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Two recursive dynamic models, based on the Newton-Euler formulation, are proposed to model the dynamics of manipulators with link flexibility. In both models, the displacement and rotation due to the link flexibility are assumed to be measurable. For a small link deformation, a first-order lumped mass/spring approximation model is proposed, in which the parameters of each link are lumped to its joint and the link flexibility is modelled as a spring at each joint. For a larger deformation, the first-order lumped mass/spring approximation model is extended to model each nonrigid link by a series of small rigid beams connected by "pseudo-joints." The link flexibility is modelled as a spring in each pseudo-joint. In both models, the effects of torsion and extension are not included in the modelling. An analytical error analysis is performed to justify the approximation and the mathematical relation between the maximum modelling error and the number of pseudo-joints on each link is derived. As the number of pseudo-joints approaches infinity, the joint torques computed by the extended lumped mass/spring approximation model approach the joint torques computed by other models obtained from the Lagrange's equation.