{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T08:27:24Z","timestamp":1787300844489,"version":"build-2736575974"},"reference-count":22,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T00:00:00Z","timestamp":1787270400000},"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":["62303420"],"award-info":[{"award-number":["62303420"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["62303420"],"award-info":[{"award-number":["62303420"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The position of the center of mass directly affects the attitude control and flight safety of moving bodies such as unmanned aerial vehicles (UAVs). Therefore, high-precision measurement of the center of mass is required. Existing methods require changing the posture of the measured object multiple times. This introduces repeated positioning errors and suffers from poor equipment versatility. To address these issues, this paper proposes a static and dynamic combined measurement method for the center of mass based on multi-view vision. First, the relationship between the swing period and the pendulum length under the simple pendulum principle is analyzed. The basic principle of determining the direction of the center of mass using the line of gravity is also examined. Second, an under-constrained compound pendulum fixture is designed. A binocular vision system is used to track circular markers, perform FFT-based period verification, and fit the gravity line using singular value decomposition (SVD). Third, using a standard cubic iron block as the test object, the influence of pendulum length and swing angle on measurement accuracy is studied. Finally, experiments verify that the proposed method can obtain three-dimensional coordinates of the center of mass under a single suspension condition. The results show that with a pendulum length of 330 mm and an initial swing angle of 4\u00b0, the root mean square error of the center of mass measurement is 0.70 mm, and the maximum deviation over five repeated measurements is 1.45 mm. This method does not require repeated lifting or changes in posture. It can meet the need for in-situ, high-precision center of mass measurement of UAVs and other aircraft.<\/jats:p>","DOI":"10.3390\/s26165293","type":"journal-article","created":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T08:14:01Z","timestamp":1787300041000},"page":"5293","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Static and Dynamic Combined Center of Mass Measurement Method Based on Multi-View Vision"],"prefix":"10.3390","volume":"26","author":[{"given":"Daojing","family":"Qu","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuhao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Genyou","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3605-2657","authenticated-orcid":false,"given":"Meibao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiyao","family":"Xiang","sequence":"additional","affiliation":[{"name":"Zhejiang Zhongli Tools Manufacturing Co., Ltd., Lishui 321405, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"066013","DOI":"10.1088\/1361-6501\/addf67","article-title":"Analysis of random error influencing factors in the three-point method for center of mass measurement","volume":"36","author":"Zhao","year":"2025","journal-title":"Meas. Sci. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3582508","DOI":"10.1155\/2018\/3582508","article-title":"Experimental Verification of a Simple Method for Accurate Center of Gravity Determination of Small Satellite Platforms","volume":"2018","author":"Modenini","year":"2018","journal-title":"Int. J. Aerosp. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"042189","DOI":"10.1088\/1757-899X\/452\/4\/042189","article-title":"Vehicle Centroid Measurement System Based on Forward Tilt Method Error Analysis","volume":"452","author":"Zhao","year":"2018","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.ymssp.2018.11.011","article-title":"Measurement of the mass properties of rigid bodies by means of multi-filar pendulums\u2014Influence of test rig flexibility","volume":"121","author":"Previati","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1007\/s00202-016-0397-y","article-title":"An analytical and experimental calculation of the inertia moment of a squirrel-cage induction motor","volume":"99","author":"Arjona","year":"2017","journal-title":"Electr. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10329","DOI":"10.1364\/AO.470899","article-title":"Method for measuring the center of mass and moment of inertia of a model using 3D point clouds","volume":"61","author":"Yang","year":"2022","journal-title":"Appl. Opt."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"He, X., Li, Z., Pan, X., and Yang, Y. (2025). High-Precision Centroid Measurement Method Based on 3D Scanning and Hooke\u2019s Law. Sensors, 25.","DOI":"10.3390\/s25237210"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Li, S., Chu, W., and Huang, X. (2020). Measurement method of aircraft barycenter based on multi posture. Sens. Rev., ahead-of-print.","DOI":"10.1108\/SR-12-2019-0305"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"113398","DOI":"10.1016\/j.measurement.2023.113398","article-title":"A method for the 3D identification of the center of gravity of an aircraft","volume":"220","author":"Seara","year":"2023","journal-title":"Measurement"},{"key":"ref_10","first-page":"5003109","article-title":"3-D Reconstruction and Measurement System Based on Multi-Mobile Robot Machine Vision","volume":"70","author":"Moemen","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"106116","DOI":"10.1016\/j.optlaseng.2020.106116","article-title":"High-resolution measurement based on the combination of multi-vision system and synthetic aperture imaging","volume":"133","author":"Chu","year":"2020","journal-title":"Opt. Lasers Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.measurement.2024.114888","article-title":"A centroid measurement method of large components for active compliant assembly","volume":"234","author":"Chu","year":"2024","journal-title":"Measurement"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lee, H., and Kim, U. (2021). Estimation and Control of Cooperative Aerial Manipulators for a Payload with an Arbitrary Center-of-Mass. Sensors, 21.","DOI":"10.3390\/s21196452"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Chen, Y., Zeng, Y., Li, H., Zhang, J., and Zhang, L. (2023). Research on the measurement technology of rotational inertia of rigid body based on the principles of monocular vision and torsion pendulum. J. Sens., 23.","DOI":"10.3390\/s23104787"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhang, X., Yu, H., Tang, W., and Wang, J. (2022). General mass property measurement equipment for large-sized aircraft. J. Sens., 22.","DOI":"10.3390\/s22103912"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1109\/JETCAS.2020.3040329","article-title":"An Event-by-Event Approach for Velocity Estimation and Object Tracking with an Active Event Camera","volume":"10","author":"Zhu","year":"2020","journal-title":"IEEE J. Emerg. Sel. Top. Circuits Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4103","DOI":"10.1109\/TITS.2018.2881556","article-title":"HOOFR SLAM System: An Embedded Vision SLAM Algorithm and Its Hardware-Software Mapping-Based Intelligent Vehicles Applications","volume":"20","author":"Nguyen","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2168","DOI":"10.1109\/TAC.2017.2755988","article-title":"Identification of a Moving Object\u2019s Velocity and Range with a Static-Moving Camera System","volume":"63","author":"Chen","year":"2018","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Hu, Y., Ma, Y., Xu, M., and Chen, X. (2016). Measurement algorithm of mounting holes based on binocular stereo vision. IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems (CYBER), IEEE.","DOI":"10.1109\/CYBER.2016.7574875"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, J. (2019). A Structure for Accurately Determining the Mass and Center of Gravity of Rigid Bodies. Appl. Sci., 9.","DOI":"10.3390\/app9122532"},{"key":"ref_21","first-page":"13","article-title":"Torsional pendulum vibration nonlinear model of the plate-like object and its application in the measurement of moment of inertia","volume":"33","author":"Lin","year":"2014","journal-title":"J. Vib. Shock"},{"key":"ref_22","first-page":"173","article-title":"The inertia moment of projectile measured by vibration pendulum method and error analysis","volume":"36","author":"Xu","year":"2016","journal-title":"J. Proj. Rockets Missiles Guid."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/16\/5293\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T08:16:10Z","timestamp":1787300170000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/16\/5293"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,21]]},"references-count":22,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["s26165293"],"URL":"https:\/\/doi.org\/10.3390\/s26165293","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,21]]}}}