Dynamic analysis of flexible manipulators, a literature review

The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies. The characteristics of the three types of reference frames used in modeling flexible multibody systems, namely, floating frame, corotational frame, and inertial frame, are compared. Future directions of research are identified. These include new applications such as micro- and nano-mechanical systems; techniques and strategies for increasing the fidelity and computational efficiency of the models; and tools that can improve the design process of flexible multibody systems. This review article cites 877 references. @DOI: 10.1115/1.1590354#

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Computational strategies for flexible multibody systems

The linear dynamics of a class of translating media with an arbitrarily varying length is investigated. The tension in the media arising from their longitudinal accelerations is incorporated. The dynamic stability of the continuous media relative to the inertial and moving coordinate systems is studied from the energy standpoint. The exact expressions for the rates of change of energies of media are derived and interpreted from both control volume and system viewpoints. The stability analyses relative to the inertial and moving coordinate systems result in the same predictions. Examples including a robotic arm through a prismatic joint and an elevator cable in a high-rise building illustrate the analysis. In particular, the results explain an inherent unstable shortening cable behavior encountered in elevator industry.

Energetics and Stability of Translating Media with an Arbitrarily Varying Length

Vibration and stability of an axially moving Rayleigh beam

The general control laws for pointwise controllers to dissipate vibratory energies of translating beams and strings with arbitrarily varying length are presented. Special domain and boundary control laws that can be easily implemented result as a special case. Sufficient conditions for uniform stability and uniform exponential stability of controlled systems are established via Lyapunov stability criteria. Numerical simulations demonstrate the effectiveness of the active controllers in stabilizing translating media during both extension and retraction. Optimal gains leading to the fastest rates of decay of vibratory energies of controlled systems are identified. It is shown that under the optimal control gains, translating media can be completely stabilized during extension and retraction.

Jin-Duo Wei

Papers

Vibrations in a moving flexible robot arm