A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces
Joint Authors
Source
Modelling and Simulation in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-11-02
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Arimoto, Suguru& Yoshida, Morio. 2011. A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces. Modelling and Simulation in Engineering،Vol. 2011, no. 2011, pp.1-8.
https://search.emarefa.net/detail/BIM-490307
Modern Language Association (MLA)
Arimoto, Suguru& Yoshida, Morio. A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces. Modelling and Simulation in Engineering No. 2011 (2011), pp.1-8.
https://search.emarefa.net/detail/BIM-490307
American Medical Association (AMA)
Arimoto, Suguru& Yoshida, Morio. A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces. Modelling and Simulation in Engineering. 2011. Vol. 2011, no. 2011, pp.1-8.
https://search.emarefa.net/detail/BIM-490307
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-490307