Longitudinal and Lateral Vibration Analysis of Cables in a Cable Robot Using Finite Element Method

In this paper, vibration equation of a variable-length cable in longitudinal, lateral and torsional directions in a cable robot is analyzed using FE method. The cable is divided into finite elements in which the virtual work equation and Galerkin method can be imposed into the equations. As a result of the stiffness matrix, the characteristic equations and Eigen values of each element can be defined. A simulation study is done in the ANSIS on a robocrane of six degrees of freedom end-effector that is controlled by the aid of six variable-length cables in the space for two different solid and flexible end-effector approaches. Whole the cable robot flexibility is analyzed simultaneously instead of separation calculation of each cable. Not only all of its 3-D vibrating behavior is studied in this paper but also the lengths of the cables are considered variable as it should be. The results are compared for two cases showing the effect of the vibrations in the position of the end-effector and the tension of the cables in different situations.