The regional-sandwiching of compliant sheets (ReCS) technique presented in this work creates flat-foldable, rigid-foldable, and self-deploying thick origami-based mechanisms. Regional-sandwiching of the compliant sheet is used to create mountain/valley assignments for each fold about a vertex, constraining motion to a single branch of folding. Strain energy in deflected flexible members is used to enable self-deployment. This work presents the methods to design origami-based mechanisms using the ReCS technique, including volume trimming at the vertex of the compliant sheet and of the panels used in the sandwich. Physical models of a simple single fold mechanism and a degree-four vertex mechanism are presented to demonstrate the ReCS technique using acrylic panels and spring steel. Consideration is given to the risk of yielding of the compliant sheet due to parasitic motion with possible mitigation of yielding by decreasing the thickness of the sheet.