VIBRATION OF NEARLY PERFECT SPRING EQUILIBRATORS

摘要

Perfect spring equilibrators balance an eccentric rotatingrnweight over a wide range of motion. The mechanism relies on arnspring of zero free length. One practical implementation uses arnspring and cable of finite free length wrapped over a pulleyrnlocated at the grounded spring attachment point of the idealrnmechanism. The pulley of finite radius introduces some error inrnthe balancing moment.rnIn this paper the kinematics of a practically implementedrnperfect spring equilibrator are developed. Two kinematic casesrnare shown to exist. In one case, the kinematics are periodic inrnthe weight arm rotation. In the other case, the geometry causesrnthe spring cable to wrap or unwrap resulting in non-periodicrnkinematics. Phase portraits are used to illustrate the nonlinearrndynamics of the system. The effect of various parameters arernexamined.