Origami-inspired integrated planar-spherical overconstrained mechanisms

This paper presents two integrated planar-spherical overconstrained mechanisms that are inspired and evolved from origami cartons with a crash-lock base. Investigating the crash-lock base of the origami cartons, the first overconstrained mechanism is evolved by integrating a planar four-bar linkage with two spherical linkages in the diagonal corners. The mechanism has mobility one and the overconstraint was exerted by the two spherical linkages. This mechanism is then evolved into another integrated planar-spherical overconstrained mechanism with two double-spherical linkages at the diagonal corners. The evolved mechanism has mobility one. It is interesting to find that the double-spherical linkage at the corner of this new mechanism is an overconstrained 6R linkage. The geometry evolution is presented and the constraint matrices of the mechanisms are formulated using screw-loop equations verifying mobility of the mechanisms. The paper further reveals the assembly conditions and geometric constraint of the two overconstrained mechanisms. Further, with mechanism decomposition, geometry and kinematics of the mechanisms are investigated with closed-form equations, leading to comparison of these two mechanisms with numerical simulation. The paper further proposes that the evolved overconstrained mechanism can in reverse lead to new origami folds and crease patterns. The paper hence not only lays the groundwork for kinematic investigation of origami-inspired mechanisms but also sheds light on the investigation of integrated overconstrained mechanisms.

[1]  Sergio Pellegrino,et al.  The Folding of Triangulated Cylinders, Part I: Geometric Considerations , 1994 .

[2]  C. H. Chiang,et al.  Kinematics of Spherical Mechanisms , 1988 .

[3]  Zhong You,et al.  A solution for folding rigid tall shopping bags , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[4]  H. Lipkin,et al.  Mobility of Overconstrained Parallel Mechanisms , 2006 .

[5]  Jian S. Dai,et al.  Dexterous Manipulation of Origami Cartons With Robotic Fingers Based on the Interactive Configuration Space , 2008 .

[6]  Jian S. Dai,et al.  Orientation capability of planar manipulators using virtual joint angle analysis , 2003 .

[7]  Tomohiro Tachi,et al.  Origamizing Polyhedral Surfaces , 2010, IEEE Transactions on Visualization and Computer Graphics.

[8]  Jian S. Dai,et al.  Synthesis of a Family of Regular Deployable Polyhedral Mechanisms (DPMs) , 2012, ARK.

[9]  Jian S. Dai,et al.  Mobility and Geometric Analysis of the Hoberman Switch-Pitch Ball and Its Variant , 2010 .

[10]  Jian S. Dai,et al.  From Origami to a New Class of Centralized 3-DOF Parallel Mechanisms , 2007 .

[11]  Jian S. Dai,et al.  Geometric analysis and synthesis of the metamorphic robotic hand , 2007 .

[12]  G. T. Bennett,et al.  The Skew Isogram Mechanism , 2022 .

[13]  Zhong You,et al.  Spatial 6R linkages based on the combination of two Goldberg 5R linkages , 2007 .

[14]  Yung-Way Liu,et al.  On the Rotatability of Spherical N-Bar Chains , 1994 .

[15]  Zhong You,et al.  Modelling rigid origami with quaternions and dual quaternions , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[16]  Jian S. Dai,et al.  A packaging robot for complex cartons , 2006, Ind. Robot.

[17]  Jian S. Dai,et al.  Kinematics and mobility analysis of carton folds in packing manipulation based on the mechanism equivalent , 2002 .

[18]  Larry L. Howell,et al.  Kinematic Representations of Pop-Up Paper Mechanisms , 2007 .

[19]  Jian S. Dai,et al.  Carton manipulation analysis using configuration transformation , 2002 .

[20]  Kenneth J. Waldron.  Hybrid overconstrained linkages , 1968 .

[21]  Jian S. Dai,et al.  Origami-based robotic paper-and-board packaging for food industry , 2010 .

[22]  Q. Liao,et al.  Constraint analysis on mobility change of a novel metamorphic parallel mechanism , 2010 .

[23]  Sergio Pellegrino,et al.  The Folding of Triangulated Cylinders, Part III: Experiments , 1996 .

[24]  J.Eddie Baker,et al.  Displacement–closure equations of the unspecialised double-Hooke's-joint linkage , 2002 .

[25]  Yan Chen,et al.  Axial crushing of thin-walled structures with origami patterns , 2012 .

[26]  Glen Mullineux,et al.  Carton erection using reconfigurable folder mechanisms. , 2009 .

[27]  J. Dai,et al.  Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds , 1998 .

[28]  Sergio Pellegrino,et al.  The Folding of Triangulated Cylinders, Part II: The Folding Process , 1994 .

[29]  Jian S. Dai,et al.  Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms , 2011 .

[30]  Larry L. Howell,et al.  Identifying links between origami and compliant mechanisms , 2011 .

[31]  Jian S. Dai,et al.  Topology and Constraint Analysis of Phase Change in the Metamorphic Chain and Its Evolved Mechanism , 2010 .