Optimal design and development of a 2-DOF PKM-based machine tool

  • Sanjay Darvekar
  • A. B. Koteswara Rao
  • S. Shankar Ganesh
  • K. Ramji


This paper presents multiobjective optimization of a typical 2-degree-of-freedom (DOF) parallel kinematic machine (PKM) tool that has only single DOF joints. Nondimensional indices, namely global stiffness index (GSI), global conditioning index (GCI), and workspace index, are considered as the objectives for optimization. The indices GSI and GCI depict the variation of stiffness and dexterity of PKM within the workspace. The leg length and distance between two rails on which actuators slide are treated as design variables as these greatly influence the characteristics of PKM. A multiobjective genetic algorithm (MOGA) approach is implemented in MATLAB to find an efficient solution to this complex optimization problem. Fitness function includes inverse kinematics equations, Jacobian and stiffness matrices to compute and optimize the nondimensional indices. First, the optimal value of each index is obtained by single-objective GA. To further improve the results, a hybrid function PATTERNSEARCH is used. This helps to select appropriate boundary conditions for MOGA. To obtain the optimal values of all the three indices, a multiobjective GA is carried out. The results are compared with a conventional exhaustive search method of optimization. The obtained results show that the use of MOGA enhances the quality of the optimization outcome. Secondly, a prototype has been designed and developed with the optimal dimensions. The actual workspace of the PKM and influence of leg collision on the workspace are studied. Finally, a preliminary experimentation was carried out. A comparison between PKM and the three-axis serial kinematic machine tool is presented.


PKM Global stiffness index Global conditioning index Workspace index MOGA Comparison with SKM 


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  1. 1.
    Merlet JP (2000) Parallel robots. Kluwer Academic Publishers, The NetherlandsMATHCrossRefGoogle Scholar
  2. 2.
    Pritschow G (2000) Parallel kinematic machine (PKM)—limitations and new solutions. CIRP Ann Manuf Technol 49(1):275–280CrossRefGoogle Scholar
  3. 3.
    Bone IA, Ryu J (1999) Workspace analysis of 6-PRRS parallel manipulators based on the vertex space concept. In Proc. of the ASME Design Engg Tech Conf, DETC 99/DAC −864Google Scholar
  4. 4.
    Xi F et al (2004) Global kinetostatic modeling of tripod based parallel kinematic machine. Mech Mach Theory 39:357–377MATHCrossRefGoogle Scholar
  5. 5.
    Wang J, Tang X (2003) Analysis and dimensional design of a novel hybrid machine tool. Intl J Mach Tools Manuf 43:647–655CrossRefGoogle Scholar
  6. 6.
    Koteswara Rao AB, SK Saha, PVM Rao. (2006) Workspace and stiffness analyses of a two degree of freedom parallel kinematic machine tool. In Proc. of the Intl. Conf. (PCEA-IFToMM) on Recent Trends in Automation & its Adaptation to Industries, PICA2006, Nagpur, 11–14 JulyGoogle Scholar
  7. 7.
    Stan S, Vistrian M, Balan R (2006) Optimal design of 2 DOF parallel kinematics machines. Proc Appl Math Mech, 705–706Google Scholar
  8. 8.
    Stan S (2006) Workspace optimization of a two degree of freedom mini parallel robot. In Proc. of the AQTR–2006 Conf. (IEEE, Cluj-Napoca, Romania), pp. 278–283Google Scholar
  9. 9.
    Majou F, Wenger P, Chablat D (2002) A novel method for the design of 2-DOF parallel mechanisms for machining applications. Caldes de Malavella, SpainGoogle Scholar
  10. 10.
    Geldart M, Webb P, Larsson H et al (2003) A direct comparison of the machining performance of a variax 5 axis parallel kinetic machining centre with conventional 3 and 5 axis machine tools. Int J Mach Tool Manuf 43(11):1107–1116CrossRefGoogle Scholar
  11. 11.
    Myriam T, Arnaud D, Jean-Yves H (2004) Qualification of parallel kinematics machines in high-speed milling on free form surfaces. Int J Mach Tool Manuf 44(7–8):865–877Google Scholar
  12. 12.
    Merlet JP (2002) An initiative for the kinematics study of parallel manipulators. Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators. Que′bec City, October 3–4Google Scholar
  13. 13.
    Liu X-J, Wang Q-m, Wang J (2005) Kinematics, dynamics and dimensional synthesis of a novel 2-DOF translational manipulator. J Intell Robot Syst 41(4):205–224CrossRefGoogle Scholar
  14. 14.
    Rao ABK, Rao PVM, Saha SK (2003) Dimensional design of hexaslides for optimal workspace and dexterity. IEEE Trans on Robotics-IEEE-TRO 21:444–449, Number 3, June 2005CrossRefGoogle Scholar
  15. 15.
    Gosselin C, Angeles J (1991) A global performance index for kinematic optimization of robotic manipulators. ASME Intl J Mech Design 113(3):220–226CrossRefGoogle Scholar
  16. 16.
    Stan S, Vistrian M, Bălan R (2007) Multi-objective design optimization of mini parallel robots using genetic algorithms. IEEE-ISIE 2007, Intl. Symposium on Industrial Electronics, June 4–7, 2007. Caixanova-Vigo, Spain, pp. 1-4244-0755-9/07/IEEE 2173–2178Google Scholar
  17. 17.
    Snyman JA et al (2000) An optimization approach to the determination of the boundaries of manipulator workspaces. J Mech Des 122:447–455CrossRefGoogle Scholar
  18. 18.
    MATLAB (2012) The MathWorks, optimization toolbox for use with Matlab 2008Google Scholar
  19. 19.
    Rao PN (2000) Manufacturing technology—metal cutting and machine tools. Tata McGraw-hill, IndiaGoogle Scholar
  20. 20.
    Sutherland JW (1988) A dynamic model of the cutting force system in the end milling process. Sensors Control Manuf ASME Bound 33:53–62Google Scholar
  21. 21.
    Sanjit M, Saurav D, Asish B et al (2010) Optimization of CNC end milling process parameters using PCA-based Taguchi method. Int J Eng Sci Technol 2(1):92–102CrossRefGoogle Scholar
  22. 22.
    Ab. Rashid MFF, Abdul Lani MR (2010) Surface roughness prediction for CNC milling process using artificial neural network, vol III, Proceedings of the World Congress on Engineering. London, U.K, June 30 - July 2Google Scholar
  23. 23.
    Central Machine Tool Institute (1982) Machining tool design handbook. Tata McGraw-Hill, New Delhi, 562Google Scholar
  24. 24.
  25. 25.

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Sanjay Darvekar
    • 1
  • A. B. Koteswara Rao
    • 1
  • S. Shankar Ganesh
    • 1
  • K. Ramji
    • 2
  1. 1.Department of Mechanical EngineeringGayatri Vidya Parishad College of EngineeringVisakhapatnamIndia
  2. 2.Mechanical DepartmentAndhra UniversityVisakhapatnamIndia

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