Dynamic solving of rotational transformation matrix using the D'ALAMBER principle

Abstract

The work deals with the problem of mechanics of robots, and the possibilities of the application of the basic equations of matrices of rotational transformations, in solving dynamics of a whose basic structure is based on joints that allow only rotation. The work also lists the Dynamic Models of the manipulator that can be made based on th use of the known laws of the Newton of Lagrange mechanics. As a result of the application of these laws, there are the equations that link the effects of the forces and their moments to the segments with kinematic parameters of the movement of the chain. Also, it gives the characteristics of the movement equations of the manipulator through the Lagrange-Oiler Method, as well as the New-ton-Oiler equations, and D'Alamber equations. Since the mechanical structure of a represents a single joint-based mechanism, a is seen as a disassembled chain, and then a definition is made of a geometric approach to solving D'Alamber. There is a separate account of the cases that occur in practical realisations, so that a computer program can be made for checking the validity of the solutions to the D'Alamber principle in the tasks relating to the kinematics of the -manipulator. The results of examination are useful in solutions related to anthropomorphic s, as well as in other applications in various areas of technology.