Grasp planning and motion synthesis for dexterous manipulation tasks are traditionally done given a pre-existing kinematic model for the robotic hand. In this paper, we introduce a framework for automatically designing hand topologies best suited for manipulation tasks given high level objectives as input. Our goal is to ultimately design a program that is able to automatically design robotic hands that can perform a set of target tasks by leveraging their physical design to encourage robust manipulations. Our framework comprises of a sequence of trajectory optimizations chained together to translate a sequence of objective poses into an optimized hand mechanism along with a physically feasible motion plan involving both the constructed hand and the object. We demonstrate the feasibility of this approach by synthesizing a series of mechanical hand designs optimized to perform specified in-hand manipulation tasks of varying difficulty. We also briefly explore the feasibility of constructing multi-purpose hands from scratch that are meant to perform multiple primitive tasks in sequence