We apply the Timoshenko theory to investigate a new mathematical modeling problem for the "shoulder-elbow-like" single flexible-link robot arms damping. Detailed analysis and derivation are given to support the mathematical modeling of this particular flexible mechanism. Moreover, by assuming that the pinned-pinned mode shape of a Euler-Bernoulli beam is the same as the more complete Timoshenko beam, an analytic solution of the new model is derived. Finally, computer simulation results are included to verify the theoretical analysis and mathematical formulation, which have shown satisfactory agreement with the new mathematical model.
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