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The approach is direct and uses a pseudo-inverse projection of the haptic device end effector onto the virtual surface. The rendering algorithm enables the user to freely move a soft fingertip model along a highly curved deformable surface and perceive surface roughness in the normal direction by feeling a nonlinear contact force. The normal force is governed by a physically based three-dimensional constitutive model, which accounts for both geometric and material nonlinearities. In experimental implementation, the soft fingertip model acts as the compliant haptic interface (robot) and the user manually guides the manipulator to explore the deformable surface properties in real time. The (nonlinear) reaction force normal to the surface is applied at the soft fingertip edge of the fingertip bone (distal phalanx). The robustness of the approach is illustrated by experimental data in rendering highly curved compliant surfaces.<\/jats:p>","DOI":"10.1177\/0959651815598257","type":"journal-article","created":{"date-parts":[[2015,8,25]],"date-time":"2015-08-25T20:33:55Z","timestamp":1440534835000},"page":"949-956","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Haptic exploration of highly curved compliant surfaces"],"prefix":"10.1177","volume":"229","author":[{"given":"Naci","family":"Zafer","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Eskisehir Osmangazi University, Eski\u015fehir, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sezcan","family":"Yilmaz","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Eskisehir Osmangazi University, Eski\u015fehir, 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