Metamorphic Oriblocks:Design and Kinematic Analysis of Metamorphic Oriblocks Constructed by Cutting and Linking Cylinders/Cones

doi:10.3901/JME.2023.13.024

Abstract

Abstract: Origami is the art of folding paper to make it have an excellent folding effect. In order to apply it to the field of robotics and mechanisms, researchers have successively proposed design methods of thick-panel origamis to enable origami to be widely used in the design of foldable mechanisms and reconfigurable mechanisms. Although the thick-panel origamis are kinematically equivalent to zero-thickness origamis, researchers only consider translating the creases to obtain rotational axes of thick-panel origamis in the design process. Therefore, all the rotational axes are parallel to the kinematically equivalent zero-thickness origamis when the thick-panel origamis are at their deployed configuration. Namely, all the rotational axes are parallel to a certain plane. To break through the limitation of the design method of thick-panel origamis, a general design method of metamorphic oriblocks was proposed based on cylinders and cones, which constructs general types of cylindrical and conical oriblocks. This research will also deduce the closure equations of these metamorphic oriblocks, and give examples to analyze the kinematics of different types of metamorphic oriblocks. The metamorphic oriblocks designed in this paper has potential application prospects in the fields of foldable mechanisms, over-constrained mechanisms and configurable mechanisms.

Key words: origami, thick-panel origami, metamorphic oriblocks, closure equations derivation, kinematic analysis

CLC Number:

TH112

JIA Guanglu, LI Bing, DAI Jiansheng. Metamorphic Oriblocks:Design and Kinematic Analysis of Metamorphic Oriblocks Constructed by Cutting and Linking Cylinders/Cones[J]. Journal of Mechanical Engineering, 2023, 59(13): 24-35.

References

[1] ZHANG Ketao,QIU Chen,DAI Jiansheng. An extensible continuum robot with integrated origami parallel modules[J]. Journal of Mechanisms and Robotics-Transactions of the ASME,2016,8(3):031010.
[2] LEAL E R,DAI Jiansheng. From origami to a new class of centralized 3-DOF parallel mechanisms[C]//ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 8:31st Mechanisms and Robotics Conference,Parts A and B. Las Vegas,Nevada,USA. Sep 4-7,2007:1183-1193.
[3] DAI J S,CALDWELL D G. Origami-based robotic paper-and-board packaging for food industry[J]. Trends in Food Science & Technology,2010,21(3):153-7.
[4] 戴建生,康熙,宋亚庆,等. 可重构机构与机器人[M]. 北京:高等教育出版社,2021. DAI Jiansheng,KANG Xi,SONG Yaqing,et al. Reconfigurable mechanisms and robots[M]. Beijing:Higher Education Press,2021.
[5] DAI Jiansheng,KANG Xi. Theoretical difficulties and research progresses of mechanism reconfiguration in mechanisms-evolution connotation,furcation principle,design synthesis and application of metamorphic mechanisms[J]. China Mechanical Engineering,2020,31(1):57-71.
[6] LANG R J,TOLMAN K A,CRAMPTON E B,et al. A review of thickness-accommodation techniques in origami-inspired engineering[J]. Applied Mechanics Reviews,2018,70(1):010805.
[7] CHEN Yan,PENG Rui,YOU Zhong. Origami of thick panels[J]. Science,2015,349(6246):396-400.
[8] DONG H,ASADI E,QIU C,et al. Geometric design optimization of an under-actuated tendon-driven robotic gripper[J]. Robotics and Computer-Integrated Manufacturing,2018,50:80-89.
[9] YELLOWHORSE A,LANG R J,TOLMAN K,et al. Creating linkage permutations to prevent self-intersection and enable deployable networks of thick-origami[J]. Scientific Reports,2018,8:12936.
[10] ZHANG Ketao,FANG Yuefa,FANG Hairong,et al. Geometry and constraint analysis of the three-spherical kinematic chain based parallel mechanism[J]. Journal of Mechanisms and Robotics-Transactions of the ASME,2010,2(3):031014.
[11] LI Yanbin,YIN Jie. Metamorphosis of three-dimensional kirigami-inspired reconfigurable and reprogrammable architected matter[J]. Materials Today Physics,2021,21:100511.
[12] LANG R J.,BROWN N,IGNAUT B,et al. Rigidly foldable thick origami using designed-offset linkages[J]. Journal of Mechanisms and Robotics-Transactions of the ASME,2020,12(2):021106.
[13] ZHAO Jingshan,WANG Jianyi,CHU Fulei,et al. Structure synthesis and statics analysis of a foldable stair[J]. Mechanism and Machine Theory,2011,46(7):998-1015.
[14] MISKIN M Z,DORSEY K J,BIRCAN B,et al. Graphene-based bimorphs for micron-sized,autonomous origami machines[J]. Proceedings of the National Academy of Sciences of the United States of America,2018,115(3):466-70.
[15] YANG Chenghao,GENG Shineng,WALKER I,et al. Geometric constraint-based modeling and analysis of a novel continuum robot with Shape Memory Alloy initiated variable stiffness[J]. The International Journal of Robotics Research,2020,39(14):1620-1634.
[16] ALLEN J T,MAGLEBY S P,HOWELL L L,et al. Quantifying and comparing surrogate fold motions in thick sheet materials[C]//ASME Conference on Smart Materials,Adaptive Structures and Intelligent Systems (SMASIS)/Symposium on Modeling,Simulation and Control of Adaptive Systems,Colorado Springs,Colorado,USA,Sep 21-23,2015.
[17] GHAFOOR A,DAI Jiansheng,DUFFY J. Stiffness modeling of the soft-finger contact in robotic grasping[J]. Journal of Mechanical Design,2004,126(4):646-656.
[18] KLETT Y,MUHS F,MIDDENDORF P,et al. Analysis of static and dynamic behavior of thick-walled paled elements[C]//ASME International Design Engineering Technical Conferences/Computers and Information in Engineering Conference,Anaheim,California,USA,Aug 18-21,2019.
[19] HARTMANN F,JAKESOVA M,MAO Guoyong,et al. Scalable microfabrication of folded parylene-based conductors for stretchable electronics[J]. Advanced Electronic Materials,2021,7(4):2001236.
[20] TACHI T. Rigid-foldable thick origami[J]. Origami,2011,5:253-64.
[21] ZIRBEL S A,LANG R J,THOMSON M W,et al. Accommodating thickness in origami-based deployable arrays[J]. Journal of Mechanical Design,2013,135(11):111005.
[22] EDMONDSON B J,LANG R J,MAGLEBY S P,et al. An offset panel technique for thick rigidly foldable origami[C]//ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference,New York,USA,Aug.17-20,2014:35606-14.
[23] CRAMPTON E B,MAGLEBY S,HOWELL L L. Realizing origami mechanisms from metal sheets[C]//ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference,Cleveland,Ohio,USA,Aug. 6-9,2017:1-10.
[24] DEFIGUEIREDO B P,PEHRSON N A,TOLMAN K A,et al. Origami-based design of conceal-and-reveal systems[J]. Journal of Mechanisms and Robotics-Transactions of the ASME,2018,11(2):020904.
[25] DEFIGUEIREDO B P,PEHRSON N A,TOLMAN K A,et al. Origami-based design of conceal-and-reveal systems[J]. Journal of Mechanisms and Robotics-Transactions of the ASME,2019,11(2):020904.
[26] LIU Shuai,WU Huajie,YANG Yang,et al. Parallel-motion thick origami structure for robotic design[C]//IEEE International Conference on Robotics and Automation (ICRA),Electr Network,May 31-Jun 15,2020:934-939.
[27] DAI Jiansheng,JONES J R. Kinematics and mobility analysis of carton folds in packing manipulation based on the mechanism equivalent[J]. Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science,2002,216(10):959-70.
[28] QIU C,AMINZADEH V,DAI Jiansheng. Kinematic analysis and stiffness validation of origami cartons[J]. Journal of Mechanical Design,2013,135(11):111004.
[29] DAI Jiansheng,CANNELLA F. Stiffness characteristics of carton folds for packaging[J]. Journal of Mechanical Design,2007,130(2):1.
[30] KU J S,DEMAINE E D. Folding flat crease patterns with thick materials[J]. Journal of Mechanisms and Robotics-Transactions of the ASME,2016,8:1-6.
[31] KU J S,DEMAINE E D. Rigid folding analysis of offset crease thick folding[C]//Proceedings of Iass Annual Symposia,Tokyo,September,2016:1-8.
[32] COLLINS C L. Kinematics of robot fingers with circular rolling contact joints[J]. Journal of Robotic Systems,2003,20(6):285-96.
[33] HALVERSON P A,HOWELL L L,MAGLEBY S P. Tension-based multi-stable compliant rolling-contact elements[J]. Mechanism and Machine Theory,2010,45(2):147-56.
[34] CAI Jianguo. Kinematic analysis of foldable plate structures with rolling joints[J]. Journal of Mechanisms and Robotics-Transactions of the ASME,2016,8(3):034502.
[35] LANG R J,NELSON T,MAGLEBY S,et al. Thick rigidly foldable origami mechanisms based on synchronized offset rolling contact elements[J]. Journal of Mechanisms and Robotics-Transactions of the ASME,2017,9(2):021013.
[36] CUI Lei,DAI jiansheng. Rolling contact in kinematics of multifingered robotic hands[J]. Advances in Robot Kinematics,2018(4):217-224.
[37] CUI Lei,SUN Jie,DAI Jiansheng. In-hand forward and inverse kinematics with rolling contact[J]. Robotica,2017,35(12):2381-2399.
[38] ARORA W J,NICHOL A J,SMITH H I,et al. Membrane folding to achieve three-dimensional nanostructures:Nanopatterned silicon nitride folded with stressed chromium hinges[J]. Applied Physics Letters,2006,88(5):1-3.
[39] JIA Guanglu,HUANG Hailin,GUO Hongwei,et al. Design of transformable hinged ori-block dissected from cylinders and cones[J]. Journal of Mechanical Design,2021,143(9):094501.
[40] 戴建生. 机构学与机器人学的几何基础与旋量代数[M]. 2版. 北京:高等教育出版社,2018. DAI Jiansheng. Geometrical foundations and screw algebra for mechanisms and robotics[M]. 2nd ed. Beijing:Higher Education Press,2018.
[41] 戴建生. 旋量代数与李群李代数[M]. 2版. 北京:高等教育出版社,2020. DAI Jiansheng. Screw algebra and Lie groups and Lie algebra[M]. 2nd ed. Beijing:Higher Education Press,2020.
[42] ZHANG Ketao,Dai Jiansheng. Screw-system-variation enabled reconfiguration of the Bennett plano-spherical hybrid linkage and its evolved parallel mechanism[J]. Journal of Mechanical Design,2015,137(6):062303.
[43] JIA Guanglu,HUANG Hailin,LI Bing,et al. Synthesis of a novel type of metamorphic mechanism module for large scale deployable grasping manipulators[J]. Mechanism and Machine Theory,2018,128:544-59.
[44] JIA Guanglu,LI Bing,HUANG Hailin,et al. Type synthesis of metamorphic mechanisms with scissor-like linkage based on different kinds of connecting pairs[J]. Mechanism and Machine Theory,2020,151:103848.
[45] JIA Guanglu,HUANG Hailin,WANG Sen,et al. Type synthesis of plane-symmetric deployable grasping parallel mechanisms using constraint force parallelogram law[J]. Mechanism and Machine Theory,2021,161:104330.
[46] 康熙,戴建生. 机构学中机构重构的理论难点与研究进展——变胞机构演变内涵、分岔机理、设计综合及其应用[J]. 中国机械工程,2020,31(1):57-71. KANG Xi,DAI Jiansheng. Theoretical difficulties and research progresses of mechanism reconfiguration in mechanisms-evolution connotation,furcation principle,design synthesis and application of metamorphic mechanisms[J]. China Mechanical Engineering,2020,31(1):57-71.
[47] KUO C H,DAI Jiansheng,YAN H S. Reconfiguration principles and strategies for reconfigurable mechanisms[C]//Proceedings of the 2009 ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots,ReMAR 2009,2009:1-7.
[48] ZHAO Chong,GUO Hongwei,ZHANG Dan,et al. Stiffness modeling of n(3RRlS) reconfigurable series-parallel manipulators by combining virtual joint method and matrix structural analysis[J]. Mechanism and Machine Theory,2020,152:103960.
[49] ZHAO Chong,WANG Ke,ZHAO Haifeng,et al. Kinematics,dynamics,and experiments of n(3rrls) reconfigurable series-parallel manipulators for capturing space noncooperative targets[J]. Journal of Mechanisms and Robotics-Transactions of the ASME,2022,14(6):1.
[50] ZHANG Y,GAO C,HUANG H,et al. Synthesis of one dof single-loop mechanisms with prismatic pairs based on the atlas method[C]//International Conference on Intelligent Robotics and Applications,2022:255-267.
[51] GAO C,ZHANG Y,KANG X,et al. Dynamic analysis of a three-fingered deployable metamorphic robotic grasper[J]. Mechanism and Machine Theory,2023,180:105140.
[52] ZHANG Y,HUANG H,MEI T,et al. Type synthesis of single-loop deployable mechanisms based on improved atlas method for single-DOF grasping manipulators[J]. Mechanism and Machine Theory,2022,169:104656.
[53] FU Z,SPYRAKOS P E,LIN Y H,et al. Analytical expressions of serial manipulator Jacobians and their high-order derivatives based on Lie theory[C]//Proceedings-IEEE International Conference on Robotics and Automation,2020:7095-100.
[54] CUI L,WANG D L,DAI Jiansheng. Kinematic geometry of circular surfaces with a fixed radius based on Euclidean invariants[J]. Journal of Mechanical Design,2009,131(10):101009.
[55] LIU H T,YAN Z B,XIAO J L. Pose error prediction and real-time compensation of a 5-DOF hybrid robot[J]. Mechanism and Machine Theory,2022,170:104737.