This paper tackles dynamic manipulability analysis and design optimization of a fully-actuated hexrotor unmanned aerial vehicle. First, a dynamical model of the hexrotor is presented. The model is then analyzed to prove that nonplanar hexrotor structure can be approximately simplified and transformed into planar rotor arrangement. Based on the fact, symmetric-coplanar-tilted-rotor (SCTR) structure is introduced as a kind of canonical structure of hexrotors. Moreover, dynamic manipulability measure (DMM) of the hexrotor is newly defined to analyze its maneuverability, and DMM of the hexrotor with SCTR structure is found suitable for performance evaluation of the structure. Finally, based on the analysis, a design optimization method for the hexrotor is presented, and numerical examples are shown.