A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces
A computable model of grasping and manipulation of a 3D rigid object with arbitrary smooth surfaces by multiple robot fingers with smooth fingertip surfaces is derived under rolling contact constraints between surfaces. Geometrical conditions of pure rolling contacts are described through the moving...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Modelling and Simulation in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2011/684034 |
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| author | Suguru Arimoto Morio Yoshida |
| author_facet | Suguru Arimoto Morio Yoshida |
| author_sort | Suguru Arimoto |
| collection | DOAJ |
| description | A computable model of grasping and manipulation of a 3D rigid object with arbitrary smooth surfaces by multiple robot fingers with smooth fingertip surfaces is derived under rolling contact constraints between surfaces. Geometrical conditions of pure rolling contacts are described through the moving-frame coordinates at each rolling contact point under the postulates: (1) two surfaces share a common single contact point without any mutual penetration and a common tangent plane at the contact point and (2) each path length of running of the contact point on the robot fingertip surface and the object surface is equal. It is shown that a set of Euler-Lagrange equations of motion of the fingers-object system can be derived by introducing Lagrange multipliers corresponding to geometric conditions of contacts. A set of 1st-order differential equations governing rotational motions of each fingertip and the object and updating arc-length parameters should be accompanied with the Euler-Lagrange equations. Further more, nonholonomic constraints arising from twisting between the two normal axes to each tangent plane are rewritten into a set of Frenet-Serre equations with a geometrically given normal curvature and a motion-induced geodesic curvature. |
| format | Article |
| id | doaj-art-9c23c3195ccf4d7cbe96d55165af3366 |
| institution | Kabale University |
| issn | 1687-5591 1687-5605 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Modelling and Simulation in Engineering |
| spelling | doaj-art-9c23c3195ccf4d7cbe96d55165af33662025-02-03T05:54:18ZengWileyModelling and Simulation in Engineering1687-55911687-56052011-01-01201110.1155/2011/684034684034A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth SurfacesSuguru Arimoto0Morio Yoshida1RIKEN-TRI Collaboration Center for Human-Interactive Robot Research, Nagoya, Aichi 463-0003, JapanRIKEN-TRI Collaboration Center for Human-Interactive Robot Research, Nagoya, Aichi 463-0003, JapanA computable model of grasping and manipulation of a 3D rigid object with arbitrary smooth surfaces by multiple robot fingers with smooth fingertip surfaces is derived under rolling contact constraints between surfaces. Geometrical conditions of pure rolling contacts are described through the moving-frame coordinates at each rolling contact point under the postulates: (1) two surfaces share a common single contact point without any mutual penetration and a common tangent plane at the contact point and (2) each path length of running of the contact point on the robot fingertip surface and the object surface is equal. It is shown that a set of Euler-Lagrange equations of motion of the fingers-object system can be derived by introducing Lagrange multipliers corresponding to geometric conditions of contacts. A set of 1st-order differential equations governing rotational motions of each fingertip and the object and updating arc-length parameters should be accompanied with the Euler-Lagrange equations. Further more, nonholonomic constraints arising from twisting between the two normal axes to each tangent plane are rewritten into a set of Frenet-Serre equations with a geometrically given normal curvature and a motion-induced geodesic curvature.http://dx.doi.org/10.1155/2011/684034 |
| spellingShingle | Suguru Arimoto Morio Yoshida A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces Modelling and Simulation in Engineering |
| title | A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces |
| title_full | A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces |
| title_fullStr | A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces |
| title_full_unstemmed | A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces |
| title_short | A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces |
| title_sort | mathematical and numerically integrable modeling of 3d object grasping under rolling contacts between smooth surfaces |
| url | http://dx.doi.org/10.1155/2011/684034 |
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