This research addresses the need for a more flexible, versatile and multifingered robotic hand to augment the dexterity of a robotic arm. Its objective is to complete a unified approach to the analysis of dexterous manipulation, and the design of robotic hands based on this functionality. The research is implemented by applying techniques in differential as well as computational geometry, nonlinear control, symbolic computation, dynamical system theory and free motion planning. With dexterous manipulation as the primary goal, criteria for robotic hand design are developed. The project has an experimental component whereby the design concepts are implemented on existing actuators. This research is expected to impact several fundamental issues in robotics, including nonholonomic motion planning, coordinated control, grasping and task planning, geometrical modeling and finger kinematics and actuator design.