Dual quaternion representation of motor motion

Year 2025, Issue: 063, 53 - 69, 30.12.2025

Azat Kulu , Erhan Ata

https://doi.org/10.59313/jsr-a.1803611

Abstract

The dual quaternion algebra, introduced in the 19th century by Clifford, is used to effectively represent the algebraic structure of motor positions and displacements. In this study, by employing point–line and screw operators, the motor operator is formulated in a concise and computationally efficient way. A dual vector with a non-zero real part is employed to represent the endpoint position in the motor representation, serving as the basis for constructing the motor operator. In order to apply the motor motion (displacement) to the motor representation, which is considered as a rigid element, a special dual quaternion is used to create a motor operator. This new motor operator, which represents motor motion (displacement), provides both a different approach to motor algebra and ease and simplicity of operation.

Keywords

dual quaternion , motor operator , rigid transformation

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