Thumb loss can diminish one's hand's functionality by up to 40% and the loss of one's entire hand can severely impact a person's ability to perform simple day-to-day tasks. Therefore, there exists a need to focus on the development of a thumb mechanism which supports dexterous grasping activities in anthropomorphic robotic hands. This paper documents the design process of a novel robotic hand, and shows experimental results validating its overall performance. A large focus was placed on developing a novel thumb mechanism which could replicate the thumb's characteristic movement types, namely flexion-extension, abduction-adduction, and opposition-reposition. Additional focus was placed on developing a mechanism for flexion-extension movement of the fingers which did not incorporate passive components and on producing a fully self-contained prototype - with the electronics and actuators contained inside the palm, and the power supply inset against the back of the palm. The hand successfully followed motion commands from a sensor glove, and was able to replicate 14 grasp configurations which demonstrated its dexterous grasping abilities.