There is an increasing need for compact mechanical systems that can accomplish sophisticated tasks. Technologies like ortho-planar and lamina emergent mechanisms (LEMs) have been developed to satisfy needs like these by stowing in planar sheets from which they emerge to perform their function. They can be compact, lightweight, monolithic, scalable, and can withstand harsh environments. They are limited, however, by their base element---planar surfaces. Applications requiring these advantages often include curved surfaces, like aircraft wings, needles, and automotive bodies. In this research, developable mechanisms are presented as a solution to satisfy the need for mechanisms that can conform to or emerge from curved surfaces. Foundational principles which enable designers to leverage the advantages of developable mechanisms are described herein.Developable mechanisms result from the union of mechanisms and developable surfaces. Developable (flattenable) surfaces act as a fitting medium because of their particular advantages in manufacturability and how well they accompany four-link, revolute joint (4R) mechanisms. The definition, including specific qualifying criteria, for developable mechanisms is given. Certain types of mechanisms and classes of developable surfaces can be combined to satisy that criteria. Developable mechanism sub-classes are defined as planar, cylindrical, conical and tangent developable mechanisms. It is shown that planar and spherical mechanisms can be used to create cylindrical and conical developable mechanisms, respectively. The Bennett and other 7R mechanisms can be used for tangent developable mechanisms. Steps for developable mechanism creation are presented, and several physical prototypes are provided to demonstrate feasibility.The cylindrically curved Lamina Emergent Torsional (LET) joint is offered as an enabling technology for producing compliant developable mechanisms. A mathematical model predicting force-deflection and stress behavior is provided and verified. The relationship between stiffness and strain energy storage for curved sheet materials with incorporated LET joints is explored. Material shape factors are used to derive an effective modulus of elasticity and an effective modulus of resilience, which are compared with original values on an Ashby plot. While there is a decrease in the modulus of resilience, there is a much more significant decrease in the modulus of elasticity. A material performance index is provided as an example for determining suitable materials for a given stiffness-reduction application. It is shown that the cylindrically curved LET joint makes it possible to create highly flexible joints that maintain much of their energy storage capability in curved sheet materials.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering

Date Submitted


Document Type





Developable surfaces, mechanisms, kinematics, compliant, lamina emergent