Effects of Flexibility and Damping on Momentum Transfer During Locking of Two Moving Links, Part I: Numerical Simulation

Abstract

The system consisting of two links and two joints is examined. The joints are idealy frictionless when unlocked. Due to flexibility of the links, the locking generates some damped vibrations. It is demonstrated that the presence of these vibrations, even of very small and seemingly neglegible amplitudes, have dramatic effects on the after-locking motion of the links. Depending on the level of flexibility and damping involved, the locking triggers a large-scale “slow” motion that may have either oscillatory or circular (clockwise or counterclockwise) characters. The links will stop at some resting configuration only at certain “critical” values of damping. The set of “critical dampings” seems to be infinite, though only two degrees-of-freedom are used to model the system. Governing equations for these phenomena are derived and discussed in Part II of this paper.