Space-deployable mechanisms can be used as supporting structures for large-diameter antennas in space engineering. This study proposes a novel method for constructing the surface design of space reflector antennas based on polar scissor units. The concurrency and deployability equations of the space scissor unit with definite surface constraints are derived using the rod and vector methods. Constraint equations of the spatial transformation for space n-edge polar scissor units are summarized. A new closed-loop deployable structure, called the polar scissor deployable antenna (PSDA), is designed by combining planar polar scissor units with spatial polar scissor units. The over-constrained problem is solved by releasing the curve constraint that locates at the end-point of the planar scissor mechanism. Kinematics simulation and error analysis are performed. The results show that the PSDA can effectively fit the paraboloid of revolution. Finally, deployment experiments verify the validity and feasibility of the proposed design method, which provides a new idea for the construction of large space-reflector antennas.
[1] C Shi, H Guo, M Li, et al. Conceptual configuration synthesis of line-foldable type quadrangular prismatic deployable unit based on graph theory. Mechanism and Machine Theory, 2018, 121: 563-582.
[2] X Song, Z Deng, H Guo, et al. Networking of Bennett linkages and its application on deployable parabolic cylindrical antenna. Mechanism and Machine Theory, 2017, 109: 95-125.
[3] S Yang, Y Li. Kinematic analysis of deployable parallel mechanisms. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2019: 095440621882532.
[4] S Yuan, B Yang. The fixed nodal position method for form finding of high-precision lightweight truss structures. International Journal of Solids and Structures, 2019, 161: 82-95.
[5] T Takano, K Miura, M Natori, et al. Deployable antenna with 10-m maximum diameter for space use. IEEE Transactions on Antennas and Propagation, 2004, 52(1): 2-11.
[6] Y Gu, J Du, D Yang, et al. Form-finding design of electrostatically controlled deployable membrane antenna based on an extended force density method. Acta Astronautica, 2018, 152: 757-767.
[7] R Nie, B He, D H Hodges, et al. Integrated form finding method for mesh reflector antennas considering the flexible truss and hinges. Aerospace Science and Technology, 2019, 84: 926-937.
[8] R Liu, H Guo, R Liu, et al. Shape accuracy optimization for cable-rib tension deployable antenna structure with tensioned cables. Acta Astronautica, 2017, 140: 66-77.
[9] T Langbecker. Kinematic analysis of deployable scissor structures. International Journal of Space Structures, 1999, 14(1): 1-15.
[10] E P Piñero. Project for a mobile theatre. Architectural Design, 1961, 12(1): 154-155.
[11] F Escrig, J P Valcarcel. Great size umbrellas with expendable bar structures. Proceedings of the 1st International Conference on Lightweight Structures in Architecture, 1986: 676-681.
[12] F Maden, K Korkmaz, Y Akgün. A review of planar scissor structural mechanisms: geometric principles and design methods. Architectural Science Review, 2011, 54(3): 246-257.
[13] F Escrig. Expandable space frame structures. Third International Conference on Space Structures, Guildford, UK, 1984: 845-850.
[14] R Liu, H Guo, R Liu, et al. Structural design and optimization of large cable–rib tension deployable antenna structure with dynamic constraint. Acta Astronautica, 2018, 151: 160-172.
[15] Y Chikahiro, I Ario, P Pawlowski, et al. Optimization of reinforcement layout of scissor-type bridge using differential evolution algorithm. Computer-Aided Civil and Infrastructure Engineering, 2019, 34(6): 523-538.
[16] E Medzmariashvili, Sh Tserodze, N Tsignadze, et al. A new design variant of the large deployable space reflector. Earth and Space 2006-10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments, Houston, United States, March 5-8, 2006: 6.
[17] W Bettini, J Quirant, J Averseng, et al. Self-deployable geometries for space applications. Journal of Aerospace Engineering, 2019, 32(1): 1-12.
[18] C Q Gao, H L Huang, B Li, et al. Design of a truss-shaped deployable grasping mechanism using mobility bifurcation. Mechanism and Machine Theory, 2019, 139: 346-358.
[19] L Alegria Mira, R Filomeno Coelho, A P Thrall, et al. Parametric evaluation of deployable scissor arches. Engineering Structures, 2015, 99: 479-491.
[20] L I W Arnouts, T J Massart, N De Temmerman, et al. Computational modelling of the transformation of bistable scissor structures with geometrical imperfections. Engineering Structures, 2018, 177: 409-420.
[21] B Li, S M Wang, C J Zhi, et al. Analytical and numerical study of the buckling of planar linear array deployable structures based on scissor-like element under its own weight. Mechanical Systems and Signal Processing, 2017, 83: 474-488.
[22] A Koumar, T Tysmans, N D Merman. Structural design of barrel vault shaped scissor structures for disaster relief. Journal of the International Association for Shell and Spatial Structures, 2018, 59(3): 171-182.
[23] Y Akgün, C J Gantes, K E Kalochairetis, et al. A novel concept of convertible roofs with high transformability consisting of planar scissor-hinge structures. Engineering Structures, 2010, 32(9): 2873-2883.
[24] S Lu, D Zlatanov, X Ding, et al. A new family of deployable mechanisms based on the Hoekens linkage. Mechanism and Machine Theory, 2014, 73: 130-153.
[25] A S K Kwan. Parabolic pantographic deployable antenna (PDA). International Journal of Space Structures, 1995, 10(4): 195-203.
[26] Z You. Deployable structure of curved profile for space antennas. Journal of Aerospace Engineering, 2000, 13(4): 139-143.
[27] Z You, S Pellegrino. Cable-stiffened pantographic deployable structures.Ⅱ-Mesh reflector. AIAA Journal, 1997, 35(8): 1348-1355.
[28] K Roovers, N De Temmerman. Deployable scissor grids consisting of translational units. International Journal of Solids and Structures, 2017, 121: 45-61.
[29] K Roovers, N De Temmerman. Geometric design of deployable scissor grids consisting of generalized polar units. Journal of the International Association for Shell and Spatial Structures, 2017, 58(3): 227-238.
[30] Y Chen, L Fan, J Feng. Kinematic of symmetric deployable scissor-hinge structures with integral mechanism mode. Computers & Structures, 2017, 191: 140-152.
[31] C Hoberman. Reversibly expandable doubly-curved truss structure: US, 4942700, 1990-07-24.
