Specifity of Including of Structural Nonlinearity in Model of Dynamics of Cable-Driven Robot

Abstract

The paper deals with a problem of modeling of the dynamics of a parallel cable-driven robot with the inclusion of structural nonlinearity of cables in a mathematical model. Mathematical model is implemented in a computer model with the possibility of using of symbolic calculations. Parallel cable robots as a type of robotics have been developing in the last two or three decades. The research in the theoretical field was being carried out and the mathematical model of the cable system was being refined with the spread of the practical use of cable robots. This is a non-trivial task to draw up a dynamic model of a cable-driven robot. Cable-driven robots are highly nonlinear systems, because of the main reason for the nonlinearity is the properties of the cable system. As an element of a mechanical system, the cable or the wire rope is a unilateral constraint, since the cable works only for stretching, but not for compression. Thus, the cables are structurally nonlinear elements of the system. On the other hand, cables have the property of sagging under their own weight. Thus, the cables are geometrically nonlinear elements of the system. Under the condition of a payload mass that is utterly greater than the mass of each cable, the cables can be considered strained without sagging and geometric nonlinearity can be neglected. Since symbolic computations can be used in a computer model which implements a mathematical model of the dynamics of a robot, in such a way it must provide the possibility of symbolic computations with the condition of structural nonlinearity. The main aim of this work is to develop a method that ensures the inclusion of the structural nonlinearity of the cable system in the mathematical model. It is supposed to consider the possibility of implementation of the computer model with symbolic computations. The problem of including a mathematical model of cables as unilateral constraints in the model of highly loaded cable robots is considered. The justification for including the activation functions in a system of differential equations of dynamics of cable-driven robot is formulated. A model of wire ropes as unilateral constraints is represented via including the activation functions in a system of differential equations. With using of the proposed method, numerical solution of a problem of forward dynamics has been obtained for high-loaded parallel cable-driven robot.