deployable, mechanical engineering, convex, cylindrical surfaces, torsion joints


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 air foil surface and a metallic deployable parabolic reflector

Original Publication Citation

Nelson, T.G., Pinto, L.M.B., Bruton, J.T., Deng, Z., Nelson, C.G., Howell, L.L., “Deployable Convex Generalized Cylindrical Surfaces Using Torsional Joints,” Journal of Mechanisms and Robotics,, Vol 13, 031101-1 to 031101-9, 2021 4 .

Document Type

Peer-Reviewed Article

Publication Date



Journal of Mechanisms and Robotics




Ira A. Fulton College of Engineering


Mechanical Engineering

University Standing at Time of Publication

Full Professor