various interpolation and approximating functions for the control moments. A comparative analysis of control moments defined by piecewise-continuous step functions, interpolation polynomials, and fifth-degree polynomials was conducted by solving the Cauchy problem for the system of differential equations. It was found that the solution corresponds to motion sufficiently close to anthropoid movement. An analysis of approximation error calculations shows that the minimum value is achieved when using an interpolation polynomial.