This article focuses on the dynamic problem of origami capture mechanism capturing space debris in orbit. It delves into the envelope characteristics of the origami capture mechanism, analyzing the motion laws of its axisymmetric folding state. Furthermore, it establishes a kinematic model for the axisymmetric envelope of the origami capture mechanism. A rigid body dynamic model of the origami capture mechanism and a generalized torque equation for the hinge at the crease were established based on the D–H parameter method and the Lagrange method. The enveloping process of the origami capture mechanism in the microgravity environment was simulated using ADAMS software, and the accuracy of the rigid body dynamics model of the origami capture mechanism and the generalized moment equation of the hinge at the crease was verified. Using Ls-Dyna software to simulate the capture process of space debris by force-driven and displacement-driven flexible origami capture mechanisms in microgravity environments, the results show that displacement-driven origami capture mechanisms can quickly capture space debris and are suitable for capturing large-sized space debris; The force-driven origami capture mechanism can quickly complete envelope capture of space debris, suitable for capturing small-sized space debris.