{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T18:42:32Z","timestamp":1780512152988,"version":"3.54.1"},"reference-count":13,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2014,1,2]],"date-time":"2014-01-02T00:00:00Z","timestamp":1388620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To address the bottleneck issues of an elastic-style six-axis force\/torque sensor (six-axis force sensor), this work proposes a no-elastic piezoelectric six-axis force sensor. The operating principle of the piezoelectric six-axis force sensor is analyzed, and a structural model is constructed. The static-active design theory of the piezoelectric six-axis force sensor is established, including a static analytical\/mathematical model and numerical simulation model (finite element model). A piezoelectric six-axis force sensor experimental prototype is developed according to the analytical mathematical model and numerical simulation model, and selected static characteristic parameters (including sensitivity, isotropic degree and cross-coupling) are tested using this model with three approaches. The measured results are in agreement with the analytical results from the static-active design method. Therefore, this study has successfully established a foundation for further research into the piezoelectric multi-axis force sensor and an overall design approach based on static characteristics.<\/jats:p>","DOI":"10.3390\/s140100659","type":"journal-article","created":{"date-parts":[[2014,1,2]],"date-time":"2014-01-02T11:29:28Z","timestamp":1388662168000},"page":"659-671","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Active Design Method for the Static Characteristics of a Piezoelectric Six-Axis Force\/Torque Sensor"],"prefix":"10.3390","volume":"14","author":[{"given":"Jun","family":"Liu","sequence":"first","affiliation":[{"name":"Key Laboratory of Optoelectronics Technology and Systems Ministry of Education,  Chongqing University, Chongqing 400044, China"},{"name":"College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Min","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Optoelectronics Technology and Systems Ministry of Education,  Chongqing University, Chongqing 400044, China"},{"name":"College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lan","family":"Qin","sequence":"additional","affiliation":[{"name":"Key Laboratory of Optoelectronics Technology and Systems Ministry of Education,  Chongqing University, Chongqing 400044, China"},{"name":"College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingcheng","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Optoelectronics Technology and Systems Ministry of Education,  Chongqing University, Chongqing 400044, China"},{"name":"College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2014,1,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1049\/iet-smt.2010.0146","article-title":"Development of a six-axis force\/moment sensor for a spherical-type finger force measuring system","volume":"6","author":"Kim","year":"2012","journal-title":"IET Sci. 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(China Invention Patent, Application Number 200710157931.2)."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.ymssp.2010.09.008","article-title":"Research on parallel load sharing principle of piezoelectric six-dimensional heavy force\/torque sensor","volume":"25","author":"Liu","year":"2011","journal-title":"Mech. Syst. Signal Process"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0924-4247(96)01324-6","article-title":"Design of a novel thin film piezoelectric accelerometer","volume":"56","author":"Nemirovsky","year":"1996","journal-title":"Sens. Actuators A Phys."},{"key":"ref_11","first-page":"2327","article-title":"Optimal design of isotropy performance of six-dimensional force sensor based on standard stewart parallel structure lying on a circular hyperboloid of one sheet","volume":"32","author":"Tong","year":"2011","journal-title":"Acta Aeronaut. et Astronaut. Sin."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.mechmachtheory.2012.07.001","article-title":"Hyperstatic analysis of a fully pre-stressed six-axis force\/torque sensor","volume":"57","author":"Wang","year":"2012","journal-title":"Mech. Mach. Theory"},{"key":"ref_13","unstructured":"Liu, J. (2011). Study on Basic Theroy and Key Technologies of Flat Piezoelectric Six Axis Force\/Torque Sensor. [Ph.D. Thesis, Chongqing University]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/1\/659\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:07:01Z","timestamp":1760216821000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/14\/1\/659"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,2]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,1]]}},"alternative-id":["s140100659"],"URL":"https:\/\/doi.org\/10.3390\/s140100659","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,2]]}}}