{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T02:51:31Z","timestamp":1773111091017,"version":"3.50.1"},"reference-count":56,"publisher":"ASME International","issue":"4","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2015,12,1]]},"abstract":"<jats:p>The development of a generic and effective force model for semi-automatic or manual virtual assembly with haptic support is not a trivial task, especially when the assembly constraints involve complex features of arbitrary shape. The primary challenge lies in a proper formulation of the guidance forces and torques that effectively assist the user in the exploration of the virtual environment (VE), from repulsing collisions to attracting proper contact. The secondary difficulty is that of efficient implementation that maintains the standard 1\u2009kHz haptic refresh rate. We propose a purely geometric model for an artificial energy field that favors spatial relations leading to proper assembly, differentiated to obtain forces and torques for general motions. The energy function is expressed in terms of a cross-correlation of shape-dependent affinity fields, precomputed offline separately for each object. We test the effectiveness of the method using familiar peg-in-hole examples. We show that the proposed technique unifies the two phases of free motion and precise insertion into a single interaction mode and provides a generic model to replace the ad hoc mating constraints or virtual fixtures, with no restrictive assumption on the types of the involved assembly features.<\/jats:p>","DOI":"10.1115\/1.4030749","type":"journal-article","created":{"date-parts":[[2015,6,4]],"date-time":"2015-06-04T16:30:38Z","timestamp":1433435438000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":10,"title":["Peg-in-Hole Revisited: A Generic Force Model for Haptic Assembly"],"prefix":"10.1115","volume":"15","author":[{"given":"Morad","family":"Behandish","sequence":"first","affiliation":[{"name":"Computational Design Laboratory, Department of Mechanical Engineering, University of Connecticut, Storrs, CT 06269 e-mail:"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Horea T.","family":"Ilie\u015f","sequence":"additional","affiliation":[{"name":"Computational Design Laboratory, Department of Mechanical Engineering, University of Connecticut, Storrs, CT 06269 e-mail:"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2015,8,20]]},"reference":[{"key":"2019100319384802700_bib1","volume-title":"Haptics Technologies: Bringing Touch to Multimedia","year":"2011","edition":"1st ed."},{"issue":"2","key":"2019100319384802700_bib2","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1051\/meca:2004018","article-title":"Applications of Virtual Reality in the Manufacturing Industry: From Design Review to Ergonomic Studies","volume":"5","year":"2004","journal-title":"M\u00e9c. Ind."},{"issue":"3","key":"2019100319384802700_bib3","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/j.cag.2006.02.012","article-title":"Haptic Technologies for the Conceptual and Validation Phases of Product Design","volume":"30","year":"2006","journal-title":"Comput. Graphics"},{"key":"2019100319384802700_bib4","first-page":"169","article-title":"Product Design Review Application Based on a Vision\u2013Sound\u2013Haptic Interface","volume-title":"Haptic and Audio Interaction Design (Lecture Notes in Computer Science)","year":"2010"},{"key":"2019100319384802700_bib5","unstructured":"Bullinger, H. J., Breining, R., and Bauer, W., 1999, \u201cVirtual Prototyping\u2014State of the Art in Product Design,\u201d 26th International Conference on Computers and Industrial Engineering, Melbourne, Australia, pp. 103\u2013107."},{"issue":"3","key":"2019100319384802700_bib6","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1115\/1.1526508","article-title":"Definition and Review of Virtual Prototyping","volume":"2","year":"2002","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"3","key":"2019100319384802700_bib7","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1016\/S0097-8493(99)00047-3","article-title":"Virtual Reality as a Tool for Verification of Assembly and Maintenance Processes","volume":"23","year":"1999","journal-title":"Comput. Graphics"},{"issue":"2","key":"2019100319384802700_bib8","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1115\/1.1384566","article-title":"Effectiveness of Haptic Sensation for the Evaluation of Virtual Prototypes","volume":"1","year":"2001","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"1","key":"2019100319384802700_bib9","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10055-009-0153-y","article-title":"Virtual Reality for Assembly Methods Prototyping: A Review","volume":"15","year":"2011","journal-title":"Virtual Reality"},{"key":"2019100319384802700_bib10","first-page":"693","article-title":"Advances in Haptics","volume-title":"Haptic Virtual Reality Assembly\u2014Moving Towards Real Engineering Applications","year":"2010"},{"key":"2019100319384802700_bib11","doi-asserted-by":"crossref","unstructured":"Vance, J. M., and Dumont, G., 2011, \u201cA Conceptual Framework to Support Natural Interaction for Virtual Assembly Tasks,\u201d 2011 ASME World Conference on Innovative Virtual Reality (WINVR'2011), Milan, Italy, pp. 273\u2013278.","DOI":"10.1115\/WINVR2011-5570"},{"issue":"3","key":"2019100319384802700_bib12","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1108\/AA-03-2013-017","article-title":"Interactive Assembly Simulation With Haptic Feedback","volume":"33","year":"2013","journal-title":"Assem. Autom."},{"issue":"3","key":"2019100319384802700_bib13","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1111\/j.1467-8659.2004.00784.x","article-title":"Real-Time Rigid Body Simulation for Haptic Interactions Based on Contact Volume of Polygonal Objects","volume":"23","year":"2004","journal-title":"Comput. Graphics Forum"},{"key":"2019100319384802700_bib14","doi-asserted-by":"crossref","unstructured":"Mirtich, B., and Canny, J., 1995, \u201cImpulse-Based Simulation of Rigid Bodies,\u201d 1995 Symposium on Interactive 3D Graphics (I3D\u20191995), Monterey, CA, pp. 181\u2013217.10.1145\/199404.199436","DOI":"10.1145\/199404.199436"},{"key":"2019100319384802700_bib15","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/BFb0119418","article-title":"A New Computational Model of Friction Applied to Haptic Rendering","volume-title":"Experimental Robotics VI","year":"2000"},{"key":"2019100319384802700_bib16","unstructured":"Renouf, M., Acary, V., and Dumont, G., 2005, \u201c3D Frictional Contact and Impact Multibody Dynamics. A Comparison of Algorithms Suitable for Real-Time Applications,\u201d ECCOMAS Thematic Conference on Mutlibody Dynamics, Madrid, Spain, pp. 1\u201320."},{"key":"2019100319384802700_bib17","doi-asserted-by":"crossref","unstructured":"Tching, L., and Dumont, G., 2008, \u201cHaptic Simulations Based on Non-Smooth Dynamics for Rigid-Bodies,\u201d 15th ACM Symposium on Virtual Reality Software and Technology (VRST\u20192008), Bordeaux, France, pp. 87\u201390.10.1145\/1450579.1450597","DOI":"10.1145\/1450579.1450597"},{"issue":"2","key":"2019100319384802700_bib18","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/S0097-8493(00)00130-8","article-title":"3D Collision Detection: A Survey","volume":"25","year":"2001","journal-title":"Comput. Graphics"},{"key":"2019100319384802700_bib19","doi-asserted-by":"crossref","unstructured":"Kockara, S., Halic, T., Iqbal, K., Bayrak, C., and Rowe, R., 2007, \u201cCollision Detection: A Survey,\u201d 2007 IEEE International Conference on Systems, Man and Cybernetics (ISIC\u20192007), Montreal, Quebec, Canada, Oct. 7\u201310, pp. 4046\u20134051.10.1109\/ICSMC.2007.4414258","DOI":"10.1109\/ICSMC.2007.4414258"},{"issue":"1","key":"2019100319384802700_bib20","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1111\/j.1467-8659.2005.00829.x","article-title":"Collision Detection for Deformable Objects","volume":"24","year":"2005","journal-title":"Comput. Graphics Forum"},{"issue":"3","key":"2019100319384802700_bib21","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1145\/285857.285860","article-title":"V-Clip: Fast and Robust Polyhedral Collision Detection","volume":"17","year":"1998","journal-title":"ACM Trans. Graphics"},{"key":"2019100319384802700_bib22","doi-asserted-by":"crossref","unstructured":"Ehmann, S. A., and Lin, M. C., 2000, \u201cAccelerated Proximity Queries Between Convex Polyhedra by Multi-Level Voronoi Marching,\u201d 2000 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS'2000), Takamatsu, Japan, Vol. 3, pp. 2101\u20132106.10.1109\/IROS.2000.895281","DOI":"10.1109\/IROS.2000.895281"},{"issue":"3","key":"2019100319384802700_bib23","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1111\/1467-8659.00543","article-title":"Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition","volume":"20","year":"2001","journal-title":"Comput. Graphics Forum"},{"issue":"2","key":"2019100319384802700_bib24","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1115\/1.1389085","article-title":"A Haptic Assembly and Disassembly Simulation Environment and Associated Computational Load Optimization Techniques","volume":"1","year":"2001","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"key":"2019100319384802700_bib25","doi-asserted-by":"crossref","unstructured":"Coutee, A. S., and Bras, B., 2002, \u201cCollision Detection for Virtual Objects in a Haptic Assembly and Disassembly Simulation Environment,\u201d ASME Paper No. DETC2002\/CIE-34385.10.1115\/DETC2002\/CIE-34385","DOI":"10.1115\/DETC2002\/CIE-34385"},{"key":"2019100319384802700_bib26","doi-asserted-by":"crossref","unstructured":"Gottschalk, S., Lin, M. C., and Manocha, D., 1996, \u201cOBBTree: A Hierarchical Structure for Rapid Interference Detection,\u201d 23rd Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH'1996), New Orleans, LA, pp. 171\u2013180.","DOI":"10.1145\/237170.237244"},{"key":"2019100319384802700_bib27","doi-asserted-by":"crossref","unstructured":"Wan, H., Gao, S., Peng, Q., Dai, G., and Zhang, F., 2004, \u201cMIVAS: A Multi-Modal Immersive Virtual Assembly System,\u201d ASME Paper No. DETC2004-57660.10.1115\/DETC2004-57660","DOI":"10.1115\/DETC2004-57660"},{"key":"2019100319384802700_bib28","doi-asserted-by":"crossref","unstructured":"McNeely, W. A., Puterbaugh, K. D., and Troy, J. J., 2005, \u201cSix Degree-of-Freedom Haptic Rendering Using Voxel Sampling,\u201d ACM SIGGRAPH\u20192005 Courses, New York.10.1145\/1198555.1198605","DOI":"10.1145\/1198555.1198605"},{"issue":"7","key":"2019100319384802700_bib29","first-page":"1","article-title":"Voxel-Based 6-DOF Haptic Rendering Improvements","volume":"3","year":"2006","journal-title":"Haptics-e"},{"key":"2019100319384802700_bib30","unstructured":"Barbi\u010d, J., and James, D., 2007, \u201cTime-Critical Distributed Contact for 6-DOF Haptic Rendering of Adaptively Sampled Reduced Deformable Models,\u201d ACM SIGGRAPH\u20192007\/Eurographics Symposium on Computer Animation (SCA'2007), San Diego, CA, pp. 171\u2013180."},{"key":"2019100319384802700_bib31","unstructured":"Sagardia, M., Hulin, T., Preusche, C., and Hirzinger, 2008, \u201cImprovements of the Voxmap-PointShell Algorithm\u2014Fast Generation of Haptic Data-Structures,\u201d 53rd Internationales Wissenschaftliches Kolloquium Technische Universit\u00e4t Ilmenau, Ilmenau, Germany."},{"key":"2019100319384802700_bib32","unstructured":"Renz, M., Preusche, C., P\u00f6tke, M., Kriegel, H. P., and Hirzinger, G., 2001, \u201cStable Haptic Interaction With Virtual Environments Using an Adapted Voxmap-PointShell Algorithm,\u201d EuroHaptics 2001, Birmingham, UK."},{"key":"2019100319384802700_bib33","doi-asserted-by":"crossref","unstructured":"Johnson, D. C., and Vance, J. M., 2001, \u201cThe Use of the Voxmap PointShell Method of Collision Detection in Virtual Assembly Methods Planning,\u201d 2001 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC\/CIE\u20192001), Pittsburgh, PA, pp. 1169\u20131172.","DOI":"10.1115\/DETC2001\/DAC-21137"},{"issue":"2","key":"2019100319384802700_bib34","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1115\/1.1738125","article-title":"Collision Detection and Part Interaction Modeling to Facilitate Immersive Virtual Assembly Methods","volume":"4","year":"2004","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"4","key":"2019100319384802700_bib35","doi-asserted-by":"publisher","first-page":"044502-1","DOI":"10.1115\/1.3006306","article-title":"Development of a Dual-Handed Haptic Assembly System: SHARP","volume":"8","year":"2008","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"8","key":"2019100319384802700_bib36","doi-asserted-by":"publisher","first-page":"081002","DOI":"10.1115\/1.4001565","article-title":"Combining Dynamic Modeling With Geometric Constraint Management to Support Low Clearance Virtual Manual Assembly","volume":"132","year":"2010","journal-title":"ASME J. Mech. Des."},{"issue":"1","key":"2019100319384802700_bib37","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0097-8493(02)00228-5","article-title":"A Constraint Manager to Support Virtual Maintainability","volume":"27","year":"2003","journal-title":"Comput. Graphics"},{"key":"2019100319384802700_bib38","doi-asserted-by":"crossref","unstructured":"Murray, N., and Fernando, T., 2004, \u201cAn Immersive Assembly and Maintenance Simulation Environment,\u201d 2004 IEEE International Symposium on Distributed Simulation and Real-Time Applications (DS-RT\u20192004), Budapest, Hungary, Oct. 21\u201323, pp. 159\u2013166.10.1109\/DS-RT.2004.7","DOI":"10.1109\/DS-RT.2004.7"},{"issue":"4","key":"2019100319384802700_bib39","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s10055-003-0106-9","article-title":"Methods and Algorithms for Constraint-Based Virtual Assembly","volume":"6","year":"2003","journal-title":"Virtual Reality"},{"issue":"2","key":"2019100319384802700_bib40","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/s12008-010-0091-7","article-title":"Interactive Simulation of CAD Models Assemblies Using Virtual Constraint Guidance","volume":"4","year":"2010","journal-title":"Int. J. Interact. Des. Manuf."},{"key":"2019100319384802700_bib41","doi-asserted-by":"crossref","unstructured":"Rosenberg, L. B., 1993, \u201cVirtual Fixtures: Perceptual Tools for Telerobotic Manipulation,\u201d 1993 IEEE Virtual Reality Annual International Symposium (VRAIS'1996), Seattle, WA, Sep. 18\u201322, pp. 76\u201382.10.1109\/VRAIS.1993.380795","DOI":"10.1109\/VRAIS.1993.380795"},{"issue":"11","key":"2019100319384802700_bib42","doi-asserted-by":"publisher","first-page":"973","DOI":"10.1007\/s00371-008-0275-3","article-title":"Contact Identification for Assembly\u2013Disassembly Simulation With a Haptic Device","volume":"24","year":"2008","journal-title":"Visual Comput."},{"key":"2019100319384802700_bib43","unstructured":"Boussuge, F., L\u00e9on, J. C., Hahmann, S., and Fine, L., 2012, \u201cAn Analysis of DMU Transformation Requirements for Structural Assembly Simulations,\u201d 8th International Conference on Engineering Computational Technology (ECT'2012), Dubrovnik, Croatia, pp. 1\u201322."},{"issue":"2","key":"2019100319384802700_bib44","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/s12008-011-0120-1","article-title":"Assembly Simulation Incorporating Component Mobility Modelling Based on Functional Surfaces","volume":"5","year":"2011","journal-title":"Int. J. Interact. Des. Manuf."},{"issue":"1","key":"2019100319384802700_bib45","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1162\/105474601750182333","article-title":"Testbed Evaluation of Virtual Environment Interaction Techniques","volume":"10","year":"2001","journal-title":"Presence"},{"key":"2019100319384802700_bib46","article-title":"Mathematical Models of Rigid Solid Objects","year":"1980"},{"key":"2019100319384802700_bib47","article-title":"Representations of Rigid Solid Objects","year":"1980"},{"issue":"2","key":"2019100319384802700_bib48","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1023\/B:JODS.0000024119.38784.ff","article-title":"Stability and Finiteness Properties of Medial Axis and Skeleton","volume":"10","year":"2004","journal-title":"ASME J. Dyn. Control Syst."},{"issue":"10","key":"2019100319384802700_bib49","doi-asserted-by":"publisher","first-page":"874","DOI":"10.1109\/TC.1980.1675470","article-title":"Set Membership Classification: A Unified Approach to Geometric Intersection Problems","volume":"29","year":"1980","journal-title":"IEEE Trans. Comput."},{"key":"2019100319384802700_bib50","article-title":"Shape Complementarity Analysis for Objects of Arbitrary Shape","year":"2014"},{"issue":"11","key":"2019100319384802700_bib51","doi-asserted-by":"publisher","first-page":"1029","DOI":"10.1016\/j.cad.2004.01.011","article-title":"Any Open Bounded Subset of rn Has the Same Homotopy Type as Its Medial Axis","volume":"36","year":"2004","journal-title":"Comput. Aided Des."},{"key":"2019100319384802700_bib52","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/b106657_6","article-title":"Stability and Computation of Medial Axes: A State-of-the-Art Report","volume-title":"Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration","year":"2009"},{"issue":"1","key":"2019100319384802700_bib53","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s007910050004","article-title":"NETGEN: An Advancing Front 2D\/3D-Mesh Generator Based on Abstract Rules","volume":"1","year":"1997","journal-title":"Comput. Visualization Sci."},{"key":"2019100319384802700_bib54","doi-asserted-by":"crossref","unstructured":"Hoff, K. E., III, Culver, T., Keyser, J., Lin, M., and Manocha, D., 1999, \u201cFast Computation of Generalized Voronoi Diagrams Using Graphics Hardware,\u201d 26th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '99), pp. 277\u2013286.10.1145\/311535.311567","DOI":"10.1145\/311535.311567"},{"key":"2019100319384802700_bib55","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/978-3-642-03596-8_13","article-title":"A New Approach to Point Membership Classification in B-Rep Solids","volume-title":"Mathematics of Surfaces XIII","year":"2009"},{"key":"2019100319384802700_bib56","doi-asserted-by":"crossref","unstructured":"Behandish, M., and Ilie\u015f, H. T., 2015, \u201cHaptic Assembly Using Skeletal Densities and Fourier Transforms,\u201d 2015 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC\/CIE\u20192015), Boston, MA.","DOI":"10.1115\/DETC2015-47923"}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4030749\/6100784\/jcise_015_04_041004.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4030749\/6100784\/jcise_015_04_041004.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T10:00:42Z","timestamp":1748426442000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/doi\/10.1115\/1.4030749\/370314\/PeginHole-Revisited-A-Generic-Force-Model-for"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,20]]},"references-count":56,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,12,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.4030749","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"value":"1530-9827","type":"print"},{"value":"1944-7078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8,20]]},"article-number":"041004"}}