Symbolic Computation of the Lie Algebra se (3) of the Euclidean Group SE (3): An Application to the Infinitesimal Kinematics of Robot Manipulators

Jaime Gallardo-Alvarado, Mario A. Garcia-Murillo (), Juan Manuel Tabares-Martinez and X. Yamile Sandoval-Castro
Additional contact information
Jaime Gallardo-Alvarado: Department of Mechanical Engineering, National Technological Institute of Mexico, Celaya Campus, Celaya 38010, Mexico
Mario A. Garcia-Murillo: Department of Mechanical Engineering, DICIS, University of Guanajuato, Salamanca 36885, Mexico
Juan Manuel Tabares-Martinez: Department of Mechanical Engineering, National Technological Institute of Mexico, Celaya Campus, Celaya 38010, Mexico
X. Yamile Sandoval-Castro: School of Engineering and Sciences, Tecnologico de Monterrey, Monterrey 64849, Mexico

Mathematics, 2024, vol. 12, issue 16, 1-24

Abstract: This paper reports an application of the Lie algebra s e ( 3 ) of the Euclidean group S E ( 3 ) , which is isomorphic to the theory of screws in the velocity and acceleration analyses of serial manipulators. The symbolic computation of the infinitesimal kinematics allows one to obtain algebraic expressions related to the kinematic characteristics of the end effector of the serial manipulator, while in the case of complex manipulators, numerical computations are preferred owing to the emergence of long terms. The algorithm presented enables the symbolic computation of the velocity and acceleration characteristics of the end effector in serial manipulators in order to allow the compact and efficient modeling of velocity and acceleration analyses of both parallel and serial robotic manipulators. Unlike other algebras, these procedures can be extended without significant effort to higher-order analyses such as the jerk and jounce.

Keywords: serial manipulator; lie algebra; screw theory; kinematics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/16/2538/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/16/2538/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:16:p:2538-:d:1458039

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().