Geometric approach to solving inverse kinematics of six DOF robot with spherical joints


  • Nacer Hadidi Ecole Nationale Polytechnique, Laboratoire de Genie Mecanique et devellopement, Department of Mechanical engineering, 10 Avenue Hassan Badi, 16200 El Harrach, Algeria
  • Mohamed Bouaziz Ecole Nationale Polytechnique, Laboratoire de Genie Mecanique et devellopement, Department of Mechanical engineering, 10 Avenue Hassan Badi, 16200 El Harrach, Algeria
  • Chawki Mahfoudi University Larbi Ben Mhidi, Campus of AinBeida, Department of Mechanical engineering, Route de Constantine, B.P. 358, 04000 Oum El Bouaghi, Algeria
  • Mohamed Zaharuddin Universiti Teknologi Malaysia, Faculty of Electrical Engineering, Department of mechatronics, 81310 Johor Bahru, Malaysia



robotic, forward kinematics, inverse kinematics, geometric modelling, space geometry


Inverse kinematics is a fundamental concept in robotics that plays a crucial role in a robot’s ability to perform tasks. In this contribution, we propose a novel geometric approach based on vector calculus to solve the inverse kinematics problem. The primary advantage of this approach originates from the solutions, which exhibit a linear form and uncoupled equations. To validate the effectiveness and correctness of our proposed method, we constructed a six-degrees-of-freedom robot. This robot is controlled by an Arduino Mega 2650 on which we have implemented the inverse kinematics algorithm. The validation process involved considering various desired trajectories of the end-effector, which were simulated in Matlab and then performed by the physical robot. Importantly, our findings confirm that the end-effector successfully tracks the predefined trajectories. Furthermore, we conducted a comparative analysis between Paul’s method and the results obtained from joint angles using our proposed approach. Interestingly, our study reveals a significant similarity between the two sets of results, reaffirming the accuracy and validity of the approach presented in this study.


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