Analysis and verification of cable pretension effect on the buckling load of a single-link flexible mechanism

This paper utilizes the extended Hamilton's principle to develop a dynamic model of a single-link flexible mechanism with two cables involving the cable pretensions. The effect of cable pretension is considered by introducing the von Kármán nonlinearity into the dynamical modelling. Before implementing the modal analysis, buckling of the flexible beam is investigated with the goal of analyzing structural stability for the single-link flexible system with two pre-tensioned cables. Based on the proposed dynamical model, a transcendental equation for determining the critical buckling load on the beam is derived. Several typical cable and beam materials are included to investigate their influence on the buckling load. An alternative approach to predict the buckling load for the flexible beam braced by cables is applied using the concept of lateral stiffness at the tip, which leads to the same stability equation as that from the presented dynamical model. Finite element simulations are accomplished in ANSYS. The buckling loads obtained from ANSYS are compared with the analytical values based on the proposed method, which demonstrates the effectiveness of the modelling. In addition, an approximate procedure for estimating the critical buckling load is also performed in ANSYS on the basis of a linear relationship between lateral stiffness and buckling load. Finally, an experimental testbench is built and the buckling phenomenon is identified with increasing cable pretensions.