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Surface location error of a parallel robot for routing processes


This paper deals with the static characterisation of a parallel manipulator for routing processes. Since accuracy and surface finishing are critical in all machining processes, the performance of a parallel machine is analysed in this paper in terms of these parameters. Using a previously developed static analysis methodology, the stiffness of the machine structure is obtained and used as an input for a process model. This approach allows the static behaviour of the machine to be evaluated in terms of the surface location error for a given routing operation in the manipulator workspace. The study focusses on certain discrete points in the operational workspace for each direction of the tool feed. Then, the global behaviour of the machine is presented using surface location maps. Furthermore, some static constraints are imposed to obtain the static workspace of the manipulator for the routing process.

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  1. 1.

    Zulaika JJ, Campa FJ, de Lacalle LNL (2011) An integrated process-machine approach for designing productive and lightweight milling machines. Int J Mach Tools Manuf 51(7–8):591–604

  2. 2.

    Pan Z, Zhang H, Zhu Z, Wang J (2006) Chatter analysis of robotic machining process. J Mater Process Technol 173(3):301–309

  3. 3.

    Ceccarelli M, Carbone G (2002) A stiffness analysis for CaPaMan (Cassino Parallel Manipulator). Mech Mach Theory 37(5):427–439. doi:10.1016/S0094-114X(02)00006-X

  4. 4.

    Rizk R, Munteanu MM, Fauraoux JC, Gogu G, Fauroux J (2007) A semi-analytical stiffness model of parallel robots from the Isoglide family via the sub-structuring principle. In: 12th IFToMM world congress. Besançon, pp 2–7

  5. 5.

    Bonnemains T, Chanal H, Bouzgarrou BC, Ray P (2009) Stiffness computation and identification of parallel kinematic machine tools. J Manuf Sci Eng 131(4):041013. doi:10.1115/1.3160328

  6. 6.

    Li Y, Jin Z, Ji S (2009) Design of a novel 3-DOF hybrid mechanical arm. Sci China, Ser E Technol Sci 52(12):3592–3600. doi:10.1007/s11431-009-0293-z. URL

  7. 7.

    Geldart M, Webb P, Larsson H, Backstrom M, Gindy N, Rask K (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 Tools Manuf 43(11):1107–1116. doi:10.1016/S0890-6955(03)00119-6

  8. 8.

    Terrier M, Dugas A, Hascoët JY (2004) Qualification of parallel kinematics machines in high-speed milling on free form surfaces. Int J Mach Tools Manuf 44(7–8):865–877. doi:10.1016/j.ijmachtools.2003.11.003

  9. 9.

    Bouzgarrou BC, Thuilot B, Ray P, Gogu G (2002) Modélisation des manipulateurs flexibles appliquée aux machines-outils UTGV. Méc Ind 3(2):173–180

  10. 10.

    Chanal H, Duc E, Ray P (2006) A study of the impact of machine tool structure on machining processes. Int J Mach Tools Manuf 46(2):98–106. doi:10.1016/j.ijmachtools.2005.05.004

  11. 11.

    Corral J, Pinto C, Zubizarreta A, Altuzarra O (2010) A procedure to obtain structural workspace based on stiffness and natural frequencies criteria. In: Emerging trends in mobile robotics—proceedings of the 13th international conference on climbing and walking robots and the support technologies for mobile machines. World Scientific, Singapore, pp 946–953. doi:10.1142/9789814329927_0116

  12. 12.

    Corral J, Pinto C, Herrero S, Altuzarra O, Ceccarelli M (2011) Caracterización estructural de manipuladores paralelos a través del espacio de trabajo estructural. In: Proceedings of the X Congreso Iberoamericano de Ingeniería Mecánica (CIBIM 2011)

  13. 13.

    Schmitz T, Ziegert J (1999) Examination of surface location error due to phasing of cutter vibrations. Precis Eng 23(1):51–62. doi:10.1016/S0141-6359(98)00025-7

  14. 14.

    Schmitz TL, Mann BP (2006) Closed-form solutions for surface location error in milling. Int J Mach Tools Manuf 46(12–13):1369–1377. doi:10.1016/j.ijmachtools.2005.10.007

  15. 15.

    Bachrathy D, Homer M, Insperger T, Stephan G (2007) Surface location error for helical mills. In: Proceedings of the high speed machining 6th international conference, San Sebastián

  16. 16.

    Tlusty J, Polacek M (1963) The stability of machine tools against self excited vibrations in machining. ASME Int Res Prod Eng 1:465–476

  17. 17.

    Ciurana Q, Quintana G, Campa FJ (2009) Machine to. In: Machine tools for high performance machining. Springer, Berlin, pp 169–174

  18. 18.

    Altintas Y (2000) Manufacturing automation. Cambridge University Press, Cambridge

  19. 19.

    Campa FJ, López de Lacalle LN, Lamikiz A, Bilbao E, Calleja A, Peñafiel J (2009) Tool deflection on peripheral milling. In: The annals of Dunarea de Jos University of Galati, Fascicle V, technologies in machine building

  20. 20.

    Corral J, Pinto C, Campa FJ, Altuzarra O (2012) Dynamic capabilities of a parallel robot based routing machine. In: Lenarčič J, Husty M (eds) Proceedings of the 13th international symposium on advances in robot kinematics. Springer, Dordrecht, pp 165–172. doi:10.1007/978-94-007-4620-6_21

  21. 21.

    Salgado O (2008) Síntesis, análisis y diseño de manipuladores paralelos de baja movilidad. PhD thesis, University of the Basque Country

  22. 22.

    Pinto C, Corral J, Altuzarra O, Hernández A (2009) A methodology for static stiffness mapping in lower mobility parallel manipulators with decoupled motions. Robotica 28(5):719–735. doi:10.1017/S0263574709990403

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Correspondence to Javier Corral.

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Corral, J., Pinto, C., Campa, F.J. et al. Surface location error of a parallel robot for routing processes. Int J Adv Manuf Technol 67, 1977–1986 (2013).

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  • Parallel machine
  • Stiffness
  • Surface location error
  • Routing