Rigidly Foldable, origami based, offset linkages, mechanical engineering


We present new families of thick origami mechanisms that achieve rigid foldability and parallel stacking of panels in the flat-folded state using linkages for some or all of the hinges between panels. A degree-four vertex results in a multi-loop eight-bar spatial mechanism that can be analyzed as separate linkages. The individual linkages are designed so that they introduce offsets perpendicular to the panels that are mutually compatible around each vertex. This family of mechanisms offers the unique combination of a planar unfolded state, parallel-stacked panels in the flat folded state, and kinematic single-degree-of-freedom motion from the flat- unfolded to the flat-folded state. The paper develops the mathematics defining the necessary offsets, beginning with a symmetric bird’s-foot vertex, then shows that the joints can be developed for asymmetric flat-foldable systems. Although in the general case there is no guarantee of achieving perfect kinematic motion, we show that for many cases of interest, the deviation is a tiny fraction of the plate thickness. Mechanical realizations of several examples are presented.

Original Publication Citation

Lang, R.J., Brown, N., Ignaut, B., Magleby, S.P., and Howell, L.L., “Rigidly Foldable Thick Origami Using Designed-Offset Linkages, 7 ” Journal of Mechanisms & Robotics, Vol. 12, No. 2, 021106-1 to 021106-13, 2020.

Document Type

Peer-Reviewed Article

Publication Date



Journal of Mechanisms & Robotics




Ira A. Fulton College of Engineering


Mechanical Engineering

University Standing at Time of Publication

Full Professor