  We determine the homotopy type of the spaces of several Legendrian knots and
links with the maximal Thurston--Bennequin invariant. In particular, we give a
recursive formula of the homotopy type of the space of Legendrian embeddings of
sufficiently positive cables, and determine the homotopy type of the space of
Legendrian embeddings of Seifert fibered links, which include all torus knots
and links, in the standard contact 3-sphere, except when one of the link
components is a negative torus knot. In general, we prove that the space of
contact structures on the complement of a sufficiently positive Legendrian
cable with the maximal Thurston-Bennequin invariant is homotopy equivalent to
the space of contact structures on the complement of the underlying Legendrian
knot, and prove that the space of contact structures on a Legendrian Seifert
fibered space over a compact oriented surface with boundary is contractible.
From this result, we find infinitely many new components of the space of
Legendrian embeddings in the standard contact 3-sphere that satisfy an
injective h-principle. These include the spaces of Legendrian embeddings of an
algebraic link with the maximal Thurston--Bennequin invariant. In particular,
the inclusion of these Legendrian embedding spaces into the corresponding
formal Legendrian embedding spaces is a homotopy injection.
