This paper investigates the in-hand manipulation capabilities of a compliant, underactuated planar robotic hand by treating the system as a simple, symmetric, 6-bar linkage mechanism with compliant joints. Although underactuated hands are generally not considered to be adept at dexterous tasks, we have found through past work that an underactuated manipulator can control n degrees of freedom with n actuators by leveraging the passive compliance to satisfy contact constraints on the object. Assuming the system to be quasi-static, the workspace of the underactuated mechanism is found through constraint-based energy minimization by sweeping through the set of allowable inputs. In this study, we investigate achievable workspaces by exploring the nondimensionalized design space, consisting of linkage ratio, joint stiffness ratio, transmission ratio, base linkage length, and object linkage length. The results of this study are useful in motivating the design of dexterous, underactuated manipulators, as well as to predict the achievable workspace of specific hand/object configurations.