This research concerns the design of a new three-fingered anthropomorphic hand mechanism for prosthetic and robotic applications. Based on the configuration and flexion/extension features of human hands, we develop a three-jointed finger mechanism using a gear-constrained planar five-bar linkage with a single degree of freedom (DOF). From an operational study of human hands, we also propose a multi-functional palm mechanism using a cam-groove submechanism. The hand can perform grasping, holding and pinching operations. To achieve the automatic shape adaptability of a human hand, a selfadaptable submechanism was designed within the palm based on the lever principle. An automatically variable speed transmission with selfadaptability was developed for this hand to achieve optimal flexing speed and optimal fingertip forces. This paper describes the mechanical structure and operational principles of this new prosthetic device.