Kinematics of an offset 3-UPU translational parallel manipulator by the homotopy continuation method

Nonlinear Analysis: Real World Applications

Volumn 10, Issue 3, 2009, Pages 1767-1774

  Varedi, S M ^a   Daniali, H M ^a   Ganji, D D ^a  

^a UNIVERSITY OF MAZANDARAN   (Iran)

Author keywords

Direct kinematics; Homotopy continuation method; Inverse kinematics; Parallel manipulator

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; INVERSE KINEMATICS; INVERSE PROBLEMS; NONLINEAR EQUATIONS;

COMPUTING TIME; DIRECT KINEMATICS; HOMOTOPY CONTINUATION METHOD; INITIAL GUESS; INVERSE KINEMATIC PROBLEMS; NOVEL METHODS; NUMERICAL - TECHNIQUES; PARALLEL MANIPULATOR; REAL SOLUTIONS; SYSTEM OF NONLINEAR EQUATIONS; TRANSLATIONAL PARALLEL MANIPULATORS;

MANIPULATORS;

EID: 60549107061     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.02.014     Document Type: Article

References (19)

1. Wu T.M. The inverse kinematics problem of spatial 4P3R robot manipulator by the homotopy continuation method with an adjustable auxiliary homotopy function. Nonlinear Analysis 64 (2006) 2373-2380
2. Wu T.M. A study of convergence on the Newton- homotopy continuation method. Applied Mathematics and Computation 168 (2005) 1169-1174
3. Wu T.M. Solving the nonlinear equations by the Newton-homotopy continuation method with adjustable auxiliary homotopy function. Applied Mathematics and Computation 173 (2006) 383-388
4. Allgower E.L., and Georg K. Numerical Continuation Methods, An Introduction (1990), Springer, NewYork
5. Sandor G.N., and Erdman A.G. Advanced Mechanism Design (2001), Prentice-Hall, New Jersey
6. A.P. Morgan, A Method for computing all Solutions to Systems of Polynomial Equations, GM Research Publication, GMR 3651, 1981
7. Morgan A.P., and Wampler C.W. Solving a planar four-bar design problem using continuation. ASME Journal of Mechanical Design 112 (1990) 544-550
8. Garcia C.B., and Zangwill W.I. Pathways to Solutions, Fixed Points, and Equilibria (1981), Prentice-Hall Book Company, Inc., Englewood Cliffs, New Jersey
9. Wu H., and Ji P. Kinematics analysis of an offset 3-UPU translational parallel robotic manipulator. Robotics and Autonomous Systems 42 (2003) 117-123
10. Tsai L.W. Kinematics of a three-DOF platform with three extensible limbs. Recent Advances in Robot Kinematics (1996), Kluwer Academic Publishers, Dordrecht 401-410
11. L.W. Tsai, R. Stamper, A parallel manipulator with only translational degrees of freedom, ASME 96-DETC-MECH-1152, USA, 1996
12. Bonev I.A., and Ryu J. A new method for solving the direct kinematics of general 6-6 Stewart Platforms. Mechanism and Machine Theory 35 (2000) 423-436
13. Dasgupta B., and Mruthyunjaya T.S. The Stewart platform manipulator: A review. Mechanism and Machine Theory 35 (2000) 15-40
14. Varedi S.M., Hosseini M.J., Rahimi M., and Ganji D.D. He's variational iteration method for solving a semi-linear inverse parabolic equation. Physics Letters A (2007) 275-280
15. Hashemi S.H., Daniali H.M., and Ganji D.D. Numerical simulation of the generalized Huxley equation by He's homotopy perturbation method. Applied Mathematics and Computation (2007) 157-161
16. Ganji D.D., Hosseini M.J., and Shayegh J. Some nonlinear heat transfer equations solved by three approximate methods. International Communications in Heat and Mass Transfer (2007) 1003-1016
17. He J.H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. International Journal of Non-Linear Mechanics 35 (2000) 37-43
18. He J.H. Variational iteration method-a kind of non-linear analytical technique: Some examples. International Journal of Non-Linear Mechanics 34 (1999) 699-708
19. S.A. El-Wakil, M.A. Abdou, New applications of the homotopy analysis method, Int. J. of Physics (2008) (in press)