In this study, a coupled multi-knuckle mechanical finger was designed. The finger is composed of same-structured knuckles in a connecting link structure, and the knuckles can be combined arbitrarily. The coupling motion is completed under the drive of a single actuator. First, the influences of the angular relationship between the knuckles and working stroke of the knuckles on the actual grasping range of the finger were evaluated, and the kinematic analysis of the knuckle was performed using the closed-loop vector method. Next, an optimization design method based on a genetic algorithm was proposed, which considered the angular relationship as the objective function to optimize the knuckle, which is illustrated with an example. The angle between each pair of knuckles is approximately constant and equal, which indicates that the finger has an approximately circular envelope curve. Subsequently, the finger motion simulation was carried out to verify the optimization design results and evaluate the error in the finger grasping process. The grasper is capable of completing accurate envelopes on cylinders with diameters ranging from 38.97 mm to 127.60 mm. Finally, the prototype of the manipulator was constructed according to the parameters obtained in the optimization design example. The feasibility of the design was verified through a grasping experiment using beakers and other objects. It provides a reference for angle optimization and envelope curve design of the grasper.