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| Content Provider | The American Society of Mechanical Engineers (ASME) Digital Collection |
|---|---|
| Author | Yang, Jingzhou Abdel-Malek, Karim |
| Copyright Year | 2005 |
| Abstract | An analytical method is presented to obtain all surfaces enveloping the workspace of a general n degree-of-freedom mechanism with non-unilateral constraints. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation method for serial manipulators. The method introduced in this paper is based upon analytical criteria for determining singular behavior of the mechanism. A perturbation approach is implemented to determine the interior and exterior of the workspace. The complete mathematical formulation is presented and illustrated using 3 and 4 DOF spatial manipulators. The paper present a rigorous analysis of the sub-Jacobians to determine a classification of singularities: Type I sets are position Jacobian singularities; Type II sets are instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III sets are domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV sets are coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one submatrix due to either of two occurrences: a Type II or Type III singularities. The paper presents a general formulation for determining the workspace. |
| Sponsorship | Design Engineering Division and Computers and Information in Engineering Division |
| Starting Page | 717 |
| Ending Page | 726 |
| Page Count | 10 |
| File Format | |
| ISBN | 0791847446 |
| DOI | 10.1115/DETC2005-84180 |
| e-ISBN | 0791837661 |
| Volume Number | Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B |
| Conference Proceedings | ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |
| Language | English |
| Publisher Date | 2005-09-24 |
| Publisher Place | Long Beach, California, USA |
| Access Restriction | Subscribed |
| Subject Keyword | Singularity Non-unilateral Jacobian row-rank deficiency Manipulators Visualization Degrees of freedom Kinematic chains |
| Content Type | Text |
| Resource Type | Article |
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