Document Type : Article

**Authors**

^{1}
- State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China. - Department of Mechanical and Manufacturing Engineering, Aalborg University, Aalborg 9200, Denmark.

^{2}
State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China

**Abstract**

A novel spatial parallel manipulator designed to assemble diagnostic instruments in SG-III is introduced in this paper. Firstly, resorting to screw theory, mobility analysis of this manipulator is investigated. Then the inverse kinematics problem is determined by the method of RPY transformation, with the singularity analyzed. As a key issue in parallel manipulators, it is more difficult to solve the forward kinematics problem, since it is highly nonlinear and coupled. In this work, three different approaches are presented to deal with this issue, which include the back propagation neural network, the simplified ant colony optimization and the proposed improved Newton iterative method. Simulation of each approach is conducted, and their merits and demerits are compared in detail. It is concluded that the improved Newton iterative method which can provide good initial iteration values possesses the best performance to estimate the nonlinear forward kinematic mapping of the considered parallel manipulator

**Keywords**

- parallel manipulator
- kinematics analysis
- Neural network
- ant colony optimization
- Newton iterative method

**Main Subjects**

References:

1. Gallardoalvarado, J., Aguilarnajera, C.R., Casiquerosas, L., Ricomartinez, J.M., and Islam, M.N. "Kinematics and dynamics of 2(3-RPS) manipulators by means of screw theory and the principle of virtual work", Mechanism and Machine Theory, 43(10), pp. 1281-1294 (2008).

2. Staicu, S. "Inverse dynamics of the 3-PRR planar parallel robot", Robotics and Autonomous Systems, 57(5), pp. 556-563 (2009).

3. Varedi, S.M., Daniali, H.M., and Ganji, D.D. "Kinematics of an offset 3-UPU translational parallel manipulator by the homotopy continuation method", Nonlinear Analysis: Real World Applications, 10(3), pp. 1767-1774 (2009).

4. Pierrot, F., Reynaud, C., and Fournier, A. "DELTA: a simple and efficient parallel robot", Robotica, 8(2), pp. 105-109 (1990).

5. Chandra, R. and Rolland, L. "On solving the forward kinematics of 3RPR planar parallel manipulator using hybrid metaheuristics", Applied Mathematics and Computation, 217(22), pp. 8997-9008 (2011).

6. Li, B., Li, Y., and Zhao, X. "Kinematics analysis of a novel over-constrained three degree-of-freedom spatial parallel manipulator", Mechanism and Machine Theory, 104, pp. 222-233 (2016).

7. Liping, W., Huayang, X., Liwen, G., and Yu, Z. "A novel 3-PUU parallel mechanism and its kinematic issues", Robotics and Computer-Integrated Manufacturing, 42, pp. 86-102 (2016).

8. Xie, Z., Liang, H., and Song, D. "Forward kinematics of 3-RPS parallel mechanism based on a continuous ant colony algorithm", China Mechanical Engineering, 26(6), pp. 799-803 (2015).

9. Gosselin, C.M. "On the kinematic design of spherical 3- DOF of parallel manipulators", International Journal of Robotics Research, 12(4), pp. 394-402 (1993).

10. Wu, G. and Zou, P. "Comparison of 3-DOF symmetrical spherical parallel manipulators with respect to motion/force transmission and stiffness", Mechanism and Machine Theory, 105, pp. 369-387 (2016).

11. Sadjadian, H. and Taghirad, H.D. "Comparison of different methods for computing the forward kinematics of a redundant parallel manipulator", Journal of Intelligent & Robotic Systems, 44(3), pp. 225-246 (2005).

12. Zhang, D. and Lei, J. "Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach", Robotics and Computer-Integrated Manufacturing, 27(1), pp. 157- 163 (2011).

13. Gan, D., Liao, Q., Dai, J.S., Wei, S., and Seneviratne, L.D. "Forward displacement analysis of the general 6-6 Stewart mechanism using Grobner bases", Mechanism and Machine Theory, 44(9), pp. 1640-1647 (2009).

14. Lee, T.Y. and Shim, J.K. "Forward kinematics of the general 6-6 Stewart platform using algebraic elimination", Mechanism and Machine Theory, 36(9), pp. 1073-1085 (2001).

15. Zhou, W., Chen, W., Liu, H., and Li, X. "A new forward kinematic algorithm for a general Stewart platform", Mechanism and Machine Theory, 87, pp. 177-190 (2015).

16. Dong, X., Yu, J., Chen, B., and Zong, G. "Geometric approach for kinematic analysis of a class of 2-DOF rotational parallel manipulators", Chinese Journal of Mechanical Engineering, 25(2), pp. 241-247 (2012).

17. Ruggiu, M. and Kong, X. "Mobility and kinematic analysis of a parallel mechanism with both PPR and planar operation modes", Mechanism and Machine Theory, 55, pp. 77-90 (2012).

18. Parikh, P.J. and Lam, S.S. "Solving the forward kinematics problem in parallel manipulators using an iterative artificial neural network strategy", International Journal of Advanced Manufacturing Technology, 40(5-6), pp. 595-606 (2009).

19. Rahmani, A. and Ghanbari, A. "Application of neural network training in forward kinematics simulation for a novel modular hybrid manipulator with experimental validation", Intelligent Service Robotics, 9(1), pp. 79- 91 (2016).

20. Shahamiri, S.R. and Salim, S. "Real-time frequencybased noise-robust automatic speech recognition using multi-nets artificial neural networks: A multi-views multi-learners approach", Neurocomputing, 129, pp. 199-207 (2014).

21. Yang, C., Zheng, S., Jin, J., Zhu, S., and Han, J. "Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method", Journal of Central South University of Technology, 17(6), pp. 1264-1270 (2010).

22. Ferrari, D. and Giberti, H. "A genetic algorithm approach to the kinematic synthesis of a 6-DOF parallel manipulator", IEEE Conference on Control Applications, France, Antibes, pp. 222-227 (2014).

23. Rokbani, N. and Alimi, A.M. "Inverse kinematics using particle swarm optimization, a statistical analysis", Procedia Engineering, 64, pp. 1602-1611 (2013).

24. Morell, A., Tarokh, M., and Acosta, L. "Solving the forward kinematics problem in parallel robots using support vector regression", Engineering Applications of Artificial Intelligence, 26(7), pp. 1698-1706 (2013).

25. Xiong, Z., Wang, H., Cao, T., Yuan, X., Yao, C., Zhang, Z., Zhou, M., and Ma, G. "Error analysis on assembly and alignment of laser optical unit", Advances in Mechanical Engineering, 7(7), pp. 1-10 (2015).

26. Sanchezalonso, R.E., Gonzalezbarbosa, J., Castillocastaneda, E., and Gallardoalvarado, J. "Kinematic analysis of a novel 2 (3-RUS) parallel manipulator", Robotica, 34(10), pp. 2241-2256 (2016).

27. Gosselin, C. and Angeles, J. "Singularity analysis of closed-loop kinematic chains", IEEE Transactions on Robotics and Automation, 6(3), pp. 281-290 (1990).

28. Dorigo, M. and Blum, C. "Ant colony optimization theory: a survey", Theoretical Computer Science, 344(2-3), pp. 243-278 (2005).

29. Xiao, J. and Li, L. "A hybrid ant colony optimization for continuous domains", Expert Systems with Applications, 38(9), pp. 11072-11077 (2011).

2. Staicu, S. "Inverse dynamics of the 3-PRR planar parallel robot", Robotics and Autonomous Systems, 57(5), pp. 556-563 (2009).

3. Varedi, S.M., Daniali, H.M., and Ganji, D.D. "Kinematics of an offset 3-UPU translational parallel manipulator by the homotopy continuation method", Nonlinear Analysis: Real World Applications, 10(3), pp. 1767-1774 (2009).

4. Pierrot, F., Reynaud, C., and Fournier, A. "DELTA: a simple and efficient parallel robot", Robotica, 8(2), pp. 105-109 (1990).

5. Chandra, R. and Rolland, L. "On solving the forward kinematics of 3RPR planar parallel manipulator using hybrid metaheuristics", Applied Mathematics and Computation, 217(22), pp. 8997-9008 (2011).

6. Li, B., Li, Y., and Zhao, X. "Kinematics analysis of a novel over-constrained three degree-of-freedom spatial parallel manipulator", Mechanism and Machine Theory, 104, pp. 222-233 (2016).

7. Liping, W., Huayang, X., Liwen, G., and Yu, Z. "A novel 3-PUU parallel mechanism and its kinematic issues", Robotics and Computer-Integrated Manufacturing, 42, pp. 86-102 (2016).

8. Xie, Z., Liang, H., and Song, D. "Forward kinematics of 3-RPS parallel mechanism based on a continuous ant colony algorithm", China Mechanical Engineering, 26(6), pp. 799-803 (2015).

9. Gosselin, C.M. "On the kinematic design of spherical 3- DOF of parallel manipulators", International Journal of Robotics Research, 12(4), pp. 394-402 (1993).

10. Wu, G. and Zou, P. "Comparison of 3-DOF symmetrical spherical parallel manipulators with respect to motion/force transmission and stiffness", Mechanism and Machine Theory, 105, pp. 369-387 (2016).

11. Sadjadian, H. and Taghirad, H.D. "Comparison of different methods for computing the forward kinematics of a redundant parallel manipulator", Journal of Intelligent & Robotic Systems, 44(3), pp. 225-246 (2005).

12. Zhang, D. and Lei, J. "Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach", Robotics and Computer-Integrated Manufacturing, 27(1), pp. 157- 163 (2011).

13. Gan, D., Liao, Q., Dai, J.S., Wei, S., and Seneviratne, L.D. "Forward displacement analysis of the general 6-6 Stewart mechanism using Grobner bases", Mechanism and Machine Theory, 44(9), pp. 1640-1647 (2009).

14. Lee, T.Y. and Shim, J.K. "Forward kinematics of the general 6-6 Stewart platform using algebraic elimination", Mechanism and Machine Theory, 36(9), pp. 1073-1085 (2001).

15. Zhou, W., Chen, W., Liu, H., and Li, X. "A new forward kinematic algorithm for a general Stewart platform", Mechanism and Machine Theory, 87, pp. 177-190 (2015).

16. Dong, X., Yu, J., Chen, B., and Zong, G. "Geometric approach for kinematic analysis of a class of 2-DOF rotational parallel manipulators", Chinese Journal of Mechanical Engineering, 25(2), pp. 241-247 (2012).

17. Ruggiu, M. and Kong, X. "Mobility and kinematic analysis of a parallel mechanism with both PPR and planar operation modes", Mechanism and Machine Theory, 55, pp. 77-90 (2012).

18. Parikh, P.J. and Lam, S.S. "Solving the forward kinematics problem in parallel manipulators using an iterative artificial neural network strategy", International Journal of Advanced Manufacturing Technology, 40(5-6), pp. 595-606 (2009).

19. Rahmani, A. and Ghanbari, A. "Application of neural network training in forward kinematics simulation for a novel modular hybrid manipulator with experimental validation", Intelligent Service Robotics, 9(1), pp. 79- 91 (2016).

20. Shahamiri, S.R. and Salim, S. "Real-time frequencybased noise-robust automatic speech recognition using multi-nets artificial neural networks: A multi-views multi-learners approach", Neurocomputing, 129, pp. 199-207 (2014).

21. Yang, C., Zheng, S., Jin, J., Zhu, S., and Han, J. "Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method", Journal of Central South University of Technology, 17(6), pp. 1264-1270 (2010).

22. Ferrari, D. and Giberti, H. "A genetic algorithm approach to the kinematic synthesis of a 6-DOF parallel manipulator", IEEE Conference on Control Applications, France, Antibes, pp. 222-227 (2014).

23. Rokbani, N. and Alimi, A.M. "Inverse kinematics using particle swarm optimization, a statistical analysis", Procedia Engineering, 64, pp. 1602-1611 (2013).

24. Morell, A., Tarokh, M., and Acosta, L. "Solving the forward kinematics problem in parallel robots using support vector regression", Engineering Applications of Artificial Intelligence, 26(7), pp. 1698-1706 (2013).

25. Xiong, Z., Wang, H., Cao, T., Yuan, X., Yao, C., Zhang, Z., Zhou, M., and Ma, G. "Error analysis on assembly and alignment of laser optical unit", Advances in Mechanical Engineering, 7(7), pp. 1-10 (2015).

26. Sanchezalonso, R.E., Gonzalezbarbosa, J., Castillocastaneda, E., and Gallardoalvarado, J. "Kinematic analysis of a novel 2 (3-RUS) parallel manipulator", Robotica, 34(10), pp. 2241-2256 (2016).

27. Gosselin, C. and Angeles, J. "Singularity analysis of closed-loop kinematic chains", IEEE Transactions on Robotics and Automation, 6(3), pp. 281-290 (1990).

28. Dorigo, M. and Blum, C. "Ant colony optimization theory: a survey", Theoretical Computer Science, 344(2-3), pp. 243-278 (2005).

29. Xiao, J. and Li, L. "A hybrid ant colony optimization for continuous domains", Expert Systems with Applications, 38(9), pp. 11072-11077 (2011).

Transactions on Mechanical Engineering (B)

January and February 2019Pages 346-357