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Kinematics analysis and statics of a 2SPS+UPR parallel manipulator

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Abstract

In this paper, the kinematics and statics of a 2SPS+UPR parallel manipulator are studied systematically. First, its simulation mechanism is created, and formulae for solving the inverse/forward displacement kinematics are derived. Second, formulae for solving inverse/forward velocity and active/constrained forces are derived. Third, formulae for solving inverse/forward acceleration are derived, and a workspace is analysed. The analytic results are verified by its simulation mechanism.

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Abbreviations

B,m :

the base and the moving platform

r i :

the active leg and its length

l i ,L i :

the sideline of m and the sideline of B

P,S :

the prismatic joint and the spherical joint

R 1,R 2,R 3 :

the revolute joints

U :

the universal joint with R 1 & R 2

O,o :

the center point of B and the center point of m

{m}:

coordinate o-xyz fixed on m

{B}:

coordinate O-XYZ fixed on B

b i ,B i :

the vertices of m and the vertices of B

v ri :

the input velocity of active leg

e,E :

the distances from b i to o and from B i to O

δ i ,f j :

the unit vectors of r i and F pj

F,T :

the central force and torque applied on m at o

F x F y F z T x T y T z :

the components of Fand T

F ai :

the active forces exerted on r i

T a :

the active torque exerted on R 1

F pj ,T p :

the constraint forces (j=1,2), constraint torque

J,H :

the Jacobian matrix and Hessian matrix

x l ,x m ,x n :

direction cosine between x  &  X,x  &  Y,x  &  Z

y l ,y m ,y n :

direction cosine between y  &  X,y  &  Y,y  &  Z

z l ,z m ,z n :

direction cosine between z  &  X,z  &  Y,z  &  Z

α,β,λ :

rotational angles of m about (Z,X 1,y)

X o ,Y o ,Z o :

the position components of o in {B}

V :

the forward general velocity, V=[vω]T

A :

the forward general acceleration, A=[aε]T

W :

the reachable workspace

∥,⊥ :

parallel and perpendicular constraints

References

  1. Niku, S.B.: Introduction to Robotics Analysis, Systems, Applications. Pearson Education, Beijing (2004)

    Google Scholar 

  2. Huang, Z., Kong, L.F., Fang, Y.F.: Theory on Parallel Robotics and Control. Machinery Industry Press, Beijing (1997)

    Google Scholar 

  3. Carricato, M.: Fully isotropic four-degrees-of-freedom parallel mechanisms for Schoenflies motion. Int. J. Robot. Res. 24(5), 397–414 (2005)

    Article  Google Scholar 

  4. Fang, Y., Tsai, L.W.: Structure synthesis of a class of 4-dof and 5-dof parallel manipulators with identical limb structures. Int. J. Robot. Res. 21(9), 799–810 (2002)

    Article  Google Scholar 

  5. Li, Q., Huang, Z.: Type synthesis of 4-dof parallel manipulators. In: IEEE Int. Conf. on Robotics and Automation, Taipei, 14–19 September 2003, pp. 755–760

  6. Kong, X., Gosselin, C.M.: Type synthesis of 3T1R 4-dof parallel manipulators based on screw theory. IEEE Trans. Robot. Autom. 20(2), 181–190 (2004)

    Article  Google Scholar 

  7. Company, O., Marquet, F., Pierrot, F.: A new high speed 4-dof parallel robot. Synthesis and modeling issues. IEEE Trans. Robot. Autom. 19(3), 411–420 (2003)

    Article  Google Scholar 

  8. Choi, H.B., et al.: Design and control of a novel 4-dofs parallel robot H4. In: IEEE Int. Conf. on Robotics and Automation, Taipei, 14–19 September 2003, pp. 1185–1190

  9. Alizade, R.I., Bayram, C.: Structural synthesis of parallel manipulators. Mech. Mach. Theory 39(8), 857–870 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gao, F., Li, W., Zhao, X.: New kinematic structures for 2-, 3-, 4-, and 5-DOF parallel manipulator designs. Mech. Mach. Theory 37, 1395–1411 (2002)

    Article  MATH  Google Scholar 

  11. Chen, W.-J.: A novel 4-dof parallel manipulator and its kinematic modelling. In: IEEE Int. Conf. on Robotics and Automation, Seoul, 23–25 May 2001, pp. 3350–3355

  12. Tanev, T.K.: Forward displacement analysis of a three legged four-degree-of-freedom parallel manipulator. In: Proceedings of the Symposium on Advances in Robot Kinematics, pp. 147–154. Kluwer, Dordrecht (1998)

    Google Scholar 

  13. Han, C., Kim, J., Kim, J., Park, F.C.: Kinematic sensitivity analysis of the 3-UPU parallel mechanism. Mech. Mach. Theory 37, 787–798 (2002)

    Article  MATH  Google Scholar 

  14. Zhang, D., Gosselin, C.M.: Kinetostatic modelling of N-DOF parallel mechanisms with a passive constraining leg and prismatic actuators. ASME J. Mech. Des. 123(3), 375–384 (2001)

    Article  Google Scholar 

  15. Huang, T., Li, M., Zhao, X.M., Mei, J.P., Chetwynd, D.G., Hu, S.J.: Conceptual design and dimensional synthesis for a 3-DOF module of the TriVariant—a novel 5-DOF reconfigurable hybrid robot. IEEE Trans. Robot. 21(3), 449–456 (2005)

    Article  Google Scholar 

  16. Güursel, A., Bijan, S.: Topology optimisation and singularity analysis of a 3-SPS parallel manipulator with a passive constraining spherical joint. Mech. Mach. Theory 39, 215–235 (2004)

    Article  MathSciNet  Google Scholar 

  17. Joshi, S.A., Tsai, L.W.: Jacobian analysis of limited-DOF parallel manipulators. Trans. ASME J. Mech. Des. 124(2), 254–258 (2002)

    Article  Google Scholar 

  18. Kim, S.G., Ryu, J.: New dimensionally homogeneous Jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators. IEEE Trans. Robot. Autom. 19(4), 731–737 (2003)

    Article  Google Scholar 

  19. Fang, Y.F., Huang, Z.: Kinematics of a three-degree-of-freedom in-parallel actuated manipulator mechanism. Mech. Mach. Theory 32(7), 789–796 (1997)

    Article  Google Scholar 

  20. Canfield, S.L., Soper, R.R., Reinholtz, C.F.: Velocity analysis of parallel manipulators by truss transformations. Mech. Mach. Theory 34(3), 345–357 (1999)

    Article  MATH  Google Scholar 

  21. Dasgupta, B., Mruthyunjayja, T.S.: A Newton–Euler formulation for the inverse dynamics of the Stewart platform manipulator. Mech. Mach. Theory 33(8), 1135–1152 (1998)

    MATH  MathSciNet  Google Scholar 

  22. Tsai, L.W.: Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work. Trans. ASME J. Mech. Des. 122(1), 3–9 (2000)

    Article  Google Scholar 

  23. Gallardo, J., Rico, J.M., Frisoli, A., Checcacci, D., Bergamasco, M.: Dynamics of parallel manipulators by means of screw theory. Mech. Mach. Theory 38(11), 1113–1131 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  24. Lu, Y.: Using virtual work theory and CAD functionalities for solving driving force and passive force of spatial parallel manipulators. Mech. Mach. Theory 42, 839–858 (2007)

    Article  MATH  Google Scholar 

  25. Lu, Y.: Using CAD functionalities for the kinematics analysis of spatial parallel manipulators with 3-, 4-, 5-, 6-linearly driven limbs. Mech. Mach. Theory 39(1), 41–60 (2004)

    Article  MATH  Google Scholar 

  26. Lu, Y., Zhao, Y.H.: Position and workspace analyses of 3-SPR and 3-RPS parallel manipulators. ASME 2005 International Design Engineering Technical Conference & Computers and Information in Engineering Conference, Long Beach, California, USA, 24–28 September 2005, pp. 957–962

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Authors and Affiliations

  1. Robotics Research Centre, School of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei, 066004, China

    Yi Lu, Bo Hu & Yan Shi

Authors
  1. Yi Lu
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  2. Bo Hu
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  3. Yan Shi
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Corresponding author

Correspondence to Yi Lu.

Additional information

The authors would like to acknowledge the financial support of the Natural Sciences Foundation Council of China (NSFC) 50575198 and of Doctoral Fund from National Education Ministry of China No. 20060216006.

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Lu, Y., Hu, B. & Shi, Y. Kinematics analysis and statics of a 2SPS+UPR parallel manipulator. Multibody Syst Dyn 18, 619–636 (2007). https://doi.org/10.1007/s11044-007-9054-6

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  • DOI: https://doi.org/10.1007/s11044-007-9054-6

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