Optimal Curve Fitting for Serial Chain in Six-Crease Origami Unit

Abstract

Origami-inspired structures have been widely used in aerospace and robotics for three-dimensional (3D) symmetrical configurations using crease-symmetrical origami basic patterns. These patterns offer advantages in repeatable and systematic modeling and mass production. However, few studies have focused on 3D nonsymmetrical structures using symmetrical origami basic patterns due to their structure complexity, limiting their application. Therefore, we aim to analyze the folding behavior in 3D nonsymmetrical structures using a 6-crease symmetry origami base pattern. To achieve this goal, we first focus on behavior in a two-dimensional (2D) plane. This article presents a scheme for the behavior of origami units with an optimal curve-fitting algorithm. The curve can be any 2D space curve. The fitting curve, constructed by numerical analysis and an optimal approaching scheme, can satisfy error requirements and retain foldable origami unit features. The article verifies the feasibility of the curve-fitting scheme by presenting two curve examples, including a quadratic curve and a sin wave function. The results show that the fitting error is reduced by 99% when no boundary conditions are applied. This research provides valuable insights into understanding origami unit kinematic optimization through forward and inverse kinematics. It offers potential applications in the engineering design of foldable structures and precision origami-inspired mechanism, thereby opening avenues for further exploration of complex origami structures and their applications in emerging technologies.