MATHEMATICAL FORMULATION OF THE KINEMATIC EQUATIONS FOR THE CONTROL OF THE ROBOT SYSTEM WITH APPLICATION FOR THE MACHINING CONICAL SURFACES

With the performance of various technological operations (welding, machining, etc.) it is necessary that the end member of a robot moves along the defined path and, at the same time, the tool fulfils certain criteria in relation to the machined surface. The aim of the article is to apply theoretical knowledge to derivation of kinematic equations of a robotic mechanism control, i.e. to the solution of an inverse problem. The substance of the problem consists it the fact that based on the required position and orientation of the tool, it is necessary to determine the values of the generalized coordinates in individual joints of a robot. The solving method of the presented problem is illustrated by the specific example, i.e. the movement of the end member of a robot with conical surfaces machining.