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Nikola LJ. Zivkovic1

Jelena Z. Vidakovic1

Mihailo P. Lazarevic2

1Lola Institute Ltd., Kneza Viseslava 70a, 11030 Belgrade, Serbia
2Faculty of Mechanical Engineering, Kraljice Marije 16, 11060 Belgrade, Serbia

Received: 31 March 2023
Revised: 26 May 2023
Accepted: 5 June 2023
Published: 30 June 2023


Forward kinematics is fundamental to robot design, control, and simulation. Different forward kinematics algorithms have been developed to deal with the complex geometry of a robot. This paper presents a robot forward kinematics algorithm in dual quaternion space. The presented method uses Denavit-Hartenberg (DH) convention for uniform definition of successive rotational and translational transformations in joints along the robot’s kinematic chain. This research aims to utilize the advantages of dual quaternions and DH convection for forward kinematics computation and make the algorithm, which is compact, intuitive, numerically robust, and computationally efficient as it uses the minimal number of parameters required for the computation, suitable for implementation in ROS and similar software. The algorithm is verified on the 6DoF industrial robot RL15, with the symbolic equations and numerical simulation presented.


Forward kinematics, kinematic modelling, DH convention, coordinate frame transformations, quaternions, dual quaternions, robotics


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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0)

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December 2023

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How to Cite

N.LJ. Zivkovic,  J.Z. Vidakovic, M.P. Lazarevic, Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention. Applied Engineering Letters, 8(2), 2023: pp.52–59.

More Citation Formats

Zivkovic, N.LJ., Vidakovic, J.Z. & Lazarevic, M.P. (2023). Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention. Applied Engineering Letters, 8(2), pp.52–59.

Nikola LJ. Zivkovic, et al. ”Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention.” Applied Engineering Letters, vol. 8, no. 2, 2023, pp. 52–59, 

Nikola LJ. Zivkovic, Jelena Z Vidakovic, and Mihailo P Lazarevic. 2023. “Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention.” Applied Engineering Letters 8 (2): 52–59.

Zivkovic, N.LJ., Vidakovic, J.Z. and Lazarevic, M.P. (2023).  Forward Kinematics Algorithm in Dual Quaternion Space Based on Denavit-Hartenberg Convention. Applied Engineering Letters, 8(2), pp.52–59. doi: 10.18485/aeletters.2023.8.2.2.