{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T12:37:33Z","timestamp":1776083853690,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T00:00:00Z","timestamp":1612483200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents an analytical model to determine a closed form mathematical representation for the output displacement of a displacement amplification compliant mechanism used for energy harvesting. A symmetric five-bar compliant mechanism with right-circular and corner-filleted flexure hinges was mathematically modeled and its displacement was determined using the Castigliano energy theorem. The stresses within the flexure joints, the weakest points in the mechanism body, were calculated. The mathematical model expresses both the displacement amplification and the stresses as functions of the design parameters and the load caused by the harvester. The developed model can be used to optimize the mechanism dimensions for maximum harvested power, while minimizing its structural stresses. The mechanism was also modeled numerically using finite element methods; both the analytical and numerical models were verified experimentally. The mathematical model of the mechanism was integrated with a model representing a piezoelectric energy harvester to calculate the open-circuit voltage. As a proof of concept, experiments were performed using an unimorph piezoelectric cantilever at low-frequency (less than 1 Hz) harmonic excitation inputs. The measured open-circuit voltage was found to be in agreement with that calculated using the proposed model, when integrated with the model representing the piezoelectric beam. The power generated by the piezoelectric harvester, equipped with the proposed displacement amplification mechanism, was more than a hundred times that without amplification.<\/jats:p>","DOI":"10.3390\/s21041095","type":"journal-article","created":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T08:33:48Z","timestamp":1612514028000},"page":"1095","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Modeling of a Symmetric Five-Bar Displacement Amplification Compliant Mechanism for Energy Harvesting"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6275-7568","authenticated-orcid":false,"given":"Moataz M.","family":"Elsisy","sequence":"first","affiliation":[{"name":"Mechanical Design and Production Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1552-2034","authenticated-orcid":false,"given":"Mustafa H.","family":"Arafa","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, American University in Cairo, New Cairo 11835, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2799-7245","authenticated-orcid":false,"given":"Chahinaz A.","family":"Saleh","sequence":"additional","affiliation":[{"name":"Mechanical Design and Production Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9516-489X","authenticated-orcid":false,"given":"Yasser H.","family":"Anis","sequence":"additional","affiliation":[{"name":"Mechanical Design and Production Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"022001","DOI":"10.1088\/0957-0233\/21\/2\/022001","article-title":"Strategies for increasing the operating frequency range of vibration energy harvesters: A review","volume":"21","author":"Zhu","year":"2009","journal-title":"Meas. 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