The foldability of rigid origami has been widely studied and applied to many engineering fields. In this article we introduce the statics of rigid origami, find the form of stress and load, and prove the equivalence of static rigidity and  first-order rigidity. Another concept introduced here is the pre-stress stability . We concern what is the stability of a creased paper when it is rigid but not statically rigid and how would the pre-stress contribute to the stability. The answer to these questions is also linked with the second-order rigidity. A brief discussion on the numerical methods to determine these rigidity concludes the article .
Rigid origami is examined from the perspective of rigidity theory. First and second order rigidity are defined from local differential analysis of the consistency constraint; while the static rigidity and prestress stability are defined after finding the form of internal force and load. This article will show that first-order or static rigidity implies prestress stability, which implies second-order rigidity, which implies rigidity, but none of these is reversible. Examples are given of rigid origami structures with these different kinds of rigidity. Examining the different aspects of the rigidity of origami might give a novel perspective for the development of new folding patterns, or for the design of origami structures where some rigidity is required .
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The foldability of rigid origami has been widely studied and applied to many engineering fields. In this article we introduce the statics of rigid origami, find the form of stress and load, and prove the equivalence of
Rigid origami is examined from the perspective of rigidity theory. First and second order rigidity are defined from local differential analysis of the consistency constraint; while the
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prestress stability are defined after finding the form of internal force and load. This article will show that
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rigidity. Another concept introduced here is the pre-stress stability . We concern what is the stability of a creased paper when it is rigid but not statically rigid and how would the pre-stress contribute to the stability. The answer to these questions is also linked with the second-order rigidity. A brief discussion on the numerical methods to determine these rigidity concludes the article
or static rigidity implies prestress stability, which implies second-order rigidity, which implies rigidity, but none of these is reversible. Examples are given of rigid origami structures with these different kinds of rigidity. Examining the different aspects of the rigidity of origami might give a novel perspective for the development of new folding patterns, or for the design of origami structures where some rigidity is required