FORWARD & INVERSE KINEMATICS SOLUTION OF 6-DOF ROBOTS THOSE HAVE OFFSET & SPHERICAL WRISTS

Abstract

One of the critical design decisions that arise during the design of an industrial robot is the function of the joints to be used and their location. Of course, for the designed robot to provide the expected performance, the selection of the motors and gear reducers that will create these joints will primarily affect the determination of these joints. However, both the examination of the existing industrial robots and the fact that the motor and gear reducer information that can be supplied can be easily obtained with today’s technology, these joints can be determined quickly as a result of a short investigation. Along with the mechanical design, robot control unit design also has stages that progress in parallel and depend on or affect the mechanical design decisions. One of the most important of these is that especially inverse kinematics calculations can be performed analytically, enabling the robot control unit to make decisions and give commands in real-time. This article aims to publish the geometric calculation of inverse kinematics of commonly used exampled configuration of 6-DOF industrial robot that has offset and spherical joint along with interactive calculation tables and sheets. There are numerous articles published on the same subject but none of them has provided any verification supplement so far. Thus, it is also aimed to confirm and verify the calculations given in this article by providing convenient tables and sheets and to create a solid foundation for future studies.

Keywords

• Inverse Kinematics
• Forward Kinematics
• 6-DOF Industrial Robot
• Spherical Wrist
• Offset Wrist
• Analytical Solution
• Geometric Solution

References

1. S. Asif, and P. Webb, “Kinematics Analysis of 6-DoF Articulated Robot with Spherical Wrist”, Hindawi Mathematical Problems in Engineering Volume 2021, Article ID 6647035, 11 pages, 2020. [Online] Available: https://doi.org/10.1155/2021/6647035 [Accessed: May 7, 2022]
2. Kepçeler, T. “Esnek Robot Kollarda Optimum Hareket Sentezi”, PhD. Thesis, Graduate School of Science & Engineering, Yildiz Technical University, Istanbul, Turkey, 1999, p. 20-32
3. S. Cubero, Industrial Robotics: Theory, Modelling and Control, plV pro literatur Verlag Robert Mayer-Scholz, DOI:10.5772/44, ISBN 3-86611-285-8, pp. 117-185, 2012.
4. M. Dahari, J. D. Tan, “Forward and Inverse Kinematics Model for Robotic Welding Process Using KR-16KS KUKA Robot”, 2011 4th International Conference on Modeling, Simulation and Applied Optimization, IEEE, ICMSAO 2011, DOI: 10.1109/ICMSAO.2011.5775598, 2011.
5. W. Guojun, X. Linhong, and H. Fulun, “Offline kinematics simulation of 6-DOF welding robot”, 2009 International Conference on Measuring Technology and Mechatronics Automation, ICMTMA 2009, vol. 2, DOI: 10.1109/ICMTMA.2009.608, 2009.
6. E. Sariyildiz, E. Cakiray, and H. Temeltas, “A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework”, International Journal of Advanced Robotic Systems, issue 5, vol. 8, DOI: 10.5772/45696, ISSN: 17298814, 2011.
7. J. J. Craig, Introduction to Robotics: Mechanics and Control, 3rd Edition, Pearson Education Limited, ISBN 10: 1-292-04004-1, 2004, pp. 19-135.
8. M. E. Kütük, M. T. Das, and L. C. Dülger, “Forward and Inverse Kinematics Analysis of Denso Robot”, Proceedings of the International Symposium of Mechanism and Machine Science, 2017, AzC IFToMM-Azerbaijan Technical University, issue September, vol. 11, 2017.

9. A. Khatamian, “Solving Kinematics Problems of a 6-DOF Robot Manipulator”, Int’l Conf. Scientific Computing, CSC, 2015, pp. 228-233
10. S. Kucuk, and Z. Birgul, “Inverse Kinematics Solutions for Industrial Robot Manipulators with Offset Wrists”, Applied Mathematical Modelling, vol. 38, issue 7-8, DOI:10.1016/j.apm.2013.10.014, ISSN: 0307904X, 2014. [Online] Available: http://dx.doi.org/10.1016/j.apm.2013.10.014 [Accessed: May 7, 2022].
11. P. Masajedi, K.H. Shirazi, and A. Ghanbarzadeh, “Verification of bee algorithm based path planning for a 6DOF manipulator using ADAMS”, Journal of Vibroengineering, Vol. 15, Issue 2, 2013, pp. 805-815 [Online Document], Available: JVE Journals, https://www.extrica.com/article/14551 [Accessed: Feb. 24, 2022].
12. L. Wu, X. Yang, K. Chen, and H. Ren, “A Minimal POE-Based Model for Robotic Kinematic Calibration with only Position Measurements”, IEEE Transactions on Automation Science and Engineering, issue 2, vol. 12, DOI: 10.1109/TASE.2014.2328652, ISSN: 15455955, 2015.
13. Wikipedia The Free Encyclopedia, “Euler Angles” (), Wikipedia The Free Encyclopedia, [Online]. Available: https://en.wikipedia.org/wiki/Euler_angles [Accessed: Dec. 19, 2021].
14. S. Dikmenli, “Forward & Inverse Kinematics Solution of 6-DOF Robots Those Have Offset & Spherical Wrists - Supplementary Data”, Mendeley Data, V1, doi: 10.17632/nfbjphjvkn.1, 2022. [Online]. Available: http://dx.doi.org/10.17632/nfbjphjvkn.1 [Accessed: May 7, 2022]