Asimetrik üç serbestlik dereceli bir düzlemsel paralel robot mekanizmasının kinematik analizi

Year 2018, Volume: 22 Issue: 1, 75 - 84, 01.02.2018

Metin Toz

https://doi.org/10.16984/saufenbilder.296446

Abstract

Bu çalışmada üç Serbestlik Derecesine (SD)
sahip bir düzlemsel paralel robot mekanizmasının kinematik analizi
gerçekleştirilmiştir. Seçilen mekanizmanın diğer düzlemsel mekanizmalardan
farkı asimetrik bacak yapısına sahip olmasıdır. Asimetrik yapıyı elde etmek
için 3-RPR (R:Dönel eklem, P: Aktif prizmatik eklem) yapısındaki
simetrik bir düzlemsel robot mekanizmasının bir bacağı RRR (R:
Aktif dönel eklem) tipi bacak ile değiştirilmiş ve bu sayede RPR2RRR1
adını verdiğimiz asimetrik düzlemsel paralel robot mekanizması elde edilmiştir.
Bu mekanizma için ters kinematik, Jacobian matrisi ve tekil noktalardan
bağımsız çalışma uzayı analizi ile ilgili hesaplamalar gerçekleştirilmiştir.
Ayrıca bu mekanizmanın performansı simetrik düzlemsel bir paralel robot
mekanizması olan 3-RPR mekanizması ile karşılaştırılmıştır. Elde edilen
sonuçlara göre önerilen mekanizmanın çalışma uzayının hem uç işlevci tarafından
ulaşılabilinen nokta sayısı hem de yönelim açısının sınır değerleri yönünden
3-RPR mekanizmasından daha iyi olduğu gösterilmiştir.

Keywords

Düzlemsel paralel robot mekanizmaları, 3 DOF, kinematik analiz, Çalışma uzayı analizi

Kinematic analysis of a 3-DOF asymmetrical planar parallel robot mechanism

Abstract

In this study, kinematic analysis of a planar
parallel robot mechanism with three degrees of freedom (DOF) was performed. The
difference of the selected mechanism from the other planar mechanisms is that
it has an asymmetric leg structure. In order to provide the asymmetry, a leg of
3-RPR (R: Revolute joint, P: Active prismatic joint) symmetrical
planar robot mechanism was replaced by a RRR (R: Active revolute joint)
type leg and the asymmetrical planar parallel robot named RPR2RRR1
mechanism has been obtained. Inverse kinematics, Jacobian matrix and
singularity free workspace analysis were performed for the proposed mechanism.
In addition, the performance of this mechanism is compared with the 3-RPR
mechanism, which is a symmetric planar parallel robot mechanism. According to
the obtained results, it has been shown that the workspace of the proposed
mechanism is better than the 3-RPR mechanism in terms of both the number
of points that can be reached by the end-effector and the limit values of the
orientation angle.

Keywords

planar parallel robot mechanisms, 3 DOF, kinematic analysis, workspace analysis

References

• [1] M. Toz, S. Kucuk, “Dimensional optimization of 6-DOF 3-CCC type asymmetric parallel manipulator”, Advanced Robotics, vol. 28(9), pp. 625–637, 2014
• [2] M. Toz, S. Kucuk, “Dexterous workspace optimization of an asymmetric six-degree of freedom Stewart–Gough platform type manipulator”, Robotics and Autonomous Systems, vol.61(12), pp. 1516–1528, 2013.
• [3] X.S. Gao, D. Lei, Q. Liao, G.F. Zhang, “Generalized Stewart–Gough platforms and their direct kinematics”, IEEE Transactions on Robotics, 21(2), 141–151, 2005.
• [4] L.W. Tsai, “Robot Analysis: The Mechanics of Serial and Parallel Manipulators”, John Wiley & Sons, 1999.
• [5] Y. Singh, M. Santhakumar, “Inverse dynamics and robust sliding mode control of a planar parallel (2-PRP and 1-PPR) robot augmented with a nonlinear disturbance observer”, Mechanism and Machine Theory, vol 92, pp. 29-50, 2015.
• [6] P.S. Londhe, Y. Singh, M. Santhakumar, B.M. Patre, L.M. Waghmare, “Robust nonlinear PID-like fuzzy logic control of a planar parallel (2PRP-PPR) manipulator”, ISA Transactions, vol. 63, pp. 218-232, 2016.
• [7] M. Wu, D. Zhang, "Statics of a new asymmetrical parallel robot," 2008 IEEE International Conference on Automation and Logistics, Qingdao, pp. 2466-2470, 2008.
• [8] M. Wu, D. Zhang X. Zhao, "Conceptual Design and Kinematic Performance Evaluation of a New Asymmetrical Parallel Robot," 2007 International Conference on Mechatronics and Automation, Harbin, pp. 2854-2859, 2007.
• [9] S. Yan, L. Yi, "CAD Application to the Analysis about the Workspace of an Asymmetric Parallel Robot Influenced by the Joints”, Distribution" 2008 International Conference on Computer and Electrical Engineering, Phuket, pp. 497-501, 2008.
• [10] B. Li, J. Zhao, X. Yang, Y. Hu, “Kinematic Analysis of a Novel Three Degree-Of-Freedom Planar Parallel Manipulator”, International Journal of Robotics and Automation, vol. 24(2), pp. 158-165, 2009
• [11] S. Kucuk, A “Dexterity comparison for 3-DOF planar parallel manipulators with two kinematic chains using genetic algorithms”, Mechatronics, vol. 19(6), pp. 868-877, 2009.
• [12] A. E Firoozabadi, S. Ebrahimi, G. Amirian, “Dynamic characteristics of a 3-RPR planar parallel manipulator with flexible intermediate links”, Robotica, 33(9), pp. 1909–1925, 2015.
• [13] M. A. Mousavi, M. T. Masouleh, A. Karimi, “On the maximal singularity-free ellipse of planar 3- parallel mechanisms via convex optimization”, Robotics and Computer-Integrated Manufacturing, vol. 30(2), pp. 218-227, 2014.
• [14] R. Chandra, L. Rolland, “On solving the forward kinematics of 3RPR planar parallel manipulator using hybrid metaheuristics”, Applied Mathematics and Computation, vol. 217(22), pp. 8997-9008, 2011.
• [15] S. Caro, N. Binaud, P. Wenger, “Sensitivity Analysis of 3-RPR Planar Parallel Manipulators”, ASME. J. Mech. Des., vol. 131(12), pp. 121005-121005-13, 2009.
• [16] Q. Jiang, C. M. Gosselin, "The Maximal Singularity-Free Workspace of Planar 3-RPR Parallel Mechanisms," 2006 International Conference on Mechatronics and Automation, Luoyang, Henan, pp. 142-146, 2006.
• [17] S. M. Varedi-Koulaei, H. M. Daniali, M. Farajtabar, B. Fathi M. Shafiee-Ashtiani, “Reducing the undesirable effects of joints clearance on the behavior of the planar 3-RRR parallel manipulators”, Nonlinear Dynamics, vol. 86(2), pp. 1007–1022, 2016.
• [18] J. Jesús Cervantes-Sánchez, J. M. Rico-Martínez, I. J. Brabata-Zamora, J. D. Orozco-Muñiz, “Optimization of the Translational Velocity for the Planar 3-RRR Parallel Manipulator”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 38(6), pp. 1659–1669, 2016.
• [19] S. Kucuk, “Energy minimization for 3-RRR fully planar parallel manipulator using particle swarm optimization”, Mechanism and Machine Theory, vol. 62, pp. 129-149, 2013