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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 Cylindrical developable mechanisms are devices that conform to and emerge from a cylindrical surface. These mechanisms can be formed or cut from the cylinder wall itself. This paper presents a study on adapting traditional hinge options to achieve revolute motion in these mechanisms. A brief overview of options is given, including classical pin hinges, small-length flexural pivots, initially curved beams, and an adaptation of the membrane thickness-accommodation technique. Curved lamina emergent torsional (LET) joints are then evaluated in detail, and a thin-walled modeling assumption is checked analytically and empirically. A small-scale cylindrical developable mechanism is then evaluated with Nitinol curved LET joints. 

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 In many origami-based applications, a device needs to be maintained in one or more fold states. The origami stability integration method (OSIM) presented in this paper provides an approach for graphically combining various techniques to achieve stability. Existing stability techniques are also categorized into four groups based on whether they are intrinsic or extrinsic to the origami pattern and whether they exhibit gradual or non-gradual energy storage behaviors. These categorizations can help designers select appropriate techniques for their application. The paper also contains design considerations and resources for achieving stability. Finally, two case studies are presented which use the OSIM and the technique categorization to conceptualize stability in origami-based devices. 

Abstract We demonstrate analytically that it is possible to construct a developable mechanism on a cone that has rigid motion. We solve for the paths of rigid motion and analyze the properties of this motion. In particular, we provide an analytical method for predicting the behavior of the mechanism with respect to the conical surface. Moreover, we observe that the conical developable mechanisms specified in this article have motion paths that necessarily contain bifurcation points, which lead to an unbounded array of motion paths in the parameterization plane. 

Abstract The ability to deploy a planar surface to a desired convex profile with a simple actuation can enhance foldable or morphing airfoils, deployable antennae and reflectors, and other applications where a specific profile geometry is desired from a planar sheet. A model using a system of rigid links joined by torsional springs of tailorable stiffness is employed to create an approximate curved surface when two opposing tip loads are applied. A system of equations describing the shape of the surface during deployment is developed. The physical implementation of the model uses compliant torsion bars as the torsion springs. A multidimensional optimization algorithm is presented to place joints to minimize the error from the rigid-link approximation and account for additional manufacturing and stress considerations in the torsion bars. A proof is presented to show that equal torsion spring spacing along the horizontal axis of deployed parabolic profiles will result in minimizing the area between the model’s rigid-link approximation and smooth curve. The model is demonstrated through the physical construction of a deployable airfoil surface and a metallic deployable parabolic reflector. 

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 Cylindrical developable mechanisms are devices that conform to and emerge from a cylindrical surface. These mechanisms can be formed or cut from the cylinder wall itself. This paper presents a study on adapting traditional hinge options to achieve revolute motion in these mechanisms. A brief overview of options is given, including classical pin hinges, small-length flexural pivots, initially curved beams, and an adaptation of the membrane thickness-accommodation technique. Curved Lamina Emergent Torsional (LET) joints are then evaluated in detail, and a thin-walled modeling assumption is checked analytically and empirically. A small-scale cylindrical developable mechanism is then evaluated with Nitinol curved LET joints.