Origami robots are characterized by their compact design, quasi-two-dimensional manufacturing process, and folding joint-based transmission kinematics. The physical requirements in terms of payload, range of motion, and embedding core robotic components have made it unrealistic to rely on conventional mathematical models for designing these new robots. Therefore, origami robots require a comprehensive approach to model their mechanics. Currently, there is no generalized mechanics model to achieve this goal. Therefore, in this work, we propose a nonlinear lattice-and-plate model to simulate the mechanics of physical origami robots within several seconds, including the localized bending on flexible hinges, global displacements of rigid panels, and trajectory of predefined outputs. Moreover, this proposed model captures the large displacement and self-contact of adjacent panels during locomotion. We validate the efficiency of the model on various origami actuators, grippers, and metamaterials. To conclude, the computational model can help to accelerate the design iteration of origami robots.