The locus of the angular velocity vector of a moving rigid body is a cylindrical surface
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J. Jesús Cervantes-Sánchez
[1]
;
José M. Rico-Martínez
[1]
;
Mario A. García-Murillo
[1]
;
Ricardo García-García
[1]
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[1] Universidad de Guanajuato
Universidad de Guanajuato
México
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- Localización: Mechanics based design of structures and machines, ISSN 1539-7734, Vol. 53, Nº. 6, 2025, págs. 4812-4829
- Idioma: inglés
- Enlaces
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Resumen
This work presents a procedure that allows us to formulate logically and orderly all the equations of position, velocity, and acceleration that must be satisfied by any rigid body moving arbitrarily in three-dimensional physical space. Using Gaussian elimination, the complex system of linear equations can be changed to a more straightforward equivalent system of linearly independent equations, eliminating redundant equations and making the solution directly obtainable without much effort. This formulation allows us to systematically obtain the kinematic parameters of position, velocity, and acceleration associated with a rigid body in arbitrary motion, including the angular velocity vector and the angular acceleration vector. The particularity of the development allows us to find a unique condition that makes the position, velocity, and acceleration equations compatible. This condition gives rise to a novel and original symbolic equation representing a cylindrical surface whose points represent the locus of the angular velocity vector of the rigid body in motion. Two fully detailed case studies illustrate the applicability of the discovery. This research may help estimate a rigid body’s attitude and use accelerometers to control machines, mechanisms, and robots moving in space.
