  Grasp synergies represent a useful idea to reduce grasping complexity without
compromising versatility. Synergies describe coordination patterns between
joints, either in terms of position (joint angles) or effort (joint torques).
In both of these cases, a grasp synergy can be represented as a low-dimensional
manifold lying in the high-dimensional joint posture or torque space. In this
paper, we use the term \textit{Mechanically Realizable Manifolds} to refer to
the subset of such manifolds (in either posture or torque space) that can be
achieved via mechanical coupling of the joints in underactuated hands. We
present a method to optimize the design parameters of an underactuated hand in
order to shape the Mechanically Realizable Manifolds to fit a pre-defined set
of desired grasps. Our method guarantees that the resulting synergies can be
physically implemented in an underactuated hand, and will enable the resulting
hand to both reach the desired grasp postures and achieve quasistatic
equilibrium while loading the grasps. We demonstrate this method on three
concrete design examples motivated by a real use case, and evaluate and compare
their performance in practice.
