{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T13:38:08Z","timestamp":1762868288538,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,14]],"date-time":"2020-09-14T00:00:00Z","timestamp":1600041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51175455"],"award-info":[{"award-number":["51175455"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Symmetry has been widely and deeply researched in basic science, and many mature results have been obtained so far. However, the widespread existence of symmetry in applied science is not in direct proportion to the attention it has received. Through a large number of examples studies, almost all mechanical structures are found to have symmetry, and most of them have the characteristics of point group symmetry. Therefore, the concept of point group symmetry in crystallography was extended to the field of machinery and adjusted according to the mechanical structures. First of all, the classification of mechanical point group symmetry is proposed, and how point group symmetry is applied in machinery is illustrated with examples. Then, the requirements of symmetry are analyzed and compared. Furthermore, the data mining software RapidMiner is used to mine the association rules between requirements and symmetry. Based on the mining results, the four selection principles of point group symmetry are summarized to provide ideas for structure design. Finally, a new type of gear pump with radial force balancing is invented by comprehensively using the mining results and selection principles.<\/jats:p>","DOI":"10.3390\/sym12091507","type":"journal-article","created":{"date-parts":[[2020,9,14]],"date-time":"2020-09-14T09:04:53Z","timestamp":1600074293000},"page":"1507","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Concept System and Application of Point Group Symmetry in Mechanical Structure Design"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8057-014X","authenticated-orcid":false,"given":"Xiuming","family":"Chen","sequence":"first","affiliation":[{"name":"State Key Lab of Computer Aided Design and Computer Graphics, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Qingying","family":"Qiu","sequence":"additional","affiliation":[{"name":"State Key Lab of Computer Aided Design and Computer Graphics, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Chao","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Lab of Computer Aided Design and Computer Graphics, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Peien","family":"Feng","sequence":"additional","affiliation":[{"name":"State Key Lab of Computer Aided Design and Computer Graphics, Zhejiang University, Hangzhou 310027, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Rosen, J. (2008). Symmetry Rules: How Science and Nature Are Founded on Symmetry, Springer.","DOI":"10.1007\/978-3-540-75973-7"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.3390\/sym2031591","article-title":"Asymmetry, symmetry and beauty","volume":"2","author":"Sabelli","year":"2010","journal-title":"Symmetry"},{"key":"ref_3","first-page":"1","article-title":"Observability and Controllability of Nonlinear Networks: The Role of Symmetry","volume":"5","author":"Whalen","year":"2015","journal-title":"Phys. Rev. X"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1021\/ja9530782","article-title":"On the Question of the Symmetry of Formally Symmetrical \u03c0-(Allyl) palladium Cationic Intermediates in Allylic Alkylations","volume":"118","author":"Trost","year":"2016","journal-title":"J. Am. Chem. Soc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.sbi.2015.05.004","article-title":"Internal symmetry in protein structures: Prevalence, functional relevance and evolution","volume":"32","author":"Balaji","year":"2015","journal-title":"Curr. Opin. Struc. Biol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1163\/156853012X631379","article-title":"Animal Cultures, Subjectivity, and Knowledge: Symmetrical Reflections beyond the Great Divide","volume":"20","author":"Nimmo","year":"2012","journal-title":"Soc. Anim."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Montoya, F.G., Ba\u00f1os, R., Alcayde, A., and Manzano-Agugliaro, F. (2019). Symmetry in Engineering Sciences. Symmetry, 11.","DOI":"10.3390\/sym11060797"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1016\/j.jmva.2010.03.010","article-title":"General canonical correlations with applications to group symmetry models","volume":"101","author":"Andersson","year":"2010","journal-title":"J. Multivar. Anal."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.physletb.2011.02.054","article-title":"The Double Cover of the Icosahedral Symmetry Group and Quark Mass Textures","volume":"698","author":"Everett","year":"2011","journal-title":"Phys. Lett. B"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1002\/nme.2576","article-title":"Group-theoretic exploitations of symmetry in computational solid and structural mechanics","volume":"79","author":"Zingoni","year":"2010","journal-title":"Int. J. Meth. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1002\/(SICI)1096-987X(19980130)19:2<168::AID-JCC9>3.0.CO;2-S","article-title":"Symmetry groups for unit cells in solids","volume":"19","author":"Stewart","year":"2015","journal-title":"J. Comput. Chem."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1134\/S2079086411030029","article-title":"The application of group theory to the description of pseudosymmetry","volume":"1","author":"Gelashvili","year":"2011","journal-title":"Biol. Bull."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s00004-001-0022-9","article-title":"Group Theory and Architecture","volume":"3","author":"Leyton","year":"2001","journal-title":"Nexus Netw. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s11071-018-4192-3","article-title":"Approximate symmetry group classification for a nonlinear fractional filtration equation of diffusion-wave type","volume":"93","author":"Lukashchuk","year":"2018","journal-title":"Nonlinear Dynam."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Pahl, G., Beitz, W., Feldhusen, J., and Grote, K.H. (2007). Engineering Design: A Systematia Approach, Springer.","DOI":"10.1007\/978-1-84628-319-2"},{"key":"ref_16","unstructured":"Sun, N.P. (1998). Axiomatic Design: Advanced and Applications, Oxford University Press."},{"key":"ref_17","unstructured":"Altshuller, G.S. (1988). Creativity as an Exact Science: The Theory of Inventive Problem Solving, Gordon and Breach Publisher."},{"key":"ref_18","unstructured":"Barrenscheen, J. (1990). Systematic Exploitation of Symmetrical Properties in Construction. [Ph.D. Thesis, Technical University of Braunschweig]."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.cad.2009.10.001","article-title":"Detecting design intent in approximate CAD models using symmetry","volume":"42","author":"Li","year":"2010","journal-title":"Comput. Aided Des."},{"key":"ref_20","first-page":"490","article-title":"Symmetry detection algorithm in design for assembly","volume":"48","author":"Zheng","year":"2008","journal-title":"J. Tsinghua Univ."},{"key":"ref_21","first-page":"299","article-title":"Vibration analysis of toothed gear with cyclic symmetry modelling","volume":"25","author":"Noga","year":"2012","journal-title":"Vib. Phys. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1111\/j.1467-8659.2011.01885.x","article-title":"Symmetry Hierarchy of Man-Made Objects","volume":"30","author":"Wang","year":"2011","journal-title":"Comput. Graph. Forum"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"554","DOI":"10.3390\/sym2020554","article-title":"Symmetry as an Intrinsically Dynamic Feature","volume":"2","author":"Gesu","year":"2010","journal-title":"Symmetry"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/LSP.2016.2632167","article-title":"LBP-Structure Optimization with Symmetry and Uniformity Regularizations for Scene Classification","volume":"24","author":"Ren","year":"2016","journal-title":"IEEE Signal. Proc. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s11071-006-0749-7","article-title":"Symmetry, optima and bifurcations in structural design","volume":"43","author":"Domokos","year":"2006","journal-title":"Nonlinear Dynam."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"118","DOI":"10.3901\/JME.2017.13.118","article-title":"Assembly efficiency prediction model of parts based on multi symmetry features","volume":"53","author":"Qiu","year":"2017","journal-title":"J. Mech. Eng."},{"key":"ref_27","unstructured":"Gu, C.S., Sun, Y.C., Yang, C.J., and Cao, H.J. (2017). Novel Tailgate Limiting Stopper Assembly. (201510332118.9), Chinese Ptatent."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"M\u00fcller, U. (2013). Symmetry Relationships between Crystal Structures: Applications of Crystallographic Group Theory in Crystal Chemistry, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780199669950.001.0001"},{"key":"ref_29","unstructured":"Li, X.C., and Li, X.B. (1996). Reasonable Design Atlas of Mechanical Structure, Shanghai Scientific & Technical Publishers."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"133","DOI":"10.3901\/JME.2011.12.133","article-title":"Effects of Impeller Type on Pressure Fluctuations in Double-suction Centrifugal Pump","volume":"47","author":"Yao","year":"2011","journal-title":"J. Mech. Eng."},{"key":"ref_31","unstructured":"Zhang, X.H., Deng, P.F., and Luo, W.G. (2016). Multidirectional Vibration Energy Collection Device with Replaceable Energy Collection Module. (201520704388.3), Chinese Ptatent."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Kotu, V., and Deshpande, B. (2014). Predictive Analytics and Data Mining: Concepts and Practice with Rapidminer, Elsevier.","DOI":"10.1016\/B978-0-12-801460-8.00013-6"},{"key":"ref_33","unstructured":"Yang, Z.Q., Fei, Y.Z., and Liu, H.G. (2017). Asymmetrical Lifting Traverse. (201510481201.2), Chinese Ptatent."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"580","DOI":"10.4028\/www.scientific.net\/AMM.226-228.580","article-title":"Double-acting air-oil intensifier driven by twin roller piston air cylinder","volume":"220\u2013223","author":"Li","year":"2012","journal-title":"Appl. Mech. Mater."},{"key":"ref_35","unstructured":"Chang, Y., Zhu, S.S., Hu, M.W., Guo, X.L., and Yang, Y.C. (2017). A Gear Pump with Radial Force Balance. (201510962801.0), Chinese Ptatent."},{"key":"ref_36","unstructured":"Qiu, Q.Y., Chen, X.M., Feng, P.E., and Yang, C. (2020). A Multi-Wheel Linkage Gear Pump with Radial Force Balance. (201920869252.6), Chinese Ptatent."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/9\/1507\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:09:44Z","timestamp":1760177384000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/9\/1507"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,14]]},"references-count":36,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["sym12091507"],"URL":"https:\/\/doi.org\/10.3390\/sym12091507","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,9,14]]}}}