Origami structures morph between 2D and 3D conformations along predetermined fold lines that efficiently program the form of the structure and show potential for many engineering applications. However, the enormity of the design space and the complex relationship between origami-based geometries and engineering metrics place a severe limitation on design strategies based on intuition. The presented work proposes a systematic design method using topology optimization to distribute foldline properties within a reference crease pattern, adding or removing folds through optimization, for a mechanism design. Following the work of Schenk and Guest, foldable structures are modeled as pin-joint truss structures with additional constraints on fold, or dihedral, angles. The performance of a designed origami mechanism is evaluated in 3D by applying prescribed forces and finding displacements at set locations. The integration of the concept of origami in mechanism design thus allows for the description of designs in 2D and performance in 3D. Numerical examples indicate that origami mechanisms with desired deformations can be obtained using the proposed method. A constraint on the number of foldlines is used to simplify a design.