This paper considers the design of an anthropomorphic manipulator in the form of a human hand. The aim of the work is to describe the kinematics of a robotic hand, using the example of one finger. Based on the Denavit–Hartenberg algorithm, a kinematic model is developed for one finger of the robotic hand. The working area of the robotic finger is determined, taking into account the limitations on the rotation angles of the finger phalanges. These kinematic equations are used to solve the problem of the speeds of one fingertip. According to the results of modeling for given speeds of the fingertip, the dependencies of the rotation angles of the robotic hand links were obtained. Unlike the previously used models, the developed one makes it possible to take into account the presence of a geometric constraint between the proximal and distal finger phalanges, which is structurally made with an inextensible thread. The results of the work can be used in the design and manufacture of new robotic gloves.