On the nature of robot workspace
International Journal of Robotics Research
Robotics: control, sensing, vision, and intelligence
Robotics: control, sensing, vision, and intelligence
The singularities of redundant robot arms
International Journal of Robotics Research
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
On determining start points for a surface/surface intersection algorithm
Computer Aided Geometric Design
On the workspace of general 4R manipulators
International Journal of Robotics Research
Analytical boundary of the workspace for general 3-DOF mechanisms
International Journal of Robotics Research
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Extremal reaches in polynomial time
Proceedings of the twenty-seventh annual symposium on Computational geometry
Exact workspace boundary by extremal reaches
Proceedings of the twenty-seventh annual symposium on Computational geometry
| Hi-index | 0.00 |
Broadly applicable analytical algorithms for workspace of serial manipulators with non-unilateral constraints are developed and illustrated. The Jacobian row-rank deficiency method is employed to determine the singularities of these manipulators. There are four types of singularity sets: Type I: position Jacobian singularities; Type II: instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III: domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV: coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one sub-matrix due to either of two occurrences: a Type II or a Type III singularity. All of the singular surfaces are hypersurfaces that extend internally and externally the workspace envelope. Intersecting singular surfaces identifies singular curves that partition singular surfaces into subsurfaces, and a perturbation method is used to identify regions (curve segments/surface patches) of the hypersurfaces that are on the boundary. The formulation is illustrated by implementing it to a spatial 3-degree of freedom (DOF) and a spatial 4-DOF manipulator.