This paper proposes a multi-level coupled modeling method covering statics, kinematics, and dynamics in order to address the stability and adaptability issues faced by multi-finger manipulators in unstructured environments and to meet the urgent need for highly reliable operation tools in high-risk tasks like in-orbit maintenance of spacecraft. The underdriven finger configuration is constructed through topological optimization and the principle of variable stiffness. The pose transformation model for precise pinching and envelope grasping is established by using the D-H parameter method, and the multi-body coupling dynamic equation is derived by combining the Newton-Euler equation and Lagrange dynamics theory. ADAMS simulation and platform test verification show that: under a driving torque of 400 N mm, the three-finger contact force stabilizes within the range of 5-6 N, and the speed at the end of the twisting stage converges to 0.332 m/s, verifying the dynamic stability and anti-interference ability of the proposed method. The research results of this study provide theoretical support for the field of precision operation and can be extended to scenarios such as the operation of surgical robots on the lunar surface.