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, pin joints and the boundary conditions of linkages were firstly 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 solutions of constraint equations. Different solutions represent different kinematic configurations. The degree of freedom and kinematic paths of a Miura-ori and a rigid deployable antenna were also investigated in details.

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