Abstract
In this chapter, both the Euler–Bernoulli and Timoshenko beam theories are used to construct the dynamic models of single-link flexible manipulators. We start from the nonlinear models and then, for the purpose of vibration analysis, mechatronic design, and control synthesis of flexible manipulator systems, linearized models are derived by neglecting all deformation terms with orders higher than first order. Since the resulting dynamic models, described in terms of partial differential equations, are of infinite dimension and cannot be used directly for controller designs based on the finite dimensional model, various approximate finite dimensional modeling methods for flexible manipulators are investigated in this chapter, including the assumed modal method, finite difference method, and finite element method.
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