Hand synergy from neuroscience provides an effective tool for anthropomorphic hands to realize versatile grasping with simple planning and control. This paper aims to extend the synergy-inspired design from anthropomorphic hands to multi-fingered robot hands. The synergy-inspired hands are not necessarily humanoid in morphology but perform primary characteristics and functions similar to the human hand. At first, the biomechanics of hand synergy is investigated. Three biomechanical characteristics of the human hand synergy are explored as a basis for the mechanical simplification of the robot hands. Secondly, according to the synergy characteristics, a three-fingered hand is designed, and its kinematic model is developed for the analysis of some typical grasping and manipulation functions. Finally, a prototype is developed and preliminary grasping experiments validate the effectiveness of the design and analysis.