RESEARCH ARTICLE

Error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine

  • S. SHANKAR GANESH ,
  • A. B. KOTESWARA RAO
Expand
  • Department of Mechanical Engineering, G.V.P. College of Engineering, Visakhapatnam 530048, India

Received date: 01 Feb 2014

Accepted date: 23 Apr 2014

Published date: 22 May 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

In this paper, error modeling and analysis of a typical 3-degree of freedom translational Parallel Kinematic Machine is presented. This mechanism provides translational motion along the Cartesian X-, Y- and Z- axes. It consists of three limbs each having an arm and forearm with prismatic-revolute-revolute-revolute joints. The moving or tool platform maintains same orientation in the entire workspace due to its joint arrangement. From inverse kinematics, the joint angles for a given position of tool platform necessary for the error modeling and analysis are obtained. Error modeling is done based on the differentiation of the inverse kinematic equations. Variation of pose errors along X, Y and Z directions for a set of dimensions of the parallel kinematic machine is presented. A non-dimensional performance index, namely, global error transformation index is used to study the influence of dimensions and its corresponding global maximum pose error is reported. An attempt is made to find the optimal dimensions of the Parallel Kinematic Machine using Genetic Algorithms in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the Parallel Kinematic Machine under study.

Cite this article

S. SHANKAR GANESH , A. B. KOTESWARA RAO . Error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine[J]. Frontiers of Mechanical Engineering, 2014 , 9(2) : 120 -129 . DOI: 10.1007/s11465-014-0300-3

Acknowledgements

The authors would like to express their sincere thanks to the administration of G.V.P College of Engineering, Visakhapatnam, India for the encouragement by providing facilities in carrying out this research work.
1
StewartD. A platform with six degrees of freedom. In: Proc Auto Inst. Mech. Engg, London, 1965, 180(5): 371–386

2
Koteswara RaoA B, Dimensional design of hexaslides for optimal workspace and dexterity. IEEE Transactions on Robotics-IEEE-TRO, 2005, 21(3): 444–449

DOI

3
MerletJ P. Parallel Robots. The Netherlands: Kluwer Academic Publishers, 2000

4
ClavelR. Delta: a fast robot with parallel geometry. 18th International Symposium on Industrial Robots. Sydney, Australia, 1988: 91–100

5
PierrotF, ReynaudC, FournierA. DELTA: a simple and efficient parallel robot. Robotica, 1990, 8(02): 105–109

DOI

6
HaungT, WhitehouseD J, WangJ. The local dexterity, optimal architecture and design criteria of parallel machine tools. Annals of the CIRP, 1998, 1988(47): 347–351

7
TsaiL W. Kinematics of a three-DOF platform manipulator with three extensible limbs. In: Lenarcic J, Parenti-Castelli V, eds. Advances in Robot Kinematics Kluwer Academic Publishers, 1996, 401–410

8
LiY, XuQ, LiY M, XuQ S. Kinematic analysis and design of a new 3-DOF Translational Parallel Manipulator. Journal of Mechanical Design, 2006, 128(4): 729–738

DOI

9
KimH S, TsaiL W. Design optimization of a Cartesian parallel manipulator. Journal of Mechanical Design, 2003, 125(1): 43–51

DOI

10
NiaritsiryT F, Study of the Sources of Inaccuracy of a 3-DOF Flexure Hinge-Based Parallel Manipulator. Proceedings of IEEE International conference on Robotics and Automation New Orieans, LA. April 2004

11
WangJ, MasoryO. on the accuracy of a Stewart platform – Part 1: The effect of manufacturing tolerances. In: IEEE Int. Conf. on Robotics and Automation, Atlanta, GA, USA, 1993, 114–120

12
MasoryO, WangJ. On the accuracy of a Stewart platform – Part 2: Kinematic calibration and compensation. In: IEEE Int. Conf. on Robotics and Automation, Atlanta, GA, USA, 1993, 725–731

13
PatelA J, EhmannK F. Volumetric error analysis of a Stewart platform-based machine tool. CIRP Annals, 1997, 46(1): 287–290

DOI

14
ZhuangH Q, LiuL X. Self-calibration of a class of Parallel Manipulators. Proceedings IEEE International conference on Robotics and Automation, 1996, 0-7803-2988-4

15
RyuJ, ChaJ. Volumetric error analysis and architecture optimization for accuracy of Hexaslide type parallel manipulators. Mechanism and Machine Theory, 2003, 38(1): 227–240

DOI

16
XUQ S, LiY M. Error analysis and optimal design of a class of translational parallel kinematic machine using particle swarm optimization. Robotica, 2003, 27(1): 227–240

17
ZhaoJ W, Error analysis of a serial-parallel type machine tool. International Journal of Advanced Manufacturing Technology, 2002, 19: 174–179

18
VernerM, XiF, MechefskeC. Optimal calibration of Parallel Kinematic Machines. Journal of Mechanical Design, 2005, 127(1): 62–69

DOI

19
TianH, Error modeling, sensitivity analysis and assembly process of a class of 3-DOF Parallel Kinematic Machines with parallelogram struts. Science in China (series E), 2002, 45(5): 467–476

20
CaroS, WengerP, BennisF, ChablatD. Sensitivity analysis of the orthoglide. A 3-DOF translational parallel kinematic machine. ASME Journal of Mechanical Design, 2006, 128(2): 392–402

DOI

21
YuA, BonevI A, Zsombor-MurrayP. Geometric method for the accuracy analysis of a class of 3-DOF Planar Parallel Robots. Mechanism and Machine Theory, 2008, 43(3): 364–375

DOI

22
NicolasB, Comparision of 3-RPR Planar Parallel Manipulators with regard to their kinetostatic performance and sensitivity to geometric uncertainities. Mechanica, 2011, 46(1): 75–88

DOI

23
DaxingZeng, Performance analysis and optimal design of a 3-DOF 3-PRUR parallel mechanism. Journal of Mechanical Design, 2008, 130: 042307 (1–11)

24
OscarAltuzarraOptimal dimensioning for parallel manipulators: workspace, dexterity, and energy. Journal of Mechanical Design, 2011, 133: 041007 (1–5)

25
LiuX J, WangJ, 0. Jinsong Wang. A new methodology for optimal kinematic design of parallel Mechanisms. Mechanism and Machine Theory, 2007, 42(9): 1210–1224

DOI

26
BiZ M, LangS Y T, ZhangD, OrbanP E, VernerM. Integrated design toolbox for tripod-based parallel kinematic machines. Journal of Mechanical Design, 2007, 129(8): 799–806

DOI

Outlines

/