DYNAMICS OF A TWO-LINK FLEXIBLE SYSTEM UNDERGOING LOCKING: MATHEMATICAL MODELLING AND COMPARISON WITH EXPERIMENTS

Space structures such as the solar panels or antenna, when deployed in space, have large dimensions, low mass to size ratio, large inertias and relatively low structural rigidity. Due to space restrictions, these structures are originally in stowed configurations and are deployed into their full size in space. Typically, these systems at the end of deployment undergo locking at the joints and lose their rotational degrees of freedom at the joints. In addition, during locking vibrations are induced in these light-weight, flexible mechanisms which have to be actively or passively damped. In this paper a mathematical model with an experiment is presented for a two-link flexible system, which undergoes locking during motion. The structural flexibility is modelled by the finite element method, and the equations of motion are derived using the Lagrangian formulation. The locking at the joints is modelled by the momentum balance method, which enables one to predict the rigid body as well as the elastic motion of the system after locking. The experimental setup consists of two flexible aluminum links with a revolute joint at the end of each link, and has a locking mechanism for each joint. The links lock as a predefined angle. The links are instrumented with strain gages and the joint rotations are measured by potentiometers. The sensor readings are acquired and stored on a PC based data acquisition system. The simulation results such as the locking time, response of each joint and the strain at the base of each link match very well with the experimental results. Thus, the momentum balance method is capable of predicting fairly accurately the dynamics of a flexible system which undergo locking during motion.