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

In this paper, vibrational response of a variable-length cable in longitudinal, lateral and torsional directions is analysed in a cable robot using FE method. The flexibility of cables has remarkable effect on positioning of the end-effector in cable robots. Also considering the fact that the length of the cables are time dependent in a dynamic cable structure like robocrane, the numerical approaches are preferable compared to analytic solutions. To do so, the cable is divided into finite elements in which the virtual work equation and Galerkin method can be implemented for the equations. Considering 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 planar robocrane with 2-DOF and also for a spatial case with 6-DOF that is controlled by the aid of six variable-length flexible cables in the space for two different types of solid and flexible end-effectors. Whole the cable robot flexibility is analyzed simultaneously instead of separation calculation of each cable. Not only all of the 3-D vibrating behaviour of the whole structure is studied in this paper but also the lengths of the cables are considered as variable. The vibrating response of mode shapes, amplitude and frequencies are extracted and analysed, and the results are compared for two case of solid and flexible end-effector which shows the effect of the flexibility in the position of the end-effector and the tension of the cables in different situations.