{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:25:38Z","timestamp":1760243138637,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,11,3]],"date-time":"2015-11-03T00:00:00Z","timestamp":1446508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>This paper discusses static stability of a planar object grasped by multifingers with three joints. Each individual joint (prismatic joint or revolute joint) is modeled as a linear spring stiffness. The object mass and the link masses are also included. We consider not only pure rolling contact but also frictionless sliding contact. The grasp stability is investigated using the potential energy method. This paper makes the following contributions: (i) Grasp wrench vectors and grasp stiffness matrices are analytically derived not only for the rolling contact but also for the sliding contact; (ii) It is shown in detail that the vectors and the matrices are given by functions of grasp parameters such as the contact conditions (rolling contact and sliding contact), the contact position, the contact force, the local curvature, the link shape, the object mass, the link masses, and so on;  (iii) By using positive definiteness of the difference matrix of the grasp stiffness matrices, it is analytically proved that the rolling contact grasp is more stable than the sliding contact grasp. The displacement direction affected by the contact condition deviation is derived; (iv) By using positive definiteness of the differential matrix with respect to the local curvatures, it is analytically proved that the grasp stability increases when the local curvatures decrease. The displacement direction affected by the local curvature deviation is also derived; (v) Effects of the object mass and the joint positions are discussed using numerical examples. The numerical results are reinforced by analytical explanations. The effect of the link masses is also investigated.<\/jats:p>","DOI":"10.3390\/robotics4040464","type":"journal-article","created":{"date-parts":[[2015,11,3]],"date-time":"2015-11-03T11:17:07Z","timestamp":1446549427000},"page":"464-491","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Static Stability Analysis of a Planar Object Grasped by Multifingers with Three Joints"],"prefix":"10.3390","volume":"4","author":[{"given":"Takayoshi","family":"Yamada","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Gifu University, 1-1, Yanagido, Gifu 501-1193, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rolf","family":"Johansson","sequence":"additional","affiliation":[{"name":"Department of Automatic Control, Lund University, Box 118, SE-221-00 Lund, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anders","family":"Robertsson","sequence":"additional","affiliation":[{"name":"Department of Automatic Control, Lund University, Box 118, SE-221-00 Lund, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hidehiko","family":"Yamamoto","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Gifu University, 1-1, Yanagido, Gifu 501-1193, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,11,3]]},"reference":[{"key":"ref_1","unstructured":"Hanafusa, H., and Asada, H. (1982). Robot Motion, MIT Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/027836498800700301","article-title":"Constructing stable grasps","volume":"7","author":"Nguyen","year":"1988","journal-title":"Int. J. Robot. Res."},{"key":"ref_3","unstructured":"Li, J., and Kao, I. (1995, January 5\u20139). Grasp Stiffness Matrix-Fundamental Properties in Analysis of Grasping and Manipulation. Proceedings of the IEEE\/RSJ International Conference Intelligent Robots and Systems (IROS1995), Pittsburgh, PA, USA."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1109\/70.88036","article-title":"Computing and Controlling the Compliance of a Robotic Hand","volume":"5","author":"Cutkosky","year":"1989","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/978-1-4471-4664-3_2","article-title":"Stiffness Analysis for Grasping Tasks","volume":"10","author":"Carbone","year":"2013","journal-title":"Grasping Robot. Mech. Mach. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1163\/156855304322753281","article-title":"Task-based compliance planning for multi-fingered robotic manipulations","volume":"18","author":"Kim","year":"2004","journal-title":"Adv. Robot."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1177\/0278364913504473","article-title":"Grasp analysis tools for synergistic underactuated robotic hands","volume":"32","author":"Gabiccini","year":"2013","journal-title":"Int. J. Robot. Res."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Malvezzi, M., and Prattichizzo, D. (2013, January 6\u201310). Evaluation of Grasp Stiffness in Underactuated Compliant Hands. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA 2013), Karlsruhe, Germany.","DOI":"10.1109\/ICRA.2013.6630855"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1177\/0278364910364424","article-title":"On the Passive Force Closure Set of Planar Grasps and Fixtures","volume":"29","author":"Shapiro","year":"2010","journal-title":"Int. J. Robot. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1109\/70.149939","article-title":"Contact Stability for Two-Fingered Grasps","volume":"8","author":"Montana","year":"1992","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1177\/02783649922066682","article-title":"On the Dynamic Stability of Grasping","volume":"18","author":"Xiong","year":"1999","journal-title":"Int. J. Rob. Res."},{"key":"ref_12","unstructured":"Choi, K.K., Jing, S.L., and Li, Z. (1999, January 10\u201315). Grasping with Elastic Finger Tips. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA1999), Detroit, MI, USA."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Michalec, R., and Micaelli, A. (2010, January 6\u20138). Stiffness Modeling for Multi-Fingered Grasping with Rolling Contacts. Proceedings of the IEEE-RAS International Conference on Humanoid Robots, Nashville, TN, USA.","DOI":"10.1109\/ICHR.2010.5686334"},{"key":"ref_14","unstructured":"Funahashi, Y., Yamada, T., Tate, M., and Suzuki, Y. (1996, January 22\u201328). Grasp Stability Analysis Considering the Curvatures at Contact Points. Proceedings of the IEEE International Conference Robotics and Automation (ICRA1996), Minneapolis, MN, USA."},{"key":"ref_15","unstructured":"Howard, W.S., and Kumar, V. (1995, January 21\u201327). Modeling and Analysis of the Compliance and Stability of Enveloping Grasps. Proceedings of the IEEE International Conference Robotics and Automation (ICRA1995), Nagoya, Aichi, Japan."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1109\/70.544773","article-title":"On the stability of Grasped Objects","volume":"12","author":"Howard","year":"1996","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1109\/TRO.2004.829470","article-title":"Computation and Analysis of Natural Compliance in Fixturing and Grasping Arrangements","volume":"20","author":"Lin","year":"2004","journal-title":"IEEE Trans. Robot."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"274","DOI":"10.20965\/jrm.1999.p0274","article-title":"Stability Analysis of Planar Grasp with 2D-Virtual Spring Model","volume":"11","author":"Yamada","year":"1999","journal-title":"J. Robot. Mech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1163\/016918610X552187","article-title":"Static Stability Analysis of Spatial Grasps Including Contact Surface Geometry","volume":"25","author":"Yamada","year":"2011","journal-title":"Adv. Robot."},{"key":"ref_20","first-page":"218","article-title":"Static Grasp Stability Analysis of Two Spatial Objects Including Contact Surface Geometry","volume":"1","author":"Yamada","year":"2012","journal-title":"Trans. Control Mech. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Yamada, T., and Yamamoto, H. (2013, January 4\u20137). Grasp stability analysis of multiple objects including contact surface geometry in 3D. Proceedings of the IEEE International Conference Mechatronics and Automation (ICMA2013), Takamatsu, Kagawa, Japan.","DOI":"10.1109\/ICMA.2013.6617890"},{"key":"ref_22","first-page":"606","article-title":"Static Stability Analysis of a Single Planar Object Grasped by a Multifingered Hand","volume":"2","author":"Yamada","year":"2012","journal-title":"J. Mech. Eng. Autom."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/4\/4\/464\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:51:25Z","timestamp":1760215885000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/4\/4\/464"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,3]]},"references-count":22,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,12]]}},"alternative-id":["robotics4040464"],"URL":"https:\/\/doi.org\/10.3390\/robotics4040464","relation":{},"ISSN":["2218-6581"],"issn-type":[{"type":"electronic","value":"2218-6581"}],"subject":[],"published":{"date-parts":[[2015,11,3]]}}}