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Abstract We present a resource for designing bistable developable mechanisms (BDMs) that reach their second stable positions while exterior or interior to a cylindrical surface. Analysis of the necessary conditions to create extramobile and intramobile cylindrical BDMs is conducted through a series of three tests. These tests contain elements of both existing and new mechanism design tools, including a novel graphical method for identifying stable positions of linkages using a single dominant torsional spring, called the principle of reflection. These tests are applied to all possible mechanism cases and configurations to identify why certain configurations will always, sometimes, or never be a BDM. Two tables summarize these results as a guide when designing extramobile and intramobile BDMs. The results are compared and demonstrated with a numerical simulation of 30,000+ mechanisms, including several example mechanisms that illustrate the concepts discussed in the work. Discussion is then provided on the implication of these results. 

Abstract Mechanisms that can both deploy and provide motions to perform desired tasks offer a multifunctional advantage over traditional mechanisms. Developable mechanisms (DMs) are devices capable of conforming to a predetermined developable surface and deploying from that surface to achieve specific motions. This paper builds on the previously identified behaviors of extramobility and intramobility by introducing the terminology of extramobile and intramobile motions, which define the motion of developable mechanisms while interior and exterior to a developable surface. The limits of motion are identified using defined conditions. It is shown that the more difficult of these conditions to kinematically predict may be treated as a non-factor during the design of cylindrical developable mechanisms given certain assumptions. The impact of toggle positions for each case is discussed. Physical prototypes demonstrate the results. 

Abstract This paper presents the development of an origami-inspired support system (the OriGuide) that enables the insertion of flexible instruments using medical robots. Varying parameters of a triangulated cylindrical origami pattern were combined to create an effective highly compressible anti-buckling system that maintains a constant inner diameter for supporting an instrument and a constant outer diameter throughout actuation. The proposed origami pattern is composed of two repeated patterns: a bistable pattern to create support points to mitigate flexible shaft buckling and a monostable pattern to enable axial extension and compression of the support system. The origami-based portion of the device is combined with two rigid mounts for interfacing with the medical robot. The origami-based portion of the device is fabricated from a single sheet of polyethylene terephthalate. The length, outer diameter, and inner diameter that emerge from the fold pattern can be customized to accommodate various robot designs and flexible instrument geometries without increasing the part count. The support system also adds protection to the instrument from external contamination. 

Abstract Mechanisms that can both deploy and perform desired tasks offer a multifunctional advantage over traditional mechanisms. Developable mechanisms (DMs) are devices capable of conforming to a predetermined developable surface and deploying from that surface to achieve specific motions. This paper presents new terminology that defines motion of developable mechanisms while interior and exterior to a developable surface. The limits of motion are identified using defined conditions, and it is shown that the more difficult of these conditions may be treated as a non-factor during the design of cylindrical developable mechanisms given certain assumptions. 

Abstract Stopping origami in arbitrary fold states can present a challenge for origami-based design. In this paper two categories of kirigami-based models are presented for stopping the fold motion of individual creases using deployable hard stops. These models are transcrease (across a crease) and deploy from a flat sheet. The first category is planar and has behavior similar to a four-bar linkage. The second category is spherical and behaves like a degree-4 origami vertex. These models are based on the zero-thickness assumption of paper and can be applied to origami patterns made from thin materials, limiting the motion of the base origami pattern through self-interference within the original facets. Model parameters are based on a desired fold or dihedral angle, as well as facet dimensions. Examples show model benefits and limitations.