Summary: For a sub-Riemannian manifold and a given Riemannian extension of the metric, we define a canonical global connection. This connection coincides with both the Levi-Civita connection on Riemannian manifolds and the Tanaka-Webster connection on strictly pseudoconvex CR manifolds. We define a notion of normality generalizing Tanaka’s notion for CR manifolds to the sub-Riemannian case. Under the assumption of normality, we construct local frames that simplify computations in a manner analogous to Riemannian normal coordinates. We then use these frames to establish Bianchi identities and symmetries for the associated curvatures. Finally we explore sub-Riemannian generalizations of the Bonnet-Myers theorem, providing some new results and some new proofs and interpretations of existing results.