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Abstract. This work develops and presents design concepts and models of thickness-utilizing deployable hard stops (ThUDS) which can be incorporated into origami-based design applications to provide stability in specific fold states. A ThUDS, like a lamina-emergent mechanism, emerges from a flat state and can reside within a sheet. A variety of planar and spherical ThUDS configurations are developed and presented, using diagrams, equations, and prototypes. Examples of ThUDS applications are given and attributes are discussed. Considerations for the design of a ThUDS are discussed. This work outlines how a ThUDS can maintain foldability while improving stability and utilizing thickness. Parameter values for prototypes are also given for reader reproduction. 

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.

 

This paper presents tools and methods to design cylindrical and conical developable mechanisms from flat, planar patterns. Equations are presented that relate the link lengths and link angles of planar and spherical mechanisms to the dimensions in a flat configuration. These flat patterns can then be formed into curved, developable mechanisms. Guidelines are established to determine if a mechanism described by a flat pattern can exhibit intramobile or extramobile behavior. A developable mechanism can only potentially exhibit intramobile or extramobile behavior if none of the links extend beyond half of the flat pattern. The behavior of a mechanism can change depending on the location of the cut of the flat pattern. Different joint designs are discussed including lamina emergent torsional (LET) joints. Physical examples are presented.

 

Developable mechanisms conform to and emerge from developable, or specially curved, surfaces. The cylindrical developable mechanism can have applications in many industries due to the popularity of cylindrical or tube-based devices. Laparoscopic surgical devices in particular are widely composed of instruments attached at the proximal end of a cylindrical shaft. In this paper, properties of cylindrical developable mechanisms are discussed, including their behaviors, characteristics, and potential functions. One method for designing cylindrical developable mechanisms is discussed. Two example developable surgical devices that exemplify these behaviors, characteristics, and functions, along with the kinematic mechanisms comprising them, are discussed in detail.

 

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. Techniques are divided into four groups based on whether they are intrinsic or extrinsic to the origami pattern and whether they exhibit differentiable or non-differentiable energy storage behaviors. These categorizations can help designers select appropriate techniques for their application. The paper also contains design considerations and resources for several intrinsic techniques. Finally, two case studies are presented which use the OSIM and the technique guidelines to conceptualize stability in origami-based devices.

 

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.