Finding Rigid Body Modes of Rigid-Foldable Origami Through the Simulation of Vertex Motion

Abstract

Designing structures through the means of origami brings many advantages for engineering applications. In current research, the underlying origami principle is often selected based on experience out of a range of known patterns and then manually altered to fit the design problem. This tedious and time-consuming procedure, if automated through computational tools, has the potential to facilitate the design of origami engineering applications. This however requires efficient kinematic simulation of origamis that is also able to accommodate to design requirements specific to foldable structures. In this paper, a simulator is implemented that is able to model the motion of origami vertices without the need for mountain-valley assignments and with a path of deployment as activation. The formulation of constraint equations through these vertex positions does not restrict the system to certain folding configurations, which is why the approach is able to detect different rigid body modes resulting from single activations. Finding rigid body modes can be beneficial for the search of design alternatives conforming to certain input requirements. The results of the simulation show promise for the incorporation of the simulator within an automated procedure for the design of origamis.

A Computational Design Synthesis Method for the Generation of Rigid Origami Crease Patterns

“…2, the authors addressed some of the above complexities by presenting the Principle of Three Units (PTU) that leads to an analytical, intrinsic condition for the rigid foldability of single degree-n vertices, where n is the number of crease lines incident to a vertex. In addition to this condition, the PTU yields an analytical kinematic model for single vertices to which the RBMs are inputs rather than the results of simulation [53]. The PTU [52] further offers guidelines for the generation of crease patterns whose kinematic motion can be explicitly determined.…”