developable mechanisms, deployable mechanisms, kinematics, curved origami


The trend toward smaller mechanism footprints and volumes, while maintaining the ability to perform complex tasks, presents the opportunity for exploration of hypercompact mechanical systems integrated with curved surfaces. Developable surfaces are shapes that a flat sheet can take without tearing or stretching, and they represent a wide range of manufactured surfaces. This work introduces “developable mechanisms” as devices that emerge from or conform to developable surfaces. They are made possible by aligning hinge axes with developable surface ruling lines to enable mobility. Because rigid-link motion depends on the relative orientation of hinge axes and not link geometry, links can take the shape of the corresponding developable surface. Mechanisms are classified by their associated surface type, and these relationships are defined and demonstrated by example. Developable mechanisms show promise for meeting unfilled needs using systems not previously envisioned.

Original Publication Citation

Nelson, T., Zimmerman, T., Magleby, S., Lang, R., and Howell, L., “Developable Mechanisms on Developable Surfaces,” Science Robotics, Vol. 4, Issue 2, DOI: 10.1126/scirobotics.aau5171, 2019.

Document Type

Peer-Reviewed Article

Publication Date


Permanent URL


Science Robotics




Ira A. Fulton College of Engineering and Technology


Mechanical Engineering

University Standing at Time of Publication

Full Professor