Skip to main content

Standing on the shoulders of giants: A brief note from the perspective of kinematics


  1. [1]

    ERDMAN A G. Modern kinematics: Developments in the last forty years[M] New York: Wiley-Interscience, 1993.

    Google Scholar 

  2. [2]

    McCarthy J M. 21st century kinematics[M] London: Springer, 2013.

    Book  Google Scholar 

  3. [3]

    DING X, KONG X, DAI J S. Advances in reconfigurable mechanisms and robots II[M] Switzerland: Springer International Publishing, 2016.

    Book  Google Scholar 

  4. [4]

    WALTER D R, HUSTY M L, PFURNER M. Chapter A: complete kinematic analysis of the SNU 3-UPU parallel manipulator[C]//BATES D J, BESANA G, Di ROCCO S, et al, eds, Interactions of Classical and Numerical Algebraic Geometry, Providence: American Mathematical Society, 2009: 331–346.

    Chapter  Google Scholar 

  5. [5]

    SOMMESE A J, WAMPLER II C W. The numerical solution of systems of polynomials arising in engineering and science[M] Singapore: World Scientific, 2005.

    Book  MATH  Google Scholar 

  6. [6]

    KONG X. Reconfiguration analysis of a 3-DOF parallel mechanism using Euler parameter quaternions and algebraic geometry method[J]. Mechanism and Machine Theory, 2014, 74: 188–201.

    Article  Google Scholar 

  7. [7]

    SCHMIEDELER J P, CLARK B C, KINZEL E C, et al. Kinematic synthesis for infinitesimally and multiply separated positions using geometric constraint programming[J]. Journal of Mechanical Design, 2014, 136(3): 034503.

    Article  Google Scholar 

  8. [8]

    JOHNSON A, KONG X, RITCHIE J M. Determination of the workspace of a three-degrees-of-freedom parallel manipulator using a three-dimensional computer-aided-design software package and the concept of virtual chains[J]. Journal of Mechanisms and Robotics, 2016, 8(2): 024501.

    Article  Google Scholar 

  9. [9]

    SEAWARD J. Remarks on the comparative advantages of long and short connecting rods and long, and short stroke engines[J]. Minutes of the Proceedings of the Institution of Civil Engineers, 1841, 1: 53–55.

    Article  Google Scholar 

  10. [10]

    HILl M J M. The problem of the connecting rod[J]. Minutes of the Proceedings of the Institution of Civil Engineers, 1896, 124: 390–401.

    Article  Google Scholar 

  11. [11]

    UNWIN W C. Determination of crank angle for greatest piston velocity[J]. Minutes of the Proceedings of the Institution of Civil Engineers, 1896, 125: 363–366.

    Article  Google Scholar 

  12. [12]

    BURLS G A. Note on maximum crosshead velocity[J]. Minutes of the Proceedings of the Institution of Civil Engineers, 1898, 131: 338–346.

    Article  Google Scholar 

  13. [13]

    VOGEL W F. Crank mechanism motions: New methods for their exact determination–III[J]. Production Engineering, 1941, 12(8): 423–428.

    Google Scholar 

  14. [14]

    FREUDENSTEIN F. On the maximum and minimum velocities and the accelerations in four-link mechanisms[J]. Transactions of ASME, 1956, 78: 779–787.

    MathSciNet  Google Scholar 

  15. [15]

    CHING-U IP, PRICE L C. A simple formula for determining the position of maximum slider velocity in a slider-crank mechanism[J]. Transactions of ASME, 1958, 80: 415–418.

    Google Scholar 

  16. [16]

    ZHANG W J, LI Q. A closed-form solution to the crank position corresponding to the maximum velocity of the slider in a centric slider-crank mechanism[J]. Journal of Mechanical Design, 2006, 128(2): 654–656.

    Article  Google Scholar 

  17. [17]

    FRISOLI A, CHECCACCI D, SALSEDO F, et al. Synthesis by screw algebra of translating in-parallel actuated mechanisms[C]//LENARCIC J, STANISIC M M, eds, Advances in Robot Kinematics, Norwell: Kluwer Academic Publishers, 2000: 433–440.

    Chapter  Google Scholar 

  18. [18]

    LI Q, HUANG Z, HERVE J M. Type synthesis of 3R2T 5-DOF parallel mechanisms using the Lie group of displacements[J]. IEEE Transactions on Robotics and Automation, 2004, 22(2): 173–180.

    Article  Google Scholar 

  19. [19]

    ANGELES J. The qualitative synthesis of parallel manipulators[J]. Journal of Mechanical Design, 2004, 126(4): 617–624.

    Article  Google Scholar 

  20. [20]

    HUANG Z, LI Q, DING H. Theory of parallel mechanisms[M] Dordrecht: Springer, 2013.

    Book  Google Scholar 

  21. [21]

    FANG Y, TSAI L W. Analytical identification of limb structures for translational parallel manipulators[J]. Journal of Robotic Systems, 2004, 21(5): 209–218.

    Article  MATH  Google Scholar 

  22. [22]

    KONG X, GOSSELIN C. Type synthesis of parallel mechanisms[M] Berlin: Springer, 2007.

    MATH  Google Scholar 

  23. [23]

    ZHAO T, DAI J S, HUANG Z. Geometric synthesis of spatial parallel manipulators with fewer than six degrees of freedom[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2002, 216(12): 1175–1185.

    Google Scholar 

  24. [24]

    YANG T L, LIU A X, LUO Y F, et al. Theory and application of robot mechanism topology[M] Beijing: Science Press, 2012. (in Chinese).

    Google Scholar 

  25. [25]

    GOGU G. Structural synthesis of parallel robots: Part 1–methodology[M] Dordrecht: Springer, 2009

    Book  MATH  Google Scholar 

  26. [26]

    HE J, GAO F, MENG X, et al. Type synthesis for 4-DOF parallel press mechanism using GF set theory[J]. Chinese Journal of Mechanical Engineering, 2015, 28(4): 851–859.

    Article  Google Scholar 

  27. [27]

    MENG J, LIU G F, LI Z X. A geometric theory for analysis and synthesis of sub-6 DoF parallel manipulators[J]. IEEE Transactions on Robotics, 2007, 23: 625–649.

    Article  Google Scholar 

  28. [28]

    LIU X J, WANG J. Parallel kinematics: Type, kinematics, and optimal design[M] Berlin: Springer, 2014.

    Book  Google Scholar 

  29. [29]

    ZHAO J, FENG Z, CHU F, et al. Advanced theory of constraint and motion analysis for robot mechanisms[M] Oxford: Elsevier, 2014.

    Google Scholar 

  30. [30]

    KONG X, GOSSELIN C M. Type synthesis of three-degreeof- freedom spherical parallel manipulators[J]. The International Journal of Robotics Research, 2004, 23(3): 237–245.

    Article  Google Scholar 

  31. [31]

    HUNT K H. Constant-velocity shaft couplings: A general theory[J]. Journal of Engineering for Industry, 1973, 95(2): 455–464.

    Article  Google Scholar 

  32. [32]

    HUNT K H. Structural kinematics of in-parallel-actuated robot-arms[J]. Journal of Mechanisms, Transmissions and Automation in Design, 1983, 105(4): 705–712.

    Article  Google Scholar 

  33. [33]

    BROGARDH T. Design of high performance parallel arm robots for industrial applications[C]//Proceedings of A Symposium Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball Upon the 100th Anniversary of A Treatise on the Theory of Screws, Cambridge, UK, July 9–12, 2000: Ball2000-15.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Xianwen Kong.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kong, X. Standing on the shoulders of giants: A brief note from the perspective of kinematics. Chin. J. Mech. Eng. 30, 1–2 (2017).

Download citation