Mathematical analogy of the propagation of mechanical motion in a robotic structure through the model of the equation of thermal conductivity

In this study, mathematical modeling of the problem of increasing the smoothness of the mechanical movement of robotic structures is performed. Important analogies have been established with the physico-mathematical model of the thermal conductivity equation, which in this case describes the degree of propagation of mechanical motion in various positions of a robotic limb. The method of separation of Fourier variables and spatial transformation is applied to reduce the solution with 15 degrees of freedom. The method is also common for cases of different spatial locations of the described model along with its corresponding cylindrical coordinate system. As a conclusion, the main theses and the necessary evidence are presented, demonstrating a decrease in the degree of wear and friction forces for models with an increased degree of smoothness. At the same time, it is assumed that the model will be further expanded using visualization.