Architectures of Parallel Robotic Machine

  • Dan ZhangEmail author


One of the objectives of this book is to find the most promising kinematic structures that can be used for machine tool design. Hence, some well-known principles are applied to investigate all the possibilities of structure in detail. A mechanism is defined as a kinematic chain with one of its components (link or joint) connected to the frame. A kinematic chain consists of a set of links, coupled by joints (cylindrical, planar, screw, prismatic, revolute, spherical, and Hooke) between adjacent links. In this chapter, a topological study of different combinations of kinematic chain structures are performed using a graph representation approach. The number of links and joints for the desired system and their interconnections, neglecting geometric details (link length and link shape), are described. The possible architectures that provide 5 degrees of freedom between the tool and the workpiece are generated. In Sect. 3.2, basic kinematic elements of mechanisms are introduced, and the classification of mechanisms is given based on the motion relation. In Sect. 3.3, the basic concept of the graph representation of a kinematic structure is addressed. Then, the Chebychev–Grübler–Kutzbach criterion is introduced in Sect. 3.4. A topological study of the kinematic structures is described in Sect. 3.5. Requirements for possible kinematic structures are set up. Furthermore, the structural representation of kinematic chains and architectures with consideration of parallel and hybrid cases is illustrated. In Sect. 3.6, a remark on the role of redundancy is given. A summary with discussion of related work is presented in Sect. 3.7.


Parallel Mechanism Kinematic Chain Revolute Joint Parallel Robot Spherical Joint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 8.
    Alizade R, Bayram C (2004) Structural synthesis of parallel manipulators. Mech Mach Theory 39:857–870zbMATHCrossRefMathSciNetGoogle Scholar
  2. 13.
    Arsenault M, Gosselin CM (2006) Kinematic and static analysis of a planar modular 2-dof tensegrity mechanism. In: Proceedings of the 2006 IEEE international conference on robotics and automation, pp 4193–4198Google Scholar
  3. 16.
    Baker JE (1992) On mobility and relative freedoms in multiloop linkages and structures. Mech Mach Theory 16(6):583–597CrossRefGoogle Scholar
  4. 30.
    Cervantes-Sánchez JJ, Rendón-Sánchez JG (1999) A simplified approach for obtaining the workspace of a class of 2-dof planar parallel manipulators. Mech Mach Theory 34:1057–1073zbMATHCrossRefGoogle Scholar
  5. 33.
    Chen NX, Song SM (1992) Direct position analysis of the 4–6 stewart platform. Robot Spat Mech Mech Syst 45:75–80Google Scholar
  6. 39.
    Company O, Pierrot F, Fauroux JC (2005) A method for modeling analytical stiffness of a lower mobility parallel manipulator. In: Proceedings of the 2005 IEEE international conference on robotics and automation, Barcelona, pp 3232–3237Google Scholar
  7. 44.
    Earl CF, Rooney J (1983) Some kinematic structures for robot manipulator designs. J Mech Transm Autom Des 105(1):15–22CrossRefGoogle Scholar
  8. 48.
    Fichter EF (1986) A stewart platform-based manipulator: general theory and practical construction. Int J Robot Res 5(2):157–182CrossRefGoogle Scholar
  9. 50.
    Gallardo-Alvarado J, Rico-Martnez JM, Alici G (2006) Kinematics and singularity analyses of a 4-dof parallel manipulator using screw theory. Mech Mach Theory 41:1048–1061zbMATHCrossRefMathSciNetGoogle Scholar
  10. 56.
    Gosselin CM (1988) Kinematic analysis,optimization and programming of parallel robotic manipulators. PhD thesis, McGill UniversityGoogle Scholar
  11. 63.
    Griffis M, Duffy J (1989) A forward displacement analysis of a class of stewart platform. J Robot Syst 6(6):703–720CrossRefGoogle Scholar
  12. 67.
    Harary F (1969) Graph theory. Addison-Wesley, Reading, MAGoogle Scholar
  13. 76.
    Hunt KH (1978) Kinematic geometry of mechanisms. Clarendon Press, OxfordzbMATHGoogle Scholar
  14. 77.
    Hunt KH (1983) Structural kinematics of in-parallel-actuated robot-arms. ASME J Mech Transm Autom Des 105(4):705–712Google Scholar
  15. 85.
    Kong XW, Gosselin CM (2004) Type synthesis of 3t1r 4-dof parallel manipulators based on screw theory. IEEE Trans Robot Autom 20:181–190CrossRefGoogle Scholar
  16. 99.
    Lin W, Crane III CD, Griffis M (1994) Closed-form forward displacement analyses of the 4–5 in-parallel platforms. ASME J Mech Des 116:47–53CrossRefGoogle Scholar
  17. 100.
    Lu Y, Hu B (2007) Analyzing kinematics and solving active/constrained forces of a 3spu + upr parallel manipulator. Mech Mach Theory 42:1298–1313zbMATHCrossRefGoogle Scholar
  18. 106.
    Merlet JP (2000) Parallel robots. Kluwer, New YorkzbMATHGoogle Scholar
  19. 128.
    Rey L, Clavel R (1999) The delta parallel robot. In: Boër CR, Molinari-Tosatti L, Smith KS (eds) Parallel kinematic machines – theoretical aspects and industrial requirements. Springer, New York, pp 401–418Google Scholar
  20. 146.
    Tsai LW, Lee JJ (1989) Kinematic analysis of tendon-driven robotics mechanisms using graph theory. ASME J Mech Transm Autom Des 111:59–65Google Scholar
  21. 169.
    Zhang CD, Song SM (1992) Forward position analysis of nearly general stewart platform. Robot Spat Mech Mech Syst 45:81–87Google Scholar
  22. 179.
    Zhang GL, Fu Y, Yang RQ (2002) Kinematics analysis of a new 3 dof planar redundant parallel manipulator. Mech Des Res 18:19–21zbMATHGoogle Scholar
  23. 180.
    Zhang WJ (1994) An integrated environment for CADCAM of mechanical systems. PhD thesis, Delft University of TechnologyGoogle Scholar
  24. 181.
    Zhang WJ, Li Q (1999) On a new approach to mechanism topology identification. ASME J Mech Des 121:57–64CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Faculty of Engineering and Applied ScienceUniversity of Ontario Institute of Technology (UOIT)OshawaCanada

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