Volumes of two-bridge knots in spaces of constant curvature

We investigate the existence of hyperbolic, spherical or Euclidean structure on cone manifolds whose underlying space is the three-dimensional sphere and singular set is a given two-bridge knot. For two-bridge knots with not more than 7 crossings we present trigonometrical identities involving the lengths of singular geodesics and cone angles of such cone manifolds. Then these identities are used to produce exact integral formulae for volume of the corresponding cone manifold modeled in the hyperbolic, spherical and Euclidean geometries.