# New Forward Kinematic Model of Parallel Robot Par4

• Sonda Abid M’hiri
• Neila Mezghani Ben Romdhane
• Tarak Damak
Article

## Abstract

Modeling parallel robots is a famous problem of research especially the Forward Kinematic Model (FKM). It is very difficult to solve it compared to serial manipulators and it is also hard to obtain its analytic solution. Most researchers have resorted to the numerical methods. But, these have a lot of problems : the divergence caused by the bad choice of the initial condition and providing more than one feasible solution. To solve these problems, an analytical method is proposed in this article. In this paper, the FKM of the parallel robot Par4 is determined using the Modified Denavit Hartenberg Method (MDHM). This method facilitates greatly the forward kinematic problem of parallel robot. The MDHM is powerful, useful and can be easily used for the closed loop robots. It is very accurate and provides a unique solution. In the best of our knowledge, the MDHM isn’t applied to the parallel robot Par4 to give a relationship between its operational and articular variables. After a short presentation of the robot Par4, the FKM is determined using the MDHM method. The results of this method will be compared to the existing numerical method like the iterative Newton method (INM).

## Keywords

Modified Denavit Hartenberg method Geometric modeling Parallel robot Par4 Iterative Newton method

## References

1. 1.
Gui, G., Zhang, H., Zhang, D.: Analysis of the kinematic accuracy reliability of a 3 -DOF parallel robot manipulator. Int. J. Adv. Robot. Syst. 12, 324–332 (2015)Google Scholar
2. 2.
Baron, L., Angeles, J.: The direct kinematics of parallel manipulators under joint-sensor redundancy. IEEE Trans Robot Autom. 16, 12–19 (2000)
3. 3.
Arian, B., Mansour, N.B.: Optimal design of a spatial six-cable robot, Proc 2nd IASTED Int. Conf. Robot, pp. 134–141 (2011)Google Scholar
4. 4.
Bahrami, A., Tafaoli, M., Bahrami, N.M.: Fuzzy Logic Based Active Vibration Control of Piezoelectric Stewart Platform. International Journal of Mechanical, Industrial Science and Engineering 8(1), 72–79 (2014)Google Scholar
5. 5.
Merlet, J.P.: Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis. Int. J. Robot. Res. 23, 221–235 (2004)
6. 6.
Bahrami, A., Tafaoli-Masoule, M., Bahrami, M.: Fuzzy control of Piezoelectric Stewart Platform for active vibration control purpose, TSEST, Transaction on Control and Mechanical Systems, pp. 356—361 (2012)Google Scholar
7. 7.
Lee, T.Y., Shim, J.K.: Forward kinematics for the general Stewart platform using algebraic elimination. Mech. Theory 36, 1073—1085 (2001)
8. 8.
Raghavan, D.: The Stewart platform of general geometry has 40 configurations. ASME Design and Auto, Conf Chicago, pp. 277–281 (1993)Google Scholar
9. 9.
Bahrami, A., Tafaoli, M., Bahrami, M.N.: Active vibration control of piezoelectric stewart platform based on fuzzy control, International Journal of Material and Mechanical Engineering (IJMME), pp. 17—22 (2013)Google Scholar
10. 10.
Nabat, V., Company, O., Krut, S.: Par4: Very high speed parallel robot for pick-and-place, IEEE international conference on intelligent robots and systems, Canada, pp. 553–558 (2005)Google Scholar
11. 11.
Corbel, D., Company, O., Nabat, V.: Geometrical calibration of the high speed robot Par4 using a laser tracker, Proceedings of the 12t h IEEE international conference on methods and models in automation and robotics Poland, pp. 687—692 (2006)Google Scholar
12. 12.
Arian, B., Behnam, A., Mansour, N.B.: Design optimization of a 3-D three cable driven manipulator, ASME international design engineering technical conferences (IDETC/CIE), pp. 753—761 (2012)Google Scholar
13. 13.
Arian, B., Mansour, N.B.: Optimal design of a spatial four-cable-driven parallel manipulator, IEEE International Conference on Robotics and Biomimetics New York, pp. 2143–2149 (2011)Google Scholar
14. 14.
Arian, B., Mansour, N.B.: Multi objective design of spatial cable robots. In: Proc 2nd IASTED Int. Conf. Robot, pp. 345–352 (2011)Google Scholar
15. 15.
Bahrami, A., Teimourian, A.: Workspace analysis of 6–6 cable-suspended parallel robots. International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering 10(12), 1923–1927 (2016)Google Scholar
16. 16.
Jahanbakhsh, H., Arian, B., Mansour, N.B.: Workspace sensitivity analysis of spatial cable robots, International Conference on Robotics (IASTED), At Phuket,, Thailand (2010)Google Scholar
17. 17.
Griffi, M.: A forward displacement analysis of clan of stewart platforms. J. Robot. Syst. 6, 703–720 (1989)
18. 18.
Wohlkart, K.: Dislpacement analysis of the general spherical Stewart platform. Mech. Mach. Theory 29, 581–589 (1994)
19. 19.
Zhao, Y., Zhu, H., Cai, G.: Geometric solution for direct kinematic of Delta parallel robot, Harbin Gongye Daxue Xuebao. Journal of Harbin Institute of Technology 35, 25–27 (2003)Google Scholar
20. 20.
Hertz, R.B., Hughes, P.C.: Kinematic analysis of a general double-tripod parallel manipulator. Mech. Mach. 33(6), 683–696 (1998)
21. 21.
Song, S.K., Kwon, D.S.: A tetrahedrom approach for a unique closed -form solution of the forward kinematics of six-dof parallel mechanisms with multiconnected joints. J. Robot. Syst. 19, 269–281 (2002)
22. 22.
Zhao, J., Zhu, Y.H., Cai, H.G.: Geometric solution for direct kinematic solution for direct kinematics of Delta parallel robot. Journal of Harlin Institue of Technology 35, 25–27 (2003). HarbinGoogle Scholar
23. 23.
Huang, X., Liao, Q., Wei, S., Qiang, X., Huang, S.: Forward kinematics of the 6 - 6 stewart platform with planar base and platform using algebraic elimination, Proceedings of the IEEE international conference on automation and Zogistics, ICAL, pp. 2655–2659 (2007)Google Scholar
24. 24.
Huang, X., Liao, Q., Wei, S., Li, D.: Forward kinematics analisis of the general 6 - 6 platform parallel mechanism based on algebraic elimination. J. Mech. Eng. 45, 56–61 (2009)
25. 25.
Deshmukh, G., Pecht, M.: A modified Powell method for six degrees-of-freedom platform kinematics. Comput. Struct. 34, 485–491 (1990)
26. 26.
Denavit, J., Hartenberg, R.: A kinematic notation for lower-pair mechanisms based on matrices. Asme journal of applied Mechanisms 22, 215–221 (1955)
27. 27.
Khalil, W., Kleinfinger, J.: A new geometric notation for open and closed-loop robots, Proc IEEE conf on robotics and automation, San Francisco, pp. 1174–1180 (1986)Google Scholar
28. 28.
Krut, S., Nabat, V., Company, O.: A high speed parallel robot for scara motions, Proceedings of the IEEE international conference on robotics and automation (ICRA’04), New Orleans, LA, USA, vol. 4, pp. 4109—4115 (2004)Google Scholar
29. 29.
Dai, X., Huang, Q., Jiang, H., Junwei, H.: Kinematics Analisis of a 3-dof Rotationnal parallel mecanism, Modelling, simulation and optimisation, International workshop WMSo, pp. 404–407 (2008)Google Scholar
30. 30.
Nguyen, C.C., Zhou, Z.L., Antraze, S.S., Campell, C.E.: Efficient computation of forward kinematics and jacobian matrix of a stewart platform- based manipulator, Conference Proceedings, IEEE SOUTHEAT CON, pp. 869–874 (1991)Google Scholar
31. 31.
Arshad, M.: Solution of Forward Kinematics Model of Six Degrees of Freedom Parallel Robot Manipulator. IEE International Conference on Emerging Technologies, Islamabad, vol. 18, pp. 393–398 (2005)Google Scholar
32. 32.
Jonathan, H.: A framework for generalising the Newton method and other iterative methods from Euclidean space to manifolds (2015)Google Scholar
33. 33.
Stoughton, R., Arai, T.: Optimal sensor placement for forward kinematics evaluation of a 6-Dof parallel link manipulator, IEEE RSJ Int workshop intelligent robots systems, pp. 785–790 (1991)Google Scholar
34. 34.
Han, K., hung, W., Youm, Y.: Local structurization for thr forward kinematics of parallel manipulators using extra sensor data. In: Proc IEEE int conference robotics automatics, pp. 514–520 (1995)Google Scholar
35. 35.
Dehghani, M., Ahmadi, A., Khayatian, A., Eghtesad, M., Farid, M.: Neural network solution for forward kinematics problem of HEXA parallel robot, Proceedings of the American control conferences, pp. 4214–4219 (2008)Google Scholar
36. 36.
Sadjadian, H., Taghird, H.: Compaison of different methods for computing the forward kinematics of a redundant parallel manipulator. Adv. Robot. 22, 657–687 (2008)
37. 37.
Janot, A.: Contribution à la modélisation et à l’identification des interfaces haptiques [Ph.D. thesis], Nantes univercity (2007)Google Scholar
38. 38.
Boudreau, R., Turkhan, N.: Solving the forward kinematics of parallel manipulators with a genetic algorithms, vol. 13. Moncton (1996)Google Scholar
39. 39.
Li, L., Zhu, Q., Xu, L.: Solution for forward kinematics of 6-dof parallel robot based on particle swarm optimisation, Proceedings of IEEE international conference on mechatronics and automatics, pp. 2968–2973 (2007)Google Scholar
40. 40.
Rolland, L., Chandra, R.: Forward kinematics of the 6-6 general parallel manipulator using real coded genetic algorithms, IEEE, ASME international conference on advanced Intelligent Mechatronics, AIM, pp. 1637–1642 Singapore (2009)Google Scholar
41. 41.
Singh1, Y., Mohan2, S.: Inverse kinematic modeling of a 6 - D O F(6 - C R S) parallel spatial manipulator, 5th international and 26th all India manufacturing technology, design and research conference, Guwahati, Assam, India (2014)Google Scholar
42. 42.
Ammar, A: Modelisation dynamique d’un robot parallele forme de plusieurs module empiles. Magister en Génie Mécanique, Univercity l’Arbi Ben M’Hidi D’oum el Bouaghi (2011)Google Scholar
43. 43.
Maya, M., Castillo, E., Lomelí, A.: Workspace and Payload-Capacity of a New Reconfigurable Delta Parallel Robot. Adv. Robot. 10, 56–58 (2013)Google Scholar
44. 44.
Peter, C.: Robotics vision and control: Fundamental algorithms in MATLAB. Springer Tracts in Advanced Robotics, Berlin (2011)
45. 45.
Khalil, W.: Dynamic modelling of robots using recursive Newton-Euler techniques, Robot Manipulators and Control Systems (2011)Google Scholar
46. 46.
Merlet, J.P.: Parallel robots, 2nd edn., p. 128. Springer, Nol (2006)
47. 47.
Kovalchuk, A., Akhmetova, F.: Denavit-Hertanberg coordinate system for Robot with tree-like Kinematic structure, International Journal of Robotic and Automatic (IJRA) Russia (2017)Google Scholar
48. 48.
Yao–nan, W., GAOXiao, L.: Manipulator control system based on CAN, Institute of automation, East China university of science and technology, Shanghai, China (2016)Google Scholar

## Authors and Affiliations

• Sonda Abid M’hiri
• 1
• Neila Mezghani Ben Romdhane
• 2
• Tarak Damak
• 1
1. 1.Laboratory of Sciences and Techniques of Automatic and Industrial Data National School of EngineeringSfaxTunisia
2. 2.Laboratory of Sciences and Techniques of Automatic and Industrial Data High Institute of Industrials systemsGabesTunisia