Large amount of efforts have been devoted to design better under-actuated robot hands. The most widely adopted approaches include rigid coupled hands and self-adaptive hands. The objective of this research is to design a robot finger which combines advantages of both traditional ways and overcomes their disadvantages. The concept of Coupling and Self-Adaptation (COSA) was introduced. A linkage-based 2-DOF (Degree of Freedom) COSA robot finger was designed, optimized and studied in this paper. The theoretical analysis and the experiments on the finger show that it is able to execute human-like motion and adaptive grasps in multiple patterns. The research exposes a promising novel under-actuated mechanism for hands design with wide applications.