Section: New Results
Non-Linear Computational Geometry
Participants : Sény Diatta, Laurent Dupont, George Krait, Sylvain Lazard, Guillaume Moroz, Marc Pouget.
Reliable location with respect to the projection of a smooth space curve
Consider a plane curve
In a previous work [49], we have shown how to
describe the set of singularities of
Workspace, Joint space and Singularities of a family of Delta-Like Robots
Our paper [7] presents the workspace, the joint space and the singularities of a family of delta-like parallel robots by using algebraic tools. The different functions of the SIROPA library are introduced and used to estimate the complexity representing the singularities in the workspace and the joint space. A Groebner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three-dimensional plotting tools describing the shape of the workspace and of the joint space which will help engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configurations of the manipulator by comparing the complexity of the singularity equations.
In collaboration with Ranjan Jha, Damien Chablat, Luc Baron and Fabrice Rouillier.