Abstract: Motion path analysis is essential for designing origami structures. Existing approaches often model origami as spatial linkage mechanisms, with crease rotation angles as the primary unknowns. This study applies a rigid-body motion resolution method based on Moore–Penrose generalized inverse matrix, using nodal coordinates as unknowns and incorporating rigid-body motion equations (Unit-Rigid model), to analyze motion paths across various origami patterns. A moment-equivalent loading method using M–P generalized inverse matrix is developed to define load boundary conditions in rigid-body units. For zero-thickness origami, differences in the folding behavior between the Unit-Rigid model and bar-system-based models (Unit-0/Unit-1) are compared. These differences are explained using matrix condition numbers and structural degrees of freedom. The Unit-Rigid model demonstrates its high extensibility, effectively analyzing multi-module Miura-ori patterns and intricate origami with kinematic singularities, like square twist origami. For the thick-panel Miura-ori, a contact-aware load iteration update method is introduced for deployment analysis, with results validated against multibody dynamics simulations in COMSOL Multiphysics. This approach offers a systematic framework and a numerical tool for the kinematic analysis of thick-panels and of complex origami structures.