Dimension Optimization of Polycentric Knee Mechanism Using The Bees Algorithm and Genetic Algorithm

Abstract

: In knee prostheses, the curve of the instantaneous center of rotation (ICR) and, therefore, stability of the prothesis are the most important parameters to be considered. The ICR curve depends on many parameters. One of them and the most effective one is the dimensions of four bar mechanism. In polycentric knee mechanisms, it has become inevitable to use optimization techniques while determining the dimensions of the mechanism for the stability of the prosthesis in the stance position. In this study, definitions of knee prostheses and polycentric knee mechanisms are given, optimization studies written in this field are mentioned thorough literature research. The study aims to find mechanism dimensions that gives ICR curve close to the reference curve by optimizing the mechanism dimensions of four-bar knee mechanisms. The Bees Algorithm and Genetic Algorithm (GA) were used for this purpose. The limits and objective function for the optimization were determined, and after many trials, separate mechanism dimensions with The Bees Algorithm and the Genetic Algorithm are obtained. By comparing the results, it has been observed that the dimensions obtained by The Bees Algorithm produced a better approximation to the reference instantaneous center of rotation curve.

Keywords

• Knee Prosthesis
• Polycentric Knee
• Four-Bar Mechanism
• Lower-Limb Prosthesis
• Voluntary Control
• Instantaneous Center of Rotation

Dört Çubuk Mekanizmalı Diz Protezlerinin Arı Algoritması ve Genetik Algoritma ile Boyut Optimizasyonu

Öz

Diz protezlerinde kullanılan dört çubuk mekanizmalarda duruş durumunda ani dönme merkezi koordinatları ve buna bağlı olarak amputenin dengesi dikkat edilmesi gereken en önemli parametredir. Ani dönme merkezi eğrisi birçok parametreye bağlıdır. Bunların arasından dikkat edilmesi gereken en önemli parametrelerden biri de mekanizmanın boyutlarından geçmektedir. Dört çubuk mekanizmasının kullanıldığı diz protezlerinde duruş konumunda amputenin dengede olması için mekanizmanın boyutları belirlenirken optimizasyon tekniklerinin kullanılması kaçınılmaz bir hal almıştır. Bu çalışmada, diz protezleri ve diz protezlerinde kullanılan dört çubuk mekanizmaları hakkında tanımlamalar verilmiş, literatür araştırması yaparak bu alanda yazılan optimizasyon çalışmalarından bahsedilmiştir. Yapılan çalışma, diz protezlerinde kullanılan dört çubuk mekanizmanın sentezini yaparak referans ani dönme merkezi eğrisine yakın mekanizma boyutları bulmayı amaçlamaktadır. Mekanizma boyutları için Arı Algoritması ve Genetik Algoritma kullanılmıştır. Optimizasyon için gerekli sınırlar ve amaç fonksiyonu belirlenmiş, birçok deneme sonrası Arı Algoritması ve Genetik Algoritma için ayrı ayrı mekanizma boyutları elde edilmiştir. Elde edilen sonuçlar karşılaştırılmış ve Arı Algoritmasının referans ani dönme merkezi eğrisine daha iyi yakınlaşan mekanizma boyutları verdiği görülmüştür.

Anahtar Kelimeler

• Diz Protezleri
• Çok Merkezli Diz Mekanizması
• Dört Çubuk Mekanizması
• Arı Algoritması
• Genetik Algoritma
• Ani Dönme Merkezi

Kaynakça

1. Al-Maliky F. T., Chiad J. S. Study and evaluation of four bar polycentric knee used in the prosthetic limb for transfemoral amputee during the gait cycle. Materials Today: Proceedings, 42, 2706–2712, 2021. https://doi.org/10.1016/j.matpr.2020.12.709
2. Anand T. S., Sujatha S. A method for performance comparison of polycentric knees and its application to the design of a knee for developing countries. Prosthetics and Orthotics International, 41(4), 402–411, 2017. https://doi.org/10.1177/0309364616652017
3. Andrysek J., Klejman S., Torres-Moreno R., Heim W., Steinnagel B., Glasford S. Mobility function of a prosthetic knee joint with an automatic stance phase lock. Prosthetics and Orthotics International, 35(2), 163–170, 2011. https://doi.org/10.1177/0309364611408495
4. Chauhan S. S., Bhaduri S. C. Evaluation of the Polycentric above Knee Prosthesis. 15th National Conference on Machines and Mechanisms, 1–10, 2011.
5. El-Sayed A. M., Hamzaid N. A., Abu Osman N. A. Technology efficacy in active prosthetic knees for transfemoral amputees: A quantitative evaluation. In Scientific World Journal, 2014. https://doi.org/10.1155/2014/297431
6. Eqra N., Abiri A. H., Vatankhah R. Optimal synthesis of a four-bar linkage for path generation using adaptive PSO. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(9), 2018. https://doi.org/10.1007/s40430-018-1392-1
7. Eser O., Çakan A., Kalyoncu M., Botsalı F. Arı Algoritması (AA) ve Parçacık Sürü Optimizasyonu (PSO) Kullanarak Çeyrek Araç Modeli Tasarım Parametrelerinin Belirlenmesi. Konya Journal of Engineering Sciences, 621–632, 2021. https://doi.org/10.36306/konjes.881062
8. Fu, H., Zhang, X., Wang, X., Yang, R., Li, J., Wang, L., Zhang, N., Li, G., Liu, T., Fan, B., Inoue Y. A novel prosthetic knee joint with a parallel spring and damping mechanism. International Journal of Advanced Robotic Systems, 13(4), 2016. https://doi.org/10.1177/1729881416658174

9. Hobson D. A., Torfason L. E. Optimization of Four-Bar Knee Mechanism-a Computerized Approach. Journal of Biomechanics, 7(4), 371–376, 1974.
10. Holland J. H. Genetic Algorithms. 267(1), 66–73, 1992. https://doi.org/10.2307/24939139
11. İlgen S., Durdu A., Gülbahçe E., Çakan A., Kalyoncu M. The Bees Algorithm Approach to Determining SMC Controller Parameters for the Position Control of a SCARA Robot Manipulator. European Journal of Science and Technology. 2022. https://doi.org/10.31590/ejosat.883266
12. Marisami P., Venkatachalam R. Towards optimal toe-clearance in synthesizing polycentric prosthetic knee mechanism. Computer Methods in Biomechanics and Biomedical Engineering, 25(6), 656–667, 2022. https://doi.org/10.1080/10255842.2021.1972291
13. Muñoz-César J. J., Hernández-Gómez L. H., López-Suárez O. I., Urriolagoitia-Sosa G., Beltrán-Fernández J. A., Urriolagoitia-Calderón G., Pava-Chipol N. D., Quintero-Gómez I. J. Optimization of the Design of a Four Bar Mechanism for a Lower Limb Prosthesis Using the Taboo Search Algorithm. In Advanced Structured Materials (Vol. 40, pp. 107–125), 2013. https://doi.org/10.1007/978-3-319-00479-2_9
14. Otto Bock 3R20, 2023. Avalaible online: https://www.protesicave.com/Prótesis-Con-3r20 (accessed on 13 May 2023)
15. Otto Bock 3R20/3R36 User Manuel. (n.d.), 2023. Otto Bock.
16. Pfeifer S., Riener R., Vallery H. An Actuated Transfemoral Prosthesis with Optimized Polycentric Knee Joint. The Fourth IEEE RAS/EMBS International Conference on Biomedical Robotics and Biomechatronics, 1807–1812, 2012.
17. Pham D. T., Kalyoncu M. Optimisation of a fuzzy logic controller for a flexible single-link robot arm using the bees algorithm. IEEE International Conference on Industrial Informatics (INDIN), 475–480, 2009. https://doi.org/10.1109/INDIN.2009.5195850
18. Pham D. T., Ghanbarzadeh A., Koc E., Otri S., Rahim S., Zaidi M. The Bees Algorithm, 2005.
19. Pham D. T., Ghanbarzadeh A., Koç E., Otri S., Rahim S., Zaidi M. The Bees Algorithm- A Novel Tool for Complex Optimisation Problems. Intelligent Production Machines and Systems, 454–459, 2006.
20. Pham D. T., Kalyoncu M., Koç E., Tınkır M. Hierarchical PID Controller Design for a Flexible Link Robot Manipulator Using the Bees Algorithm. Proceedings of 6th International Symposium on Intelligent Manufacturing Systems, 2008. https://www.researchgate.net/publication/280921975
21. Poliakov O. M., Lazarev V. B., Chepenyuk O. O. Transfemoral Prosthesis with Polycentric Knee Mechanism: Design, Kinematics, Dynamics and Control Strategy. In Journal of Rehabilitation Robotics (Issue 1), 2013.
22. Radcliffe C. W. Four-bar linkage prosthetic knee mechanisms: kinematics, alignment and prescription criteria. In Prosthetics and Orthotics Iniemational 18, 1994.
23. Radcliffe C. W., Professor D. M. Biomechanics of Knee Stability Control with Four-Bar Prosthetic Knees. ISPO Australia Annual Meeting, 2003.
24. Roy L., Sen A., Chetia R. P., Borah M. J. Analysis and Synthesis of Four bar Mechanism. International Journal of Theoretical and Applied Mechanics, 3(2), 171–186, 2008. http://www.ripublication.com/ijtam.htm
25. Sancisi N., Caminati R., Parenti-Castelli V. Optimal Four-Bar Linkage for the Stability and the Motion of the Human Knee Prostheses. 2009.
26. Soriano J. F., Rodríguez J. E., Valencia L. A. Performance comparison and design of an optimal polycentric knee mechanism. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42(5), 2020. https://doi.org/10.1007/s40430-020-02313-6
27. Şen M. A. Balina Optimizasyon Algoritması Kullanılarak Dört Çubuk Mekanizmasının Optimum Yörünge Sentezi. 20. Ulusal Makina Teorisi Sempozyumu, 276–282, 2021. https://www.researchgate.net/publication/366589931
28. Şen M. A., Kalyoncu M. İki Tekerlekli Kendi Kendini Dengeleyen Robotun Yörünge Takibi için Arı Algoritması kullanarak LQR Kontrolcü Tasarımı. Uluslararası Katılımlı 17. Makina Teorisi Sempozyumu, 1–7, 2015. https://www.researchgate.net/publication/280932255
29. Şen M. A., Bilgiç H. H., Kalyoncu M. Determination of LQR Controller Parameters for Stabilization and Position Control of Double Inverted Pendulum Using The Bees Algorithm. Mühendis ve Makina, 57(679), 53–62, 2016.
30. Zhang Y., Wang E., Wang M., Liu S., Ge W. Design and Experimental Research of Knee Joint Prosthesis Based on Gait Acquisition Technology. Biomimetics, 6(28), 1–15, 2021. https://doi.org/10.3390/biomimetics