Accepted Manuscript Not Copyedited Repelling-Screw Based Force Analysis of Origami Mechanisms Chen Qiu ASME Student Member Centre for Robotic Research King’s College London London, WC2R 2LS, UK Email: chen.qiu@kcl.ac.uk Ketao Zhang ASME Member Centre for Robotic Research Kings’s College London London, WC2R 2LS, UK Email: ketao.zhang@kcl.ac.uk Jian S. Dai ∗ ASME Fellow, Chair of Mechanisms and Robotics MoE Key Laboratory for Mechanism Theory and Equipment Design Tianjin University Tianjin, PR China Centre for Robotic Research King’s College London London, WC2R 2LS, UK Email: jian.dai@kcl.ac.uk ABSTRACT This paper provides an approach to model the reaction force of origami mechanisms when they are deformed. In this approach, an origami structure is taken as an equivalent redundantly-actuated mechanism, making it possible to apply the forward-force analysis to calculating the reaction force of the origami structure. Theoretical background is provided in the framework of screw theory, where the repelling screw is introduced to integrate the resistive torques of folded creases into the reaction-force of the whole origami mechanism. Two representative origami structures are then selected to implement the developed modeling approach, as the widely used waterbomb base and the waterbomb-based integrated parallel mechanism. With the proposed kinematic equivalent, their reaction forces are obtained and validated, presenting a ground for force analysis of origami-inspired mechanisms. 1 INTRODUCTION Origami is an art from China and Japan which folds a flat-sheet of paper into a 3D object with various shapes [1, 2]. With the growing interest from both academy and industry, the knowledge of origami in artistic discipline is being integrated in a wide range of research and engineering applications. Dai and Rees Jones [3, 4] used origami to investigate complex decorative cartons with their versatility in a design in the packaging industry. Howell et al. [5] discovered the link between origami and compliant mechanisms and used it to generate a new concept for nano-manufacture [6] and to develop novel compliant mechanical systems [7]. Song et al. [8] and Ma and You [9] utilized origami patterns to design thin-walled structures for energy absorption. For the thick-wall problem, Zirbel et al. [10] and Chen, Peng and You [11] addressed it in the origami folding process. Under axial loading, these structures are able to deform following origami patterns and smooth crushing process. Further, with the rapid development of 2D fabrication and micro-actuation technologies [12,13], passive origami structures have now been turned into active robots, such as a deformable wheel robot by Lee et al. [14], continuum manipulators by Onal et al. [15], Hoff et al. [16] and a robot end-effector by Zhang et al. [17] Among these applications, foldability is the primary concern of most developed origami structures. Foldability of an origami structure represents its ability to deform after it is folded, which is mainly determined by the motion of its crease pattern [18,19]. The design of crease-pattern draws a substantial amount of attention in the study of origami folding geometry ∗ Corresponding author. Jian S. Dai JMR-15-1122 1 Journal of Mechanisms and Robotics. Received May 31, 2015; Accepted manuscript posted August 27, 2015. doi:10.1115/1.4031458 Copyright (c) 2015 by ASME Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 09/09/2015 Terms of Use: http://www.asme.org/about-asme/terms-of-use