{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T16:10:02Z","timestamp":1778947802095,"version":"3.51.4"},"reference-count":20,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[2000,9,1]],"date-time":"2000-09-01T00:00:00Z","timestamp":967766400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2000,9]]},"abstract":"<jats:p>\n                    In this paper, we develop the theoretical work on the properties and mapping of stiffness matrices between joint and Cartesian spaces of robotic hands and fingers, and propose the conservative congruence transformation (CCT). In this paper, we show that the conventional formulation between the joint and Cartesian spaces, K\n                    <jats:sub>\u03b8<\/jats:sub>\n                    = J\n                    <jats:sup>T<\/jats:sup>\n                    <jats:sub>\u03b8<\/jats:sub>\n                    K\n                    <jats:sub>p<\/jats:sub>\n                    J\n                    <jats:sub>\u03b8<\/jats:sub>\n                    , first derived by Salisbury in 1980, is only valid at the unloaded equilibrium configuration. Once the grasping configuration is deviated from its unloaded configuration (for example, by the application of an external force), the conservative congruence transformation should be used. Theoretical development and numerical simulation are presented. The conservative congruence transformation accounts for the change in geometry via the differential Jacobian (Hessian matrix) of the robot manipulators when an external force is applied. The effect is captured in an effective stiffness matrix, K\n                    <jats:sub>g<\/jats:sub>\n                    , of the conservative congruence transformation. The results of this paper also indicate that the omission of the changes in Jacobian in the presence of external force would result in discrepancy of the work and lead to contradiction to the fundamental conservative properties of stiffness matrices. Through conservative congruence transformation, conservative and consistent physical properties of stiffness matrices can be preserved during mapping regardless of the usage of coordinate frames and the existence of external force.\n                  <\/jats:p>","DOI":"10.1177\/02783640022067201","type":"journal-article","created":{"date-parts":[[2004,12,17]],"date-time":"2004-12-17T20:23:10Z","timestamp":1103314990000},"page":"835-847","source":"Crossref","is-referenced-by-count":286,"title":["Conservative Congruence Transformation for Joint and Cartesian Stiffness                 Matrices of Robotic Hands and Fingers"],"prefix":"10.1177","volume":"19","author":[{"given":"Shih-Feng","family":"Chen","sequence":"first","affiliation":[{"name":"Manufacturing and Automation Laboratory, Department of Mechanical                         Engineering, State University of New York at Stony Brook, Stony Brook, New                         York 11794-2300, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Imin","family":"Kao","sequence":"additional","affiliation":[{"name":"Manufacturing and Automation Laboratory, Department of Mechanical                         Engineering, State University of New York at Stony Brook, Stony Brook, New                         York 11794-2300, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2000,9,1]]},"reference":[{"key":"atypb1","unstructured":"Ball, R. S. 1900. A Treaties on the Theory of Screws. Cambridge, UK: Cambridge University Press ."},{"key":"atypb2","unstructured":"Chen, S.F., and Kao, I. 1998. Simulation of conservative properties of stiffness matrices in congruence transformation . Proceedings of IEEE\/RSJ International Conference on Intelligent Robots and Systems, Victoria, BC, Canada, pp. 311\u2013316 ."},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"Chen, S.F., and Kao, I. 1999. The conservative congruence transformation of stiffness control in robotic grasping and manipulation . The 9th International Symposium on Robotics Research, Snowbird, UT, pp. 7\u201314 .","DOI":"10.1007\/978-1-4471-0765-1_2"},{"key":"atypb4","unstructured":"Ciblak, N., and Lipkin, H. 1994. Asymmetric Cartesian stiffness for the modeling of compliant robotic systems. Robotics: Kinematics, Dynamics and Control, ASME DE Vol. 72, pp. 197\u2013204."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1109\/70.88036"},{"key":"atypb6","unstructured":"Dimentberg, F. M. 1965. The screw calculus and its applications in mechanics. Technical Report FTD-HT-23-1632-67, U.S. Department of Commerce Translation ."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(93)90088-D"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"Hogan, N. 1990. Mechanical impedance of single-and multi-articular systems. In Multiple Muscle Systems: Biomechanics and Movement Organization, ed. J. M. Winters and S. L.Y. Woo, 149\u2013164. New York: Springer-Verlag .","DOI":"10.1007\/978-1-4613-9030-5_9"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/S0094-114X(97)00040-2"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1109\/70.678455"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1109\/70.611319"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1177\/027836499901800204"},{"key":"atypb13","unstructured":"Lon\u010dari\u0107 c, J. 1985.\n                      Geometrical Analysis of Compliant Mechanisms in Robotics\n                      . Ph.D. dissertation, Harvard University, Cambridge, MA."},{"key":"atypb14","unstructured":"Malvern, L. E. 1969. Introduction to the Mechanics of a Continuous Medium. Englewood Cliffs, NJ: Prentice Hall ."},{"key":"atypb15","unstructured":"Mason, M. T., and Salisbury, J. K. 1985. Robot Hands and the Mechanics of Manipulation. Cambridge, MA: MIT Press ."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.05-10-02732.1985"},{"key":"atypb17","unstructured":"Ngo, C. 1998.\n                      Conservative Properties of Grasp Stiffness Matrix\n                      . Master\u2019s thesis, Department of Mechanical Engineering, State University of New York at Stony Brook."},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"Pigoski, T., Griffis, M., and Duffy, J. 1992. Stiffness mapping employing different frames of reference . Proceedings of the 22nd Biennial ASME Mechanisms Conference, ASME, Phoenix, AZ, pp. 445\u2013452 .","DOI":"10.1115\/DETC1992-0411"},{"key":"atypb19","doi-asserted-by":"crossref","unstructured":"Salisbury, J. K. 1980. Active stiffness control of a manipulator in Cartesian coordinates . Proceedings of the 19th IEEE Conference on Decision and Control, Albuquerque, NM, pp. 87\u201397 .","DOI":"10.1109\/CDC.1980.272026"},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"\u017defran, M., and Kumar, V. 1997. Affine connections for the Cartesian stiffness matrix . Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque, NM, pp. 1376\u20131381 .","DOI":"10.1109\/ROBOT.1997.614329"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783640022067201","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783640022067201","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:16:19Z","timestamp":1777457779000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/02783640022067201"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9]]},"references-count":20,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2000,9]]}},"alternative-id":["10.1177\/02783640022067201"],"URL":"https:\/\/doi.org\/10.1177\/02783640022067201","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,9]]}}}