Two-Configuration Synthesis of Origami-Guided Planar, Spherical and Spatial Revolute–Revolute Chains

This paper presents a topological and dimensional kinematic synthesis methodology that can be used to constrain the movement of kinematic planar, spherical, and spatial revolute–revolute dyads (RR dyads). The approach is inspired by a subcategory of origami called rigid origami, which deals with highly overconstrained spatial deployable linkages. An example is the Miura-ori folding pattern used to deploy solar panels in space. In addition to this application, this linkage also provides an interesting way to constrain general RR dyads so that they perform a single DOF motion. Here, these mechanisms are called origami-guided RR chains, and computer aided design models (CAD) of the planar, spherical and spatial type are presented. The dimensional synthesis approach allows us to constrain consecutive links using R or C joints so that the links satisfy two arbitrarily predefined task positions. This leads to what we call the two-configuration synthesis of linkages, and we examine a concrete synthesis procedure for an origami-guided spatial RR chain, which is also built using rapid prototyping. The procedure actually combines the two-configuration synthesis approach with the synthesis of the spatial TS dyad, and the paper provides an outlook on further ways to apply the two-configuration synthesis and also to synthesize the origami-guided RR chains.

[1]  Alba Perez Gracia,et al.  Kinematic Synthesis of Multi-Fingered Robotic Hands for Finite and Infinitesimal Tasks , 2012, ARK.

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

[3]  Gim Song Soh,et al.  The Kinematic synthesis of mechanically constrained planar 3R chains , 2006 .

[4]  Simon D. Guest,et al.  Origami folding: A Structural Engineering Approach , 2011 .

[5]  Vijay Kumar,et al.  Kinematic and Kinetostatic Synthesis of Planar Coupled Serial Chain Mechanisms , 2002 .

[6]  Alba Perez,et al.  Dimensional synthesis of Bennett linkages , 2003 .

[7]  Thomas C. Hull.  The Combinatorics of Flat Folds: a Survey , 2013 .

[8]  Tomohiro Tachi.  Geometric Considerations for the Design of Rigid Origami Structures , 2010 .

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

[10]  Manfred Husty,et al.  A NEW METHOD FOR THE SYNTHESIS OF BENNETT MECHANISMS , 2005 .

[11]  Simon D. Guest,et al.  A plane symmetric 6R foldable ring , 2013 .

[12]  Sergio Pellegrino,et al.  Origami Sunshield Concepts for Space Telescopes , 2013 .

[13]  Tomohiro Tachi.  Generalization of rigid foldable quadrilateral mesh origami , 2009 .

[14]  J. Michael McCarthy,et al.  The Synthesis of Planar 4R Linkages With Three Task Positions and Two Specified Velocities , 2005 .

[15]  Thomas C. Hull,et al.  Modelling the folding of paper into three dimensions using affine transformations , 2002 .

[16]  J. Michael McCarthy,et al.  Introduction to theoretical kinematics , 1990 .

[17]  David A. Huffman,et al.  Curvature and Creases: A Primer on Paper , 1976, IEEE Transactions on Computers.

[18]  Zongquan Deng,et al.  Synthesis of Deployable/Foldable Single Loop Mechanisms With Revolute Joints , 2011 .

[19]  Lung-Wen Tsai,et al.  A note on the design of revolute-revolute cranks , 1973 .

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

[21]  J.Eddie Baker.  A collapsible network of similar pairs of nested Bennett linkages , 2013 .

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

[23]  Yan Chen,et al.  Folding a Patterned Cylinder by Rigid Origami , 2011 .

[24]  J. Michael McCarthy,et al.  Dual quaternion synthesis of constrained robotic systems , 2003 .

[25]  Jian S. Dai,et al.  Geometry and kinematic analysis of an origami-evolved mechanism based on artmimetics , 2009, 2009 ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots.

[26]  Carlos E. Castro,et al.  Design and Fabrication of DNA Origami Mechanisms and Machines , 2012 .

[27]  Koryo Miura,et al.  Method of Packaging and Deployment of Large Membranes in Space , 1985 .

[28]  Constantinos Mavroidis,et al.  Solving the Geometric Design Problem of Spatial 3R Robot Manipulators Using Polynomial Homotopy Continuation , 2002 .

[29]  Jian S. Dai,et al.  Kinematics of an Overconstrained 6R Linkage with 2-Fold Rotational Symmetry , 2012, ARK.

[30]  McCarthy,et al.  Geometric Design of Linkages , 2000 .