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Abstract There are two major structural paradigms in robotics: soft machines, which are conformable, durable, and safe; and traditional rigid robots, which are fast, precise, and capable of applying high forces. Here, the paradigms are bridged by enabling soft machines to behave like traditional rigid robots on command. This task is accomplished via laminar jamming, a structural phenomenon in which a laminate of compliant strips becomes strongly coupled through friction when a pressure gradient is applied, causing dramatic changes in mechanical properties. Rigorous analytical and finite element models of laminar jamming are developed, and jamming structures are experimentally characterized to show that the models are highly accurate. Then jamming structures are integrated into soft machines to enable them to selectively exhibit the stiffness, damping, and kinematics of traditional rigid robots. The models allow jamming structures to efficiently meet arbitrary performance specifications, and the physical demonstrations illustrate how to construct systems that can behave like either soft machines or traditional rigid robots at will, such as continuum manipulators that can rapidly have joints appear and disappear. This study aims to foster a new generation of mechanically versatile machines and structures that cannot simply be classified as “soft” or “rigid.”