A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact
This paper investigates the kinematics of spin-rolling motion of rigid objects. This paper does not consider slipping but applies a Darboux frame to develop kinematics of spin-rolling motion, which occurs in a nonholonomic system. A new formulation of spin-rolling motion of the moving object is deri...
| Main Authors: | , |
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| Format: | Journal Article |
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IEEE Press
2010
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| Online Access: | http://hdl.handle.net/20.500.11937/22245 |
| _version_ | 1848750816512442368 |
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| author | Cui, Lei Dai, J. |
| author_facet | Cui, Lei Dai, J. |
| author_sort | Cui, Lei |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper investigates the kinematics of spin-rolling motion of rigid objects. This paper does not consider slipping but applies a Darboux frame to develop kinematics of spin-rolling motion, which occurs in a nonholonomic system. A new formulation of spin-rolling motion of the moving object is derived in terms of contravariant vectors, rolling velocity, and geometric invariants, including normal curvature, geodesic curvature, and geodesic torsion of the respective contact curve. The equation is represented with geometric invariants. It can be readily generalized to suit both arbitrary parametric surface and contact trajectory and can be differentiated to any order. Effect of the relative curvatures and torsion on spin-rolling kinematics is explicitly presented. The translation velocity of an arbitrary point on the moving object is also derived based on the Darboux frame. |
| first_indexed | 2025-11-14T07:42:51Z |
| format | Journal Article |
| id | curtin-20.500.11937-22245 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:42:51Z |
| publishDate | 2010 |
| publisher | IEEE Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-222452017-09-13T13:49:38Z A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact Cui, Lei Dai, J. kinematics rolling nonholonomic grasping spin-rolling point contact multifingered hand motion Darboux frame This paper investigates the kinematics of spin-rolling motion of rigid objects. This paper does not consider slipping but applies a Darboux frame to develop kinematics of spin-rolling motion, which occurs in a nonholonomic system. A new formulation of spin-rolling motion of the moving object is derived in terms of contravariant vectors, rolling velocity, and geometric invariants, including normal curvature, geodesic curvature, and geodesic torsion of the respective contact curve. The equation is represented with geometric invariants. It can be readily generalized to suit both arbitrary parametric surface and contact trajectory and can be differentiated to any order. Effect of the relative curvatures and torsion on spin-rolling kinematics is explicitly presented. The translation velocity of an arbitrary point on the moving object is also derived based on the Darboux frame. 2010 Journal Article http://hdl.handle.net/20.500.11937/22245 10.1109/TRO.2010.2040201 IEEE Press fulltext |
| spellingShingle | kinematics rolling nonholonomic grasping spin-rolling point contact multifingered hand motion Darboux frame Cui, Lei Dai, J. A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact |
| title | A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact |
| title_full | A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact |
| title_fullStr | A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact |
| title_full_unstemmed | A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact |
| title_short | A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact |
| title_sort | darboux-frame-based formulation of spin-rolling motion of rigid objects with point contact |
| topic | kinematics rolling nonholonomic grasping spin-rolling point contact multifingered hand motion Darboux frame |
| url | http://hdl.handle.net/20.500.11937/22245 |