Rescuing falling objects from small-diameter deep wells has always been difficult in the rescue field. Aiming at a series of problems, such as the unique condition of the small-diameter deep well and the difficulty of rescue, a small-diameter deep well rescue robot is proposed. Combined with the secondary injuries that may occur during the rescue process, the frame structure, lifting mechanism, walking mechanism, grasping mechanism, and bracket mechanism scheme of the deep well rescue robot are designed. Furthermore, the virtual prototype model of each mechanism is established based on SolidWorks' three-dimensional design software. According to the functions realized by each mechanism, a kinematic mathematical model of the bracket mechanism is established, the D-H parameter table in the process of movement is obtained, and the kinematic expression is derived. The coordinate transformation matrix in the movement process is obtained. Based on the Lagrange dynamic analysis method, a mathematical model of the dynamics of the bracket mechanism is established, the dynamic expression is derived, and the moment expression during the movement is obtained. Based on this, using SolidWorks software, the motion characteristics of the bracket mechanism of the deep well rescue robot are simulated, and the change law of the motion parameters during the movement is obtained, providing a reference for the optimization of the mechanism and the stability of the rescue.