As one new type of deployable structures, foldable plate structures based on origami are more and more widely used in aviation and building structures in recent years. The mobility and kinematic paths of foldable origami structures are studied in this paper. Different constraints including the rigid plate, spherical joints, and the boundary conditions of linkages were first used to generate the system constraint equations. Then, the degree-of-freedom (DOF) of the foldable plate structures was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints were found by using this method, and multiple kinematic paths existing in origami structures were studied by obtaining all the solutions of constraint equations. Different solutions represent different kinematic configurations. The DOF and kinematic paths of a Miura-ori and a rigid deployable antenna were also investigated in detail.

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