{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T23:48:37Z","timestamp":1779234517500,"version":"3.51.4"},"reference-count":42,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,12]],"date-time":"2021-01-12T00:00:00Z","timestamp":1610409600000},"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":["No. 51876030"],"award-info":[{"award-number":["No. 51876030"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["No. DUT19JC60"],"award-info":[{"award-number":["No. DUT19JC60"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Untethered microrobots provide the prospect for performing minimally invasive surgery and targeted delivery of drugs in hard-to-reach areas of the human body. Recently, inspired by the way the prokaryotic flagella rotates to drive the body forward, numerous studies have been carried out to study the swimming properties of helical swimmers. In this study, the resistive force theory (RFT) was applied to analyze the influence of dimensional and kinematical parameters on the propulsion performance of conventional helical swimmers. The propulsion efficiency index was applied to quantitatively evaluate the swimming performance of helical swimmers. Quantitative analysis of the effect of different parameters on the propulsion performance was performed to optimize the design of structures. Then, RFT was modified to explore the tapered helical swimmers with the helix radius changing uniformly along the axis. Theoretical results show that the helical swimmer with a constant helix angle exhibits excellent propulsion performance. The evaluation index was found to increase with increased tapering, indicating that the tapered structures can produce more efficient motion. Additionally, the analysis method extended from RFT can be used to analyze the motion of special-shaped flagella in microorganisms.<\/jats:p>","DOI":"10.3390\/s21020494","type":"journal-article","created":{"date-parts":[[2021,1,12]],"date-time":"2021-01-12T20:11:31Z","timestamp":1610482291000},"page":"494","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Enhancing Swimming Performance by Optimizing Structure of Helical Swimmers"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1849-7065","authenticated-orcid":false,"given":"Jiaqi","family":"Miao","sequence":"first","affiliation":[{"name":"R&amp;D Institute of Fluid and Power Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolong","family":"Li","sequence":"additional","affiliation":[{"name":"R&amp;D Institute of Fluid and Power Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Liang","sequence":"additional","affiliation":[{"name":"R&amp;D Institute of Fluid and Power Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiongzhe","family":"Wang","sequence":"additional","affiliation":[{"name":"R&amp;D Institute of Fluid and Power Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2034-0104","authenticated-orcid":false,"given":"Xiaofei","family":"Xu","sequence":"additional","affiliation":[{"name":"R&amp;D Institute of Fluid and Power Engineering, Dalian University of Technology, Dalian 116024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhang, T., Yang, L., Yang, X., Tan, R., Lu, H., and Shen, Y. (2020). Millimeter-Scale Soft Continuum Robots for Large-Angle and High-Precision Manipulation by Hybrid Actuation. Adv. Intell. Syst., 2000189.","DOI":"10.1002\/aisy.202000189"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1146\/annurev-bioeng-010510-103409","article-title":"Microrobots for Minimally Invasive Medicine","volume":"12","author":"Nelson","year":"2010","journal-title":"Annu. Rev. Biomed. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"eaaq1155","DOI":"10.1126\/scirobotics.aaq1155","article-title":"Multifunctional biohybrid magnetite microrobots for imaging-guided therapy","volume":"2","author":"Yan","year":"2017","journal-title":"Sci. Robot."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3944","DOI":"10.1038\/s41467-018-06491-9","article-title":"A bioinspired multilegged soft millirobot that functions in both dry and wet conditions","volume":"9","author":"Lu","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"eabc8191","DOI":"10.1126\/scirobotics.abc8191","article-title":"An agglutinate magnetic spray transforms inanimate objects into millirobots for biomedical applications","volume":"5","author":"Yang","year":"2020","journal-title":"Sci. Robot."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4445","DOI":"10.1039\/C6LC00981F","article-title":"Programmable assembly of heterogeneous microparts by an untethered mobile capillary microgripper","volume":"16","author":"Diller","year":"2016","journal-title":"Lab Chip."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1119\/1.10903","article-title":"Life at low Reynolds number","volume":"45","author":"Purcell","year":"1977","journal-title":"Am. J. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5119","DOI":"10.1038\/ncomms6119","article-title":"Swimming by reciprocal motion at low Reynolds number","volume":"5","author":"Qiu","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"eaat8829","DOI":"10.1126\/scirobotics.aat8829","article-title":"Development of a magnetic microrobot for carrying and delivering targeted cells","volume":"3","author":"Li","year":"2018","journal-title":"Sci. Robot."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"eaba5726","DOI":"10.1126\/scirobotics.aba5726","article-title":"Multifunctional surface microrollers for targeted cargo delivery in physiological blood flow","volume":"5","author":"Alapan","year":"2020","journal-title":"Sci. Robot."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3663","DOI":"10.1021\/nl901869j","article-title":"Characterizing the Swimming Properties of Artificial Bacterial Flagella","volume":"9","author":"Zhang","year":"2009","journal-title":"Nano Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1485","DOI":"10.1109\/TMECH.2012.2204070","article-title":"Meshworm: A Peristaltic Soft Robot with Antagonistic Nickel Titanium Coil Actuators","volume":"18","author":"Seok","year":"2013","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1137\/1018040","article-title":"Flagellar hydrodynamics","volume":"18","author":"Lighthill","year":"1976","journal-title":"SIAM Rev."},{"key":"ref_14","first-page":"620","article-title":"The Propulsion of Sea-Urchin Spermatozoa","volume":"32","author":"Gray","year":"1955","journal-title":"J. Exp. Biol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1017\/S0022112087003008","article-title":"A boundary-element analysis of flagellar propulsion","volume":"184","author":"Ramia","year":"1987","journal-title":"J. Fluid Mech."},{"key":"ref_16","unstructured":"Johnson, R.E. (1977). Slender-Body Theory for Stokes Flow and Flagellar Hydrodynamics. [Ph.D. Thesis, California Institute of Technology]."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"011701","DOI":"10.1063\/1.4861026","article-title":"Propulsion by a helical flagellum in a capillary tube","volume":"26","author":"Liu","year":"2014","journal-title":"Phys. Fluids."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4185","DOI":"10.1109\/LRA.2019.2931234","article-title":"Visual Servoing of Miniature Magnetic Film Swimming Robots for 3-D Arbitrary Path Following","volume":"4","author":"Huang","year":"2019","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Liu, J., Wu, X., Huang, C., Manamanchaiyaporn, L., Shang, W., Yan, X., and Xu, T. (2020). 3-D Autonomous Manipulation System of Helical Microswimmers With Online Compensation Update. IEEE Trans. Autom. Sci. Eng., 1\u201312.","DOI":"10.1109\/TASE.2020.3006131"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6269","DOI":"10.1039\/C9SM00717B","article-title":"Effect of external shear flow on sperm motility","volume":"15","author":"Kumar","year":"2019","journal-title":"Soft Matter"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"046014","DOI":"10.1088\/1748-3182\/9\/4\/046014","article-title":"Magnetic polymer composite artificial bacterial flagella","volume":"9","author":"Peyer","year":"2014","journal-title":"Bioinspir. Biomim."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/TRO.2013.2281551","article-title":"Improved Kinematic Models for Two-Link Helical Micro\/Nanoswimmers","volume":"30","author":"Tabak","year":"2014","journal-title":"IEEE Trans. Robot."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1021\/acsnano.7b06398","article-title":"Sperm-Hybrid Micromotor for Targeted Drug Delivery","volume":"12","author":"Xu","year":"2018","journal-title":"ACS Nano"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1038\/s41467-019-08670-8","article-title":"Bio-inspired nitric-oxide-driven nanomotor","volume":"10","author":"Wan","year":"2019","journal-title":"Nat. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2826","DOI":"10.1038\/s41467-019-10726-8","article-title":"Intrinsic enzymatic properties modulate the self-propulsion of micromotors","volume":"10","author":"Xavier","year":"2019","journal-title":"Nat. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1115\/1.2171439","article-title":"Design Methodology for Biomimetic Propulsion of Miniature Swimming Robots","volume":"128","author":"Behkam","year":"2006","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1016\/j.bpj.2014.01.047","article-title":"Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels","volume":"106","author":"Acemoglu","year":"2014","journal-title":"Biophys. J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/S1672-6529(16)60375-X","article-title":"Design and Characterization of Magnetically Actuated Helical Swimmers at Submillimeter-scale","volume":"14","author":"Wang","year":"2017","journal-title":"J. Bionic Eng."},{"key":"ref_29","first-page":"2000204","article-title":"3D Microprinting of Iron Platinum Nanoparticle-Based Magnetic Mobile Microrobots","volume":"2","author":"Giltinan","year":"2020","journal-title":"Adv. Intell. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s12213-015-0084-5","article-title":"Influence of geometry on swimming performance of helical swimmers using DoE","volume":"11","author":"Xu","year":"2015","journal-title":"J. Micro-Bio Robot."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1901828","DOI":"10.1002\/adma.201901828","article-title":"A macrophage-magnesium hybrid biomotor: Fabrication and characterization","volume":"31","author":"Zhang","year":"2019","journal-title":"Adv. Mater."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"19841","DOI":"10.1073\/pnas.1907051116","article-title":"Neuromuscular actuation of biohybrid motile bots","volume":"116","author":"Aydin","year":"2019","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1572","DOI":"10.1039\/C4SM02437K","article-title":"A bead-spring model for running and tumbling of flagellated swimmers: Detailed predictions compared to experimental data for E. coli","volume":"11","author":"Kong","year":"2015","journal-title":"Soft Matter"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"7748","DOI":"10.1039\/C8SM01120F","article-title":"Effect of interfilament hydrodynamic interaction on swimming performance of two-filament microswimmers","volume":"14","author":"Singh","year":"2018","journal-title":"Soft Matter"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Ye, C., Liu, J., Wu, X., Wang, B., Zhang, L., Zheng, Y., and Xu, T. (2019). Hydrophobicity Influence on Swimming Performance of Magnetically Driven Miniature Helical Swimmers. Micromachines, 10.","DOI":"10.3390\/mi10030175"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"eaat4388","DOI":"10.1126\/sciadv.aat4388","article-title":"A swarm of slippery micropropellers penetrates the vitreous body of the eye","volume":"4","author":"Wu","year":"2018","journal-title":"Sci. Adv."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1146\/annurev.fl.09.010177.002011","article-title":"Fluid Mechanics of Propulsion by Cilia and Flagella","volume":"9","author":"Brennen","year":"1977","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Singleton, J., Diller, E., Andersen, T., St\u00e9phane, R., and Sitti, M. (2011, January 25\u201330). Micro-scale propulsion using multiple flexible artificial flagella. Proceedings of the 2013 IEEE\/RSJ International Conference on Intelligent Robots and Systems, San Francisco, CA, USA.","DOI":"10.1109\/IROS.2011.6048742"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1109\/TMECH.2013.2269802","article-title":"Modeling and Swimming Property Characterizations of Scaled-Up Helical Microswimmers","volume":"19","author":"Xu","year":"2014","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s12668-013-0105-6","article-title":"Tapered Flagellated Nanoswimmer: Comparison of Helical Wave and Planar Wave Propulsion","volume":"3","author":"Kotesa","year":"2013","journal-title":"BioNanoscience"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"e1601661","DOI":"10.1126\/sciadv.1601661","article-title":"Helical and rod-shaped bacteria swim in helical trajectories with little additional propulsion from helical shape","volume":"2","author":"Constantino","year":"2016","journal-title":"Sci. Adv."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1242\/jeb.204.7.1333","article-title":"A study of helical and planar waves on sea urchin sperm flagella, with a theory of how they are generated","volume":"204","author":"Woolley","year":"2001","journal-title":"J. Exp. Biol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/2\/494\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:10:06Z","timestamp":1760159406000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/2\/494"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,12]]},"references-count":42,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["s21020494"],"URL":"https:\/\/doi.org\/10.3390\/s21020494","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,12]]}}}