The dynamics of worm-like polymer chains is considered for models with constrained bond lengths and elastic or constrained bond angles. Previous work attempted either the representation of the constraints on a complete basis set, which is impractical for chains of more than a few bonds, or the analytical preaveraging of inverse constraint matrices, which is too crude an approximation for local motions. Here the constraint matrices are evaluated from equilibrium simulations. A comparison of the analytical results with dynamical simulations shows good agreement for both global and local motions, indicating that the relevant memory in chains without rotational barriers does not extend past vibrational relaxation times. The dynamical diffusion operator is diagonal on a Rouse basis set to an adequate approximation, indicating that the effects of constraints can be imitated by the inclusion of internal friction in the basic Langevin equation. The internal friction approximation is useful even for extremely stiff chains, and the dependence of the apparent internal friction on mode number, chain stiffness, and chain length is examined. With fluctuating hydrodynamic interaction included, the constraints generate a coupling between local motions and translational diffusion which causes a small decrease in the translational diffusion constant. The effects are similar to those found in a previous phenomenological study of the effects of internal friction on translational diffusion, and do not seem to vanish with increasing chain length.