Abstract
Scissor structures can meet different performance goals by actively changing their geometric configurations. This paper focuses on the inverse design problem of planar scissor structures with end constraints to obtain various forms without changing the span. Two strategies are proposed, one based on adding hinges and the other based on telescopic rods. The corresponding geometrical principles and constraint conditions are formulated. An inverse design framework from two predefined target shapes to design parameters is established, which consist of geometry optimization and mobility assessment. Seven case studies are used to illustrate the design method based on the two strategies. Results show potential for application of morphing planar scissor structure in practice.
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Abbreviations
- \(\varphi\) :
-
Relative angle between straight beams in the rigid arm
- A :
-
Rigid arm
- \(b^l,b^r\) :
-
Lengths of left and right straight beams in the rigid arm
- DOF:
-
Degree of freedom
- e, d :
-
Constraint coordinates of the right-most node
- F :
-
Optimization result, also called configuration error
- \(f_{P1},f_{P2}\) :
-
Two target shape functions
- \(j_k\) :
-
Node number of k-th hinge nodes
- l :
-
Length of straight beam for isometric arms
- m :
-
Number of hinge nodes
- n :
-
Number of scissor units
- o :
-
Internal connection node between the straight beams in the scissor unit
- \(p^l,p^r\) :
-
Left and right end nodes of rigid arms
- \(P_1,P_2\) :
-
Two target shapes in the optimization
- \(Q\left( X_j\right)\) :
-
Geometry parameter set of the j-th scissor unit
- t :
-
Configuration parameter, \(1 \le {t} \le 2\)
- X :
-
Scissor unit
- \(x_{o_j^1}^{P_t},y_{o_j^1}^{P_t}\) :
-
Coordinates of the node \(o_j^1\) at the target configuration \(P_t\)
References
Akgün Y, Gantes CJ, Kalochairetis KE, Kiper G (2010) A novel concept of convertible roofs with high transformability consisting of planar scissor-hinge structures. Eng Struct 32(9):2873–2883. https://doi.org/10.1016/j.engstruct.2010.05.006
Akgün Y, Gantes CJ, Sobek W, Korkmaz K, Kalochairetis K (2011) A novel adaptive spatial scissor-hinge structural mechanism for convertible roofs. Eng Struct 33(4):1365–1376. https://doi.org/10.1016/j.engstruct.2011.01.014
Alegria Mira L, Thrall AP, De Temmerman N (2014) Deployable scissor arch for transitional shelters. Autom Constr 43:123–131. https://doi.org/10.1016/j.autcon.2014.03.014
Alegria Mira L, Filomeno Coelho R, Thrall A, De Temmerman N (2015) Parametric evaluation of deployable scissor arches. Eng Struct 99:479–491. https://doi.org/10.1016/j.engstruct.2015.05.013
Ario I, Nakazawa M, Tanaka Y, Tanikura I, Ono S (2013) Development of a prototype deployable bridge based on origami skill. Autom Constr 32:104–111. https://doi.org/10.1016/j.autcon.2013.01.012
Arnouts LI, Massart TJ, De Temmerman N, Berke PZ (2019) Computational design of bistable deployable scissor structures: trends and challenges. J Int Assoc Shell Spatial Struct 60:19–34. https://doi.org/10.20898/j.iass.2019.199.031
Arnouts LIW, Massart TJ, De Temmerman N, Berke PZ (2020) Multi-objective optimisation of deployable bistable scissor structures. Autom Constr 114:103154. https://doi.org/10.1016/j.autcon.2020.103154
Bouleau E, Guscetti G (2016) Scissor mechanisms for transformable structures with curved shape. In: Advances in Architectural Geometry, Vdf Hochschulverlag AG an der ETH Zürich
Cai J, Xu Y, Feng J (2013) Kinematic analysis of Hoberman’s linkages with the screw theory. Mech Mach Theory 63:28–34. https://doi.org/10.1016/j.mechmachtheory.2013.01.004
Chikahiro Y, Ario I, Nakazawa M, Ono S, Holnicki-Szulc J, Pawlowski P, Graczykowski C, Watson A (2016) Experimental and numerical study of full-scale scissor type bridge. Autom Constr 71:171–180. https://doi.org/10.1016/j.autcon.2016.05.007
Chikahiro Y, Ario I, Pawlowski P, Graczykowski C, Holnicki-Szulc J (2019) Optimization of reinforcement layout of scissor-type bridge using differential evolution algorithm. Comput-Aided Civil Infrastruct Eng 34(6):523–538. https://doi.org/10.1111/mice.12432
Fenci GE, Currie NG (2017) Deployable structures classification: A review. Int J Space Struct 32(2):112–130. https://doi.org/10.1177/0266351117711290
Gantes C (1991) A design methodology for deployable structures, Ph.D. thesis, Massachusetts Institute of Technology
García-Mora CJ, Sánchez-Sánchez J (2020) Geometric method to design bistable and non-bistable deployable structures of straight scissors based on the convergence surface. Mech Mach Theory 146:103720. https://doi.org/10.1016/j.mechmachtheory.2019.103720
García-Mora CJ, Sánchez-Sánchez J (2021) The convergence surface method for the design of deployable scissor structures. Autom Constr 122:103488. https://doi.org/10.1016/j.autcon.2020.103488
Han B, Xu Y, Yao J, Zheng D, Li Y, Zhao Y (2019) Design and analysis of a scissors double-ring truss deployable mechanism for space antennas. Aerosp Sci Technol 93:105357. https://doi.org/10.1016/j.ast.2019.105357
Inoue F, Moroto R, Kurita K, Furuya N (2006) Development of adaptive structure by variable geometry truss (Application of movable monument in EXPO 2005), In: Proceedings of 23th International Symposium on Automation and Robotics in Construction, Tokyo, Japan, pp 704–709
Kaveh A, Abedi M (2019) Analysis and optimal design of scissor-link foldable structures. Eng Comput 35:593–604. https://doi.org/10.1007/s00366-018-0618-2
Kawaguchi K, Sato T, Yang X, Seo N (2019) Development of a deployable geodesic full sphere. J Int Assoc Shell Spatial Struct 60:35–46. https://doi.org/10.20898/j.iass.2019.199.033
Kim T-H, Suh J-E, Han J-H (2021) Deployable truss structure with flat-form storability using scissor-like elements. Mech Mach Theory 159:104252. https://doi.org/10.1016/j.mechmachtheory.2021.104252
Kokawa T, Hokkaido T (1997) Cable scissors arch-marionettic structure: structural morphology, towards the new millennium. In: International Conference of IASS. Nottingham, UK, pp 107–114
Krishnan S, Liao Y (2020) Geometric design of deployable spatial structures made of three-dimensional angulated members. J Architect Eng 26(3):04020029. https://doi.org/10.1061/(ASCE)AE.1943-5568.0000416
Lee D, Popovic Larsen O, Kim S-D (2013) Study of the connection joint for scissor-type deployable structure for the possible application in emergency evacuation shelter. In: Escrig F, Sánchez J (eds) New proposals for transformable architecture, engineering and design, pp 105–109
Li Y, Pellegrino S (2020) A theory for the design of multi-stable morphing structures. J Mech Phys Solids 136:103772. https://doi.org/10.1016/j.jmps.2019.103772
Lim J-S, Choi S-S, Jeong E-S, Kim S-D (2014) An experimental study on the application of shelter structure using deployable scissors systems. J Korean Assoc Spatial Struct 14(3):101–108. https://doi.org/10.9712/KASS.2014.14.3.101
Maden F, Korkmaz K, Akgün Y (2011) A review of planar scissor structural mechanisms: geometric principles and design methods. Architect Sci Rev 54(3):246–257. https://doi.org/10.1080/00038628.2011.590054
Meloni M, Cai J, Zhang Q, Sang-Hoon Lee D, Li M, Ma R, Parashkevov TE, Feng J (2021) Engineering origami: a comprehensive review of recent applications, design methods, and tools. Adv Sci 2000636
Phocas MC, Christoforou EG, Matheou M (2015) Design, motion planning and control of a reconfigurable hybrid structure. Eng Struct 101:376–385. https://doi.org/10.1016/j.engstruct.2015.07.036
Phocas MC, Christoforou EG, Dimitriou P (2020) Kinematics and control approach for deployable and reconfigurable rigid bar linkage structures. Eng Struct 208:110310. https://doi.org/10.1016/j.engstruct.2020.110310
Reksowardojo AP, Senatore G, Smith IF (2019) Experimental testing of a small-scale truss beam that adapts to loads through large shape changes. Front Built Environ 5:93. https://doi.org/10.3389/fbuil.2019.00093
Reksowardojo AP, Senatore G, Smith IF (2020) Design of structures that adapt to loads through large shape changes. J Struct Eng 146(5):04020068. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002604
Rhodes O (2013) Optimal design of morphing structures, Ph.D. thesis, Imperial College London
Roovers K, De Temmerman N (2017) Deployable scissor grids consisting of translational units. Int J Solids Struct 121:45–61. https://doi.org/10.1016/j.ijsolstr.2017.05.015
Sachse R, Bischoff M (2021) A variational formulation for motion design of adaptive compliant structures. Int J Numer Methods Eng 122(4):972–1000. https://doi.org/10.1002/nme.6570
Senatore G, Reksowardojo AP (2020) Force and shape control strategies for minimum energy adaptive structures. Front Built Environ 6:105. https://doi.org/10.3389/fbuil.2020.00105
Senatore G, Duffour P, Winslow P, Wise C (2017) Shape control and whole-life energy assessment of an ‘infinitely stiff’ prototype adaptive structure. Smart Mater Struct 27(1):015022. https://doi.org/10.1088/1361-665X/aa8cb8
Sleesongsom S, Bureerat S, Tai K (2013) Aircraft morphing wing design by using partial topology optimization. Struct Multidisc Optim 48(6):1109–1128. https://doi.org/10.1007/s00158-013-0944-3
Sun X, Jing X (2016) Analysis and design of a nonlinear stiffness and damping system with a scissor-like structure. Mech Syst Signal Process 66–67:723–742. https://doi.org/10.1016/j.ymssp.2015.05.026
Van Mele T (2008) Scissor-hinged retractable membrane roofs, Ph.D. thesis, Vrije Universiteit Brussel
Wang Y, Senatore G (2020) Minimum energy adaptive structures-all-in-one problem formulation. Comput Struct 236:106266. https://doi.org/10.1016/j.compstruc.2020.106266
Wang Y, Senatore G (2021) Design of adaptive structures through energy minimization: extension to tensegrity. Struct Multidisc Optim 64(3):1079–1110. https://doi.org/10.1007/s00158-021-02899-y
Weaver-Rosen JM, Leal PB, Hartl DJ, Malak RJ (2020) Parametric optimization for morphing structures design: application to morphing wings adapting to changing flight conditions. Struct Multidisc Optim 62(6):2995–3007. https://doi.org/10.1007/s00158-020-02643-y
Yang Y, Peng Y, Pu H, Chen H, Ding X, Chirikjian GS, Lyu S (2019) Deployable parallel lower-mobility manipulators with scissor-like elements. Mech Mach Theory 135:226–250. https://doi.org/10.1016/j.mechmachtheory.2019.01.013
Zhang R, Wang S, Chen X, Ding C, Jiang L, Zhou J, Liu L (2015) Designing planar deployable objects via scissor structures. IEEE Trans Visual Comput Graphics 22(2):1051–1062. https://doi.org/10.1109/TVCG.2015.2430322
Zhang Q, Pan N, Meloni M, Lu D, Cai J, Feng J (2021) Reliability analysis of radially retractable roofs with revolute joint clearances. Reliab Eng Syst Saf 208:107401. https://doi.org/10.1016/j.ress.2020.107401
Zhao J, Chu F, Feng Z (2009) The mechanism theory and application of deployable structures based on SLE. Mech Mach Theory 44(2):324–335. https://doi.org/10.1016/j.mechmachtheory.2008.03.014
Zhao D, Zhao J, Yan Z (2016) Planar deployable linkage and its application in overconstrained lift mechanism. J Mech Robot 8(2):021022. https://doi.org/10.1115/1.4032096
Acknowledgements
The work presented in this article was supported by the National Natural Science Foundation of China (Grant Nos. 51822805, 51878147, and U1937202), Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJKY19_0091), Scientific Research Foundation of Graduate School of Southeast University (YBPY2016) and the China Scholarship Council. We would like to thank the anonymous reviewers for their helpful remarks.
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The MATLAB codes of the proposed methods are available upon request to the first and corresponding authors.
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Zhang, Q., Jia, W., Lee, D.Sh. et al. Inverse design of planar morphing scissor structures with end constraints. Struct Multidisc Optim 65, 70 (2022). https://doi.org/10.1007/s00158-022-03175-3
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DOI: https://doi.org/10.1007/s00158-022-03175-3