<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This paper introduces a novel computational method for analyzing the higher-order acceleration field of spatial kinematics chains. The method is based on vector and quaternionic calculus, as well as dual and multidual algebra. A closed-form coordinate-free solution generated by the morphism between the Lie group of rigid body displacements and the unit multidual quaternions is presented. Presented solution is used for higher-order kinematics investigation of lower-pair serial chains. Additionally, a general method for studying the vector field of arbitrary higher-order accelerations is discribed. The method utilizes the “automatic differentiation” feature of multidual and hyper-multidual functions to obtain the higher-order derivative of a rigid body pose without need in further differentiation of the body pose regarding time. Also is proved that all information regarding the properties of the distribution of higher-order accelerations is contained in the specified unit hyper-multidual quaternion.</p>
</abstract>

This paper introduces a novel computational method for analyzing the higher-order acceleration field of spatial kinematics chains. The method is based on vector and quaternionic calculus, as well as dual and multidual algebra. A closed-form coordinate-free solution generated by the morphism between the Lie group of rigid body displacements and the unit multidual quaternions is presented. Presented solution is used for higher-order kinematics investigation of lower-pair serial chains. Additionally, a general method for studying the vector field of arbitrary higher-order accelerations is discribed. The method utilizes the “automatic differentiation” feature of multidual and hyper-multidual functions to obtain the higher-order derivative of a rigid body pose without need in further differentiation of the body pose regarding time. Also is proved that all information regarding the properties of the distribution of higher-order accelerations is contained in the specified unit hyper-multidual quaternion.

Hypercomplex Quaternions and Higher-Order Analysis of Spatial Kinematic Chains

“Gheorghe Asachi” Technical University of Iași

BULETINUL INSTITUTULUI POLITEHNIC DIN IAȘI. Secția Matematica. Mecanică Teoretică. Fizică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Hypercomplex Quaternions and Higher-Order Analysis of Spatial Kinematic Chains"}

This paper introduces a novel computational method for analyzing the higher-order acceleration field of spatial kinematics chains. The method is based on...

Hypercomplex Quaternions and Higher-Order Analysis of Spatial Kinematic Chains

Publié en ligne: 29 déc. 2023

Pages: 21 - 34

Reçu: 04 sept. 2023

Accepté: 26 oct. 2023

DOI: https://doi.org/10.2478/bipmf-2023-0002

Mots clés
Multidual algebra, Lower-pair kinematic chains, Multidual quaternions, Higher-order kinematics, Lower-pair kinematic chains

© 2023 Daniel Condurache et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Hypercomplex Quaternions and Higher-Order Analysis of Spatial Kinematic Chains

Publié en ligne: 29 déc. 2023

Pages: 21 - 34

Reçu: 04 sept. 2023

Accepté: 26 oct. 2023

DOI: https://doi.org/10.2478/bipmf-2023-0002

Mots clésMultidual algebra, Lower-pair kinematic chains, Multidual quaternions, Higher-order kinematics, Lower-pair kinematic chains

© 2023 Daniel Condurache et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Multidual algebra, Lower-pair kinematic chains, Multidual quaternions, Higher-order kinematics, Lower-pair kinematic chains