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| Content Provider | The American Society of Mechanical Engineers (ASME) Digital Collection |
|---|---|
| Author | Bandyopadhyay, Sandipan Ghosal, Ashitava |
| Abstract | The identification of principal twists of the end-effector of a manipulator undergoing multi-degree-of-freedom motion is considered to be one of the central problems in kinematics. In this paper, we use dual velocity vectors to parameterize se(3), the space of twists, and define an inner product of two dual velocities as a dual number analog of a Riemannian metric on SE(3). We show that the principal twists can be obtained from the solution of an eigenvalue problem associated with this dual metric. It is shown that the computation of principal twists for any degree-of-freedom (DoF) of rigid-body motion, requires the solution of at most a cubic dual characteristic equation. Furthermore, the special nature of the coefficients yields simple analytical expressions for the roots of the dual cubic, and this in turn leads to compact analytical expressions for the principle twists. We also show that the method of computation allows us to separately identify the rotational and translational degrees-of-freedom lost or gained at singular configurations. The theory is applicable to serial, parallel, and hybrid manipulators, and is illustrated by obtaining the principal twists and singular directions for a 3-DoF parallel, and a hybrid 6-DoF manipulator. |
| Sponsorship | Design Engineering Division and Computers and Information in Engineering Division |
| Starting Page | 1095 |
| Ending Page | 1106 |
| Page Count | 12 |
| File Format | |
| ISBN | 0791837009 |
| DOI | 10.1115/DETC2003/DAC-48819 |
| e-ISBN | 0791836983 |
| Volume Number | Volume 2: 29th Design Automation Conference, Parts A and B |
| Conference Proceedings | ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |
| Language | English |
| Publisher Date | 2003-09-02 |
| Publisher Place | Chicago, Illinois, USA |
| Access Restriction | Subscribed |
| Content Type | Text |
| Resource Type | Article |
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