Dynamic Control of Compound Structure with Links of Variable Length

The modeling of a mechanical system with an arbitrary number of links of variable length that are composed of two weightless sections of variable length and a massive absolutely solid rod located between them is considered. The problem on controlling the purposeful motion of a system with an arbitrary number of links of variable length is analyzed. Control is performed by changing the length of the weightless sections of the links and changing the angles between the links. The constraint between the links is realized by two cylindrical hinges, providing significant mechanical strength, simplicity of design, and arrangement of control drives. Changing the angles between model links is also a control. A system of differential equations of motion is constructed and written in the vector-matrix form. As an example of using the developed model, an anthropomorphic mechanical system in the form of a skier-snowboarder is considered. The skier-snowboarder model takes into account the nonholonomic constraint of the ski to the surface. A system of differential equations of motion is constructed and an analysis of changes in the equations is carried out by taking into account nonholonomic constraints. A numerical example of modeling the movement of a skier-snowboarder using control based on the constraint stabilization method is considered.