Advertisement

Synthesis of 3-PRS Manipulator Using Exact Method

  • Srinivasa Rao PundruEmail author
  • Mohan Rao Nalluri
Original Contribution

Abstract

This paper presents dimensional synthesis of 3-PRS manipulator which is based on physical constraints of the manipulator. The synthesis of the manipulator involves determination of dimensional parameters of manipulator so as to determine the directions and location of revolute joints and location of spherical joints by considering the physical constraints such that a point on the mobile platform passes through a prescribed set of positions in space. The dimensions of the manipulator are determined by considering physical constraints of the manipulator and are carried out using optimized exact method. The result of exact method approach shows that the maximum error in occupied (obtained) position \(\left( {p_{xi} , p_{yi} , p_{zi} } \right)\) of mobile platform is \(\left| { \pm \,4.5 \times 10^{ - 8} } \right|\) m and the maximum percentage of positional error is \(\left| { \pm \,4.83 \times 10^{ - 2} } \right|\%\), the maximum error in occupied (obtained) orientation \(\left( {\psi_{i} , \theta_{i} , \phi_{i} } \right)\) of mobile platform is \(\left| { \pm \,1.01 \times 10^{ - 6} } \right|\) degrees and the maximum percentage of error in orientation is \(\left| { \pm \,3.16 \times 10^{ - 3} } \right|\% .\) The actuator positions are calculated by inverse kinematics by closed-loop technique and the obtained (occupied) positions, and orientations of the manipulator are determined by direct position kinematics by vector technique. The resulting nonlinear equations are solved by using MATLAB. The numerical example for the synthesis with five positions is presented to demonstrate the synthesis procedure. The 3-PRS manipulator is used for alignment applications where tip, tilt and position motions are significant.

Keywords

Manipulator dimensions Physical constraints Position analysis 3-PRS 

References

  1. 1.
    V.E. Gough, S.G. Whitehall, Universal tyre test machine. In Proceedings of the 9th International Congress of FISTA, vol. 117 (1962), pp. 117–135Google Scholar
  2. 2.
    D. Stewart, A platform with six degrees of freedom. Proc. Inst. Mech. Eng. 180(15), 371–386 (1965)CrossRefGoogle Scholar
  3. 3.
    Y. Fang, L.-W. Tsai, Structure synthesis of a class of 3-dof rotational parallel manipulators. J. IEEE 20, 117–121 (2004)Google Scholar
  4. 4.
    H. Fang, Y. Gao, Y. Fang, Structure synthesis of symmetrical low-dof parallel manipulators. J. IEEE. 1948-1953 (2007)Google Scholar
  5. 5.
    N.M. Rao, K.M. Rao, Multi-position dimensional synthesis of a spatial 3-RPS parallel manipulator. J. ASME 128, 815–819 (2006)CrossRefGoogle Scholar
  6. 6.
    N.M. Rao, K.M. Rao, Dimensional synthesis of a spatial 3-RPS parallel manipulator for a prescribed range of motion of spherical joints. J. Mech. Mach. Theory 44, 477–486 (2009)CrossRefGoogle Scholar
  7. 7.
    H.S. Kim, L.-W. Tsai, Kinematic synthesis of a spatial 3-RPS parallel manipulator. J. ASME 125, 92–97 (2003)CrossRefGoogle Scholar
  8. 8.
    Y. Li, Q. Xu, Kinematic analysis and design of a new 3-dof translational parallel manipulator. J. ASME 128, 729–737 (2006)CrossRefGoogle Scholar
  9. 9.
    Y. Li, Q. Xu, Kinematics and dexterity analysis for a novel 3-dof translational parallel manipulator. J. IEEE 2944–2949 (2005)Google Scholar
  10. 10.
    M.-S. Tsai, T.-N. Shiau, Y.-J. Tsai, T.-H. Chang, Direct kinematic analysis of a 3-PRS parallel mechanism. J. Mech. Mach. Theory 38, 71–83 (2003)CrossRefGoogle Scholar
  11. 11.
    S.A. Joshi, L.-W. Tsai, The kinematics of a class of 3-dof, 4-legged parallel manipulators. J. ASME 125, 52–60 (2003)CrossRefGoogle Scholar
  12. 12.
    J.A. Carretero, R.P. Podhorodeski, M.A. Nahon, C.M. Gosselin, Kinematic analysis and optimization of a new three degree-of-freedom spatial parallel manipulator. J. Mech. Des. 122, 17–24 (2000)CrossRefGoogle Scholar
  13. 13.
    C.H. Liu, S. Cheng, Direct singular positions of 3RPS parallel manipulator. ASME J. Mech. Des. 126(6), 1006–1016 (2005)CrossRefGoogle Scholar
  14. 14.
    G. Pond, J. Carretero, Singularity analysis and workspace optimization of the inclined PRS manipulator. J. CSME 1–7 (2004)Google Scholar
  15. 15.
    Y. Li, Q. Xu, Kinematic analysis of a 3-PRS parallel manipulator. J. Robot. Comput.-Integr. Manuf. 23, 395–408 (2007)CrossRefGoogle Scholar

Copyright information

© The Institution of Engineers (India) 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMahatma Gandhi Institute of TechnologyHyderabadIndia
  2. 2.Department of Mechanical EngineeringJawaharlal Nehru Technological UniversityKakinadaIndia

Personalised recommendations