Acupoint is the intersection point of the main and collateral channels in a human body, through which energy circulates according to eastern philosophy. Acupuncture is the essential traditional Chinese method to treat disease by sticking the proper acupoints on the patient's body, having achieved a great therapeutic effect. Normally, acupuncture is mainly performed by skilled doctors of traditional Chinese medicine, which are far from enough for requirements. Hence it is natural to resort to robots to perform acupuncture work. There has no complete theoretical guidance for the development of an acupuncture robot so far. Thus, this paper digs out that acupuncture is essentially a visual servoing task with force constraints and the handeye-force coordination framework is first proposed. With the guidance of the framework, the acupuncture task is divided into three parts: hand-eye coordination, eye-force coordination, and hand-force coordination. The hand represents the end-effector of the acupuncture robot, the eye represents the visual sensor of the acupuncture robot, and the force represents the interaction between the acupuncture robot and the patient's body. The hand-eye coordination is the visual servoing control, eye-force coordination is to estimate force by vision, and hand-force coordination is the acupuncture operation with force constraint. The acupuncture task can be completed only when the three coordinations are well organized. The solutions are proposed for the three coordination tasks, which are finally validated by the experiments.