A position analysis of coupled spherical mechanisms found in action origami

• An origami vertex is equivalent to a spherical change-point mechanism.
• Most action origami achieves motion through coupled systems of spherical mechanisms.
• The position analysis of an origami vertex includes output angle and coupler path.
• A method for analyzing coupled systems of spherical mechanisms is proposed.
• The results can help create compact, deployable mechanisms for application.

Origami has been previously utilized in design to create deployable systems. Action origami, origami designed to move, has the ability to deploy to a larger state and have motion in the deployed state. The majority of action origami achieves motion through coupled systems of spherical mechanisms. An origami vertex, the point at which folds converge, is shown to be equivalent to a spherical change-point mechanism. A position analysis of an origami vertex is presented, resulting in a relationship between input and output angles as well as the path of the coupler link. A method for analyzing coupled systems of repeated spherical mechanisms is proposed and demonstrated using two examples. A better understanding of the kinematics of action origami increases the ability of designers to create compact, deployable mechanisms for use in packaging, space, and medical industries.