{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T14:00:38Z","timestamp":1776952838859,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2022,6,27]],"date-time":"2022-06-27T00:00:00Z","timestamp":1656288000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Innovation Research Project for Postgraduate Students of Tianjin","award":["2021YJSS068"],"award-info":[{"award-number":["2021YJSS068"]}]},{"name":"Innovation Research Project for Postgraduate Students of Tianjin","award":["20YDTPJC00610"],"award-info":[{"award-number":["20YDTPJC00610"]}]},{"name":"Project of Science and Technology Commissioner of Tianjin","award":["2021YJSS068"],"award-info":[{"award-number":["2021YJSS068"]}]},{"name":"Project of Science and Technology Commissioner of Tianjin","award":["20YDTPJC00610"],"award-info":[{"award-number":["20YDTPJC00610"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Soft pneumatic actuators are extensively used in soft robots, and their bending angles and kinematic rules at different pressures play a crucial role in practical applications. This investigation aims to model the bending angle and motion of a new type of soft pneumatic actuator that adopts a composite structure consisting of two kinds of pneumatic networks. Based on the structural and deformation characteristics of the proposed soft actuator, the constitutive model is established, and then the moment equilibrium and virtual work principle are combined to model the bending angle of two pneumatic modules. The kinematic model of the proposed soft actuator is co-opted from the kinematic modeling of rigid robots. By employing the piecewise constant curvature method and coordinate transformation, the location of any chamber of the soft actuator can be calculated. The effectiveness of the developed analytical models is then tested, and the calculated results show good agreement with the experimental results. Finally, three soft actuators are used to constitute a soft gripper, and the pinching and enveloping grasping performance are examined. All experimental test results demonstrate that the developed bending angle and kinematic models can explain the bending principle of the proposed soft actuators well.<\/jats:p>","DOI":"10.3390\/s22134851","type":"journal-article","created":{"date-parts":[[2022,6,28]],"date-time":"2022-06-28T00:07:02Z","timestamp":1656374822000},"page":"4851","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Modeling and Analysis of a Composite Structure-Based Soft Pneumatic Actuators for Soft-Robotic Gripper"],"prefix":"10.3390","volume":"22","author":[{"given":"Ming","family":"Yu","sequence":"first","affiliation":[{"name":"School of Computer and Information Engineering, Tianjin Chengjian University, Tianjin 300384, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1756-895X","authenticated-orcid":false,"given":"Wenwen","family":"Liu","sequence":"additional","affiliation":[{"name":"Tianjin Key Laboratory of Modern Mechatronics Equipment Technology, School of Mechanical Engineering, Tiangong University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Control and Mechanical Engineering, Tianjin Chengjian University, Tianjin 300384, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanyan","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Control and Mechanical Engineering, Tianjin Chengjian University, Tianjin 300384, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuewu","family":"Hong","sequence":"additional","affiliation":[{"name":"School of Control and Mechanical Engineering, Tianjin Chengjian University, Tianjin 300384, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7894-3779","authenticated-orcid":false,"given":"Hongjie","family":"Zhang","sequence":"additional","affiliation":[{"name":"Tianjin Key Laboratory of Modern Mechatronics Equipment Technology, School of Mechanical Engineering, Tiangong University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1707035","DOI":"10.1002\/adma.201707035","article-title":"Soft Robotic Grippers","volume":"30","author":"Shintake","year":"2018","journal-title":"Adv. Mater."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1089\/soro.2015.0019","article-title":"Soft Robotic Grippers for Biological Sampling on Deep Reefs","volume":"3","author":"Galloway","year":"2016","journal-title":"Soft Robot."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1016\/j.future.2020.06.046","article-title":"Design and control of soft rehabilitation robots actuated by pneumatic muscles: State of the art","volume":"113","author":"Liu","year":"2020","journal-title":"Future Gener. Comput. Syst. Int. J. eSci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1007\/s11771-019-3986-x","article-title":"Design of wearable hand rehabilitation glove with soft hoop-reinforced pneumatic actuator","volume":"26","author":"Sun","year":"2019","journal-title":"J. Cent. South Univ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1089\/soro.2018.0124","article-title":"A Versatile Soft Crawling Robot with Rapid Locomotion","volume":"6","author":"Qin","year":"2019","journal-title":"Soft Robot."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1109\/TMECH.2018.2874067","article-title":"Topology Optimized Multimaterial Soft Fingers for Applications on Grippers, Rehabilitation, and Artificial Hands","volume":"24","author":"Zhang","year":"2019","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"8734","DOI":"10.1109\/LRA.2021.3115156","article-title":"Sensor Embedded Soft Fingertip for Precise Manipulation and Softness Recognition","volume":"6","author":"Ma","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"20400","DOI":"10.1073\/pnas.1116564108","article-title":"Multigait soft robot","volume":"108","author":"Shepherd","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1109\/TRO.2015.2428504","article-title":"Modeling of Soft Fiber-Reinforced Bending Actuators","volume":"31","author":"Polygerinos","year":"2015","journal-title":"IEEE Trans. Robot."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1089\/soro.2018.0095","article-title":"Design and Computational Modeling of a 3D Printed Pneumatic Toolkit for Soft Robotics","volume":"6","author":"Pasquier","year":"2019","journal-title":"Soft Robot."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2287","DOI":"10.1109\/LRA.2017.2716445","article-title":"A soft-robotic gripper with enhanced object adaptation and grasping reliability","volume":"2","author":"Zhou","year":"2017","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Nikolov, S., Kotev, V., Kostadinov, K., Wang, F., Liang, C., and Tian, Y. (2016, January 18\u201322). Model-based design optimization of soft fiber-reinforced bending actuators. Proceedings of the 2016 IEEE International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale, Chongqing, China.","DOI":"10.1109\/3M-NANO.2016.7824949"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3243","DOI":"10.1109\/TMECH.2021.3056563","article-title":"Modified Stiffness-Based Soft Optical Waveguide Integrated Pneumatic Artificial Muscle (PAM) Actuators for Contraction and Force Sensing","volume":"26","author":"Jamil","year":"2021","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1109\/TMECH.2015.2483520","article-title":"Nonlinear control ofrobotic manipulators driven by pneumatic artificial muscles","volume":"21","author":"Robinson","year":"2016","journal-title":"IEEE ASMET Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"46291","DOI":"10.1109\/ACCESS.2022.3169278","article-title":"FEA Modeling of Soft Tissue Interaction for Active Needles with a Rotational Tip Joint","volume":"10","author":"Quagliato","year":"2022","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"105024","DOI":"10.1088\/1361-665X\/aadbff","article-title":"Design and analysis of electrohydraulic pressure systems for variable recruitment in fluidic artificial muscles","volume":"27","author":"Chapman","year":"2018","journal-title":"Smart Mater. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hao, Y. (2017). Modeling and experiments of a soft robotic gripper in amphibious environments. Int. J. Adv. Robot. Syst., 14.","DOI":"10.1177\/1729881417707148"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1089\/soro.2016.0052","article-title":"Modeling and Experimental Evaluation of Bending Behavior of Soft Pneumatic Actuators Made of Discrete Actuation Chambers","volume":"5","author":"Alici","year":"2018","journal-title":"Soft Robot."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.eml.2016.02.007","article-title":"On constitutive relations for a rod-based model of a pneu-net bending actuator","volume":"8","year":"2016","journal-title":"Extreme Mech. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1109\/LRA.2017.2650149","article-title":"Soft gripper dynamics using a line-segment model with an optimization-based parameter identification method","volume":"2","author":"Wang","year":"2017","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1793","DOI":"10.1080\/15397734.2020.1763182","article-title":"Developing an analytical solution for a thermally tunable soft actuator under finite bending","volume":"50","author":"Yarali","year":"2020","journal-title":"Mech. Based Des. Struct. Mach."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2195","DOI":"10.1109\/TMECH.2020.3034640","article-title":"Modeling and Analysis of Soft Pneumatic Network Bending Actuators","volume":"26","author":"Liu","year":"2021","journal-title":"IEEE-ASME Trans. Mechatron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6115","DOI":"10.1109\/LRA.2022.3167063","article-title":"Design and Analysis of Fiber-Reinforced Soft Actuators for Wearable Hand Rehabilitation Device","volume":"7","author":"Ma","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"990","DOI":"10.1109\/TMECH.2019.2911992","article-title":"Design, Modeling, and Testing of a Soft Pneumatic Glove with Segmented PneuNets Bending Actuators","volume":"24","author":"Wang","year":"2019","journal-title":"IEEE-ASME Trans. Mechatron."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1016\/j.euromechsol.2018.06.004","article-title":"Voltage-driven nonuniform axisymmetric torsion of a tubular dielectric elastomer actuator reinforced with one family of inextensible fibers","volume":"71","author":"He","year":"2018","journal-title":"Eur. J. Mech. A Solids"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s10999-011-9167-1","article-title":"Assessment on assorted hyper-elastic material models applied for large deformation soft finger contact problems","volume":"7","author":"Raja","year":"2012","journal-title":"Int. J. Mech. Mater. Des."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1108\/IR-01-2021-0013","article-title":"Development of a novel robotic hand with soft materials and rigid structures","volume":"48","author":"Li","year":"2021","journal-title":"Ind. Robot Int. J. Robot. Res. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1002\/acs.2874","article-title":"Dynamic modeling and adaptive robust boundary control of a flexible robotic arm with 2-dimensional rigid body rotation","volume":"32","author":"Tavasoli","year":"2018","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1109\/LRA.2020.2967269","article-title":"On an Improved State Parametrization for Soft Robots with Piecewise Constant Curvature and Its Use in Model Based Control","volume":"5","author":"Bicchi","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6231","DOI":"10.3233\/JIFS-189460","article-title":"Research and analysis of stiffness-enhanced soft gripper","volume":"40","author":"Tian","year":"2021","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"191920","DOI":"10.1109\/ACCESS.2020.3032842","article-title":"Design and Motion Analysis of Adjustable Pneumatic Soft Manipulator for Grasping Objects","volume":"8","author":"Jiang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"448","DOI":"10.3390\/machines10060448","article-title":"Design and Simulation Experiment of Rigid-Flexible Soft Humanoid Finger","volume":"10","author":"Jiteng","year":"2022","journal-title":"Machines"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1089\/soro.2020.0081","article-title":"Static Modeling of the Fiber-Reinforced Soft Pneumatic Actuators Including Inner Compression: Bending in Free Space, Block Force, and Deflection upon Block Force","volume":"9","author":"Sun","year":"2021","journal-title":"Soft Robot."},{"key":"ref_34","first-page":"395","article-title":"Virtual work principles","volume":"163","author":"Bauchau","year":"2009","journal-title":"Solid Mech. Appl."},{"key":"ref_35","first-page":"146","article-title":"A Two-Finger Soft-Robotic Gripper with Enveloping and Pinching Grasping Modes","volume":"26","author":"Liu","year":"2021","journal-title":"IEEE-ASME Trans. Mechatron."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Liu, L., Zhang, J.S., Liu, G., Zhu, Z.C., Hu, Q., and Li, P.F. (2021). Three-Fingered Soft Pneumatic Gripper Integrating Joint-Tuning Capability. Soft Robot.","DOI":"10.1089\/soro.2021.0082"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1089\/soro.2019.0115","article-title":"Toward a Common Framework and Database of Materials for Soft Robotics","volume":"8","author":"Marechal","year":"2020","journal-title":"Soft Robot."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1007\/s42235-021-00075-y","article-title":"Bioinspired Spiral Soft Pneumatic Actuator and Its Characterization","volume":"18","author":"Zhang","year":"2021","journal-title":"J. Bionic Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/13\/4851\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:39:04Z","timestamp":1760139544000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/13\/4851"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,27]]},"references-count":38,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["s22134851"],"URL":"https:\/\/doi.org\/10.3390\/s22134851","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,27]]}}}