  Twisted torus knots and links are given by twisting adjacent strands of a
torus link. They are geometrically simple and contain many examples of the
smallest volume hyperbolic knots. Many are also Lorenz links.
  We study the geometry of twisted torus links and related generalizations. We
determine upper bounds on their hyperbolic volumes that depend only on the
number of strands being twisted. We exhibit a family of twisted torus knots for
which this upper bound is sharp, and another family with volumes approaching
infinity. Consequently, we show there exist twisted torus knots with
arbitrarily large braid index and yet bounded volume.
