Algebro-geometric techniques in kinematics of robots
Lead Research Organisation:
Loughborough University
Department Name: Mathematical Sciences
Abstract
The project involves a detailed study of robot closed linkages with 6 arms. These objects consist of 6 arms forming a closed chain connected via joints that rotate or have screw motion. It is known that a random such linkages is rigid. A crucial question is to classify all such linkages that are non-rigid, as they are useful in engineering and cost effective as 6 is the optimal number for such models.
Algebro-Geometric techniques have guided the study of linkages with rotational joints. The project will develop new (algebraic) techniques that deal with screw motion of the joints.
The project is fundamentally interdisciplinary, as it uses modern machinery of algebra and geometry to tackle theoretical questions in robotics with potential applications in engineering.
Algebro-Geometric techniques have guided the study of linkages with rotational joints. The project will develop new (algebraic) techniques that deal with screw motion of the joints.
The project is fundamentally interdisciplinary, as it uses modern machinery of algebra and geometry to tackle theoretical questions in robotics with potential applications in engineering.
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509516/1 | 01/10/2016 | 30/09/2021 | |||
| 1965756 | Studentship | EP/N509516/1 | 01/10/2017 | 28/07/2021 | Tiago Guerreiro |
| Description | Linkages are mechanical objects consisting of rigid bodies which connected by joints. A closed linkage is a linkage that forms a loop and, usually, its mobility is very constrained. We were able to give mathematical conditions for many different families to have mobility. If we require "higher mobility", that is, for the mechanical object to move tracing a surface even more conditions can be achieved. We have used Algebraic Geometry and Bond Theory in order to achieve these results. |
| Exploitation Route | Over-constrained linkages are "rare" objects and we always aim to prove the existence of certain families and, ultimately, build physical models of them. There are still many questions to be answered and various possible lines of research outlined by me and my collaborators. Outside of academia, it will be interesting to see applications of such linkages. Many, for instance, are used in constructions and everyday life. |
| Sectors | Construction,Manufacturing, including Industrial Biotechology,Other |