Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
A new equation for the point closest to the origin on an axis: a review of Chasles' Theorem
Submission Author:
Luis Paulo Laus , PR
Co-Authors:
Luis Paulo Laus, Jonathan Selig
Presenter: Luis Paulo Laus
doi://10.26678/ABCM.COBEM2023.COB2023-0932
Abstract
The screw motion and some important theorems for rigid body motion are reviewed and new equations for parametrizing rigid body displacement are provided. The antisymmetric 3\times3 matrix adjoint to a three dimensional real vector is used to produce a new equation for a point on the screw axis closest to the origin which completes, in a novel fashion, the proof of the Chasles' Theorem. The use of sophisticated algebraic concepts aims to inspire students on the high value of mathematics. The new result, the closest point to the origin on a general screw axis, is itself of great relevance in the study of kinematics.
Keywords
Chasles Theorem, antisymetric matrix, instantaneous screw axis, homogeneous transformations, parameter
