Abstract
This paper presents dimensional synthesis of a 3-RPS parallel manipulator according to the limitations on the actuating link lengths and on the range of motion of the spherical joints. The synthesis of the manipulator consists of determining the dimensions of a moving platform and a fixed base along with the directions of revolute joint axes such that a point on the moving platform passes through a set of prescribed positions in space. The dimensions of the moving platform are determined using a hybrid optimization method called GA–simplex method. While determining the dimensions of the fixed base, the limitations on the motion of the joints are considered to design a practical manipulator. The synthesis procedure presented confines to that class of problems where the number of prescribed positions required to complete a task is more than the number of positions a parallel manipulator can offer. The practical applications include automated assembly, contour machining, etc. A numerical example for the synthesis with ten positions is presented. This paper also presents direct kinematic equations for the manipulators with non-equilateral triangular platforms in order to validate the results of the numerical example.
Similar content being viewed by others
References
Gough VE, Whitehall SG (1962) Universal tyre test machine. Proc 9th Int Congr F I S T T A 117:117-–135
Stewart D (1965) A platform with six degrees of freedom. Proc Inst Mech Eng London 180(15)):371–386
Kong X, Gosselin CM (2004) Type synthesis of 3-DOF translational parallel manipulators based on screw theory. ASME J Mech Des 126:83–92
Affi Z, Romdhane L, Maalej A (2004) Dimensional synthesis of a 3-translational-dof in-parallel manipulator for a desired workspace. Eur J Mech A Solids 23(2):311–324
Laribi MA, Romdhane L, Zeghloul S (2007) Analysis and dimensional synthesis of the DELTA robot for a prescribed workspace. Mech Mach Theory 42(7):859–870
Kosinska A, Galicki M, Kedzior K (2003) Designing and optimization of parameters of Delta-4 parallel manipulator for a given workspace. J Robot Syst 20(9):539–548
P. Chedmail, E. Ramstein, “Robot mechanism synthesis and genetic algorithms,” In: Proceedings of the IEEE International Conference on Robotics and Automation, 1996, pp. 3466–3471
Lee KM, Shah DK (1988) Kinematic analysis of a three degrees-of-freedom in-parallel actuated manipulator. IEEE J Robot Autom 4(3):354–360
Lee K, Shah DK (1988) Dynamic analysis of a three degrees of freedom in-parallel actuated manipulator. IEEE Trans Robot Autom 4:361–367
Yang PH, Waldron KJ, Orin DE (1996) Kinematics of a three degrees-of-freedom motion platform for a low-cost driving simulator. In: Lenareie J, Parenti-Castelli V (eds) Recent advances in robot kinematics. Kluwer, London, pp 89–98
Song SM, Zhang MD (1995) A study of reactional force compensation based on three-degree-of-freedom parallel platforms. J Robot Syst 12:783–794
Joshi SA, Tsai LW (2002) Jacobian analysis of limited-DOF parallel manipulator. ASME J Mech Des 124:254–258
Liu CH, Cheng S (2004) Direct singular positions of 3RPS parallel manipulator. ASME J Mech Des 126:1006–1016
Tsai LW, Kim HS (2003) Kinematic synthesis of a spatial 3-RPS parallel manipulator. ASME J Mech Des 125:92–97
Rao NM, Rao KM (2006) Multi-position dimensional synthesis of a spatial 3-RPS parallel manipulator. ASME J Mech Des 128:815–819
Yen J, Liao JC, Bogju Lee, Randolph D (1998) A Hybrid approach to modeling metabolic systems using a genetic algorithm and simplex method,”. Syst Man Cybern B IEEE Trans 28(2):173–191
Musil M, Wilmut M, Chapman N (1999) A hybrid simplex genetic algorithm for estimating geoacoustic parameters using matched-field inversion. IEEE J Oceanic Eng 24:358–369
Trabia MB (2004) A hybrid fuzzy simplex genetic algorithm. ASME J Mech Des 126:969–974
Rao SS, Xiong Y (2005) A hybrid genetic algorithm for mixed-discrete design optimization. ASME Jl of Mech Des 127:1101–1112
Xiao J, Kulakowski B (2006) Hybrid genetic algorithm: a robust parameter estimation technique and its application to heavy duty vehicles. ASME J Dynamic Syst Meas Control 128:523–531
Wang L et al (2005) Design optimization and remote manipulation of a tripod. Int J Comput Integr Manuf 18:85–95
Zhen G et al (2009) Design, analysis, and stiffness optimization of a three degree of freedom parallel manipulator. Robotica. doi:10.1017/S0263574709005657
Bi ZM et al (2007) Integrated design toolbox for tripod-based parallel kinematic machines. ASME J Mech Des 129(8):799–807
Deb K (2002) Optimization for engineering design algorithms and examples. Prentice-Hall, India
Rao NM, Rao KM (2009) Dimensional synthesis of a spatial 3-RPS parallel manipulator for a prescribed range of motion of spherical joints. Mech Mach Theory 44:477–486
Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York
Deb K (1998) Genetic algorithms in search and optimization: the technique and applications, Proceedings of International Workshop on Soft Computing and Intelligent Systems, (ISI). Calcutta, India), pp 58–87
Rao, S.S., 2003, Engineering optimization, New Age International (P) Ltd, New Delhi
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rao, N.M. Synthesis of a spatial 3-RPS parallel manipulator based on physical constraints using hybrid GA simplex method. Int J Adv Manuf Technol 52, 777–787 (2011). https://doi.org/10.1007/s00170-010-2781-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-010-2781-5