Direct Kinematics Solution of 3-RCC Parallel Robot using a Semi-Analytical Homotopy Method

Subject Areas : robotics

Seyyed Mojtaba Varedi-Koulaei ¹ , Masoumeh Rahimi ²

1 - Department of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Iran
2 - Department of Mechanical Engineering, Faculty of Engineering, Golestan University, Iran

Received: 2018-03-07 Accepted : 2018-07-27 Published : 2019-03-01

Keywords:

References:

[1]     Gough, V. E., Whitehall, S. G., Universal Tire Test Machine, in: Proceedings of 9th International Technical Congress, F.I.S.I.T.A., Vol. 177, 1962.

[2]     Stewart, D. A., Platform with Six Degrees of Freedom, in: Proceedings of the Institute of Mechanical Engineering, Vol. 180, No. 5, 1965, pp. 371–386.

[3]     Hunt, K. H., Kinematic Geometry of Mechanism, Clarendon Press, Oxford, 1978.

[4]     Fichter, E. F., A Stewart Platform-Based Manipulator: General Theory and Practical Construction, International Journal of Robotics Research, Vol. 5, No. 2, 1986, pp. 157–182.

[5]     Mohammadi Daniali, H. R., Zsombor Murray, P. J., and Angeles, J., Singularity Analysis of Planar Parallel Manipulators, Mechanism and Machine Theory, Vol. 30, No. 5, 1995, pp. 665–678.

[6]     Merlet, J. P., Gosselin, C. M., and Mouly, N., Workspaces of Planar Parallel Manipulators, Mechanism and Machine Theory, Vol. 33, No. 1–2, 1998, pp. 7–20.

[7]     Tsai, M. S., Shiau, T. N., Tsai, Y. J., and Chang, T. H., Direct Kinematic Analysis of a 3-PRS Parallel Mechanism, Mechanism and Machine Theory, Vol. 38, No. 1, 2003, pp. 71–83.

[8]     Korayem, M. H., Bamdad, M., Dynamic Load- Carrying Capacity of Cable- Suspended Parallel Manipulators, International Journal of Advance Design and Manufacturing Technology, Vol. 44, 2008, pp. 829–840.

[9]     Varedi Koulaei, S. M., Daniali, H. M., Farajtabar, M., Fathi, B., and Shafiee Ashtiani, M., Reducing the Undesirable Effects of Joints Clearance on the Behavior of the Planar 3-RRR Parallel Manipulators, Nonlinear Dynamics, Vol. 86, 2016, pp. 1007–1022.

[10]  Shahabi, E., Hosseini, M. A., Kinematic Synthesis of a Novel Parallel Cable Robot as the Artificial Leg, International Journal of Advance Design and Manufacturing Technology, Vol. 9, No. 3, 2016, pp. 1-10.

[11]  Varedi, S. M., Daniali, H. M., and Dardel, M., Dynamic Synthesis of a Planar Slider-Crank Mechanism with Clearances, Nonlinear Dynamics, Vol. 79, 2015, pp. 1587–1600.

[12]  Dasgupta, B., Mruthyunjaya, T. S., The Stewart Platform Manipulator: a Review, Mechanism and Machine Theory, 35, 2000, pp. 15–40.

[13]  Bonev, I. A., Ryu, J., A New Method for Solving the Direct Kinematics of General 6-6 Stewart Platforms, Mechanism and Machine Theory, Vol. 35, 2000, pp. 423–436.

[14]  Kachapi, S. H. A., Ganji, D. D., Davodi, A. G., and Varedi, S. M., Periodic Solution for Strongly Nonlinear Vibration Systems by He's Variational Iteration Method, Mathematical Methods in the Applied Sciences, Vol. 32, No. 18, 2009, pp. 2339-2349.

[15]  He, J. H., Variational Iteration Method–a Kind of Non-Linear Analytical Technique: Some Examples, International journal of Non-Linear Mechanics, Vol. 34, 1999, pp. 699–708.

[16]  He, J. H., A Coupling Method of a Homotopy Technique and a Perturbation Technique for Non-Linear Problems, International Journal of Non-Linear Mechanics, Vol. 35, 2000, pp. 37–43.

[17]  Wu, T. M., A Study of Convergence on the Newton- Homotopy Continuation Method, Applied Mathematics and Computation, Vol. 168, 2005, pp. 1169–1174.

[18]  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, Vol. 64, 2006, pp. 2373–2380.

[19]  Morgan, A. P., Wampler, C. W., Solving a Planar Four-Bar Design Problem Using Continuation, ASME Journal of Mechanism Design, Vol. 112, 1990, pp. 544 –550.

[20]  Garcia, C. B., Zangwill, W. I., Pathways to Solutions, Fixed Points, and Equilibria, Prentice-Hall Book Company, Inc., Englewood Cliffs, New Jersey, 1981.

[21]  Allgower, E. L., Georg, K., Numerical Continuation Methods, An Introduction, Springer, NewYork, 1990.

[22]  Varedi, S. M., Daniali, H. M., and Ganji, D. D., Kinematics of an Offset 3-UPU Translational Parallel Manipulator by the Homotopy Continuation Method, Nonlinear Analysis: Real World Applications, Vol. 10, 2009, pp.1767–1774.

[23]  Tari, H., Su, H. J., and Li, T. Y., A Constrained Homotopy Technique for Excluding Unwanted Solutions from Polynomial Equations Arising in Kinematics Problems, Mechanism and Machine Theory, Vol. 45, No. 6, 2010, pp. 898–910.

[24]  Tari, H., Su, H. J., A Complex Solution Framework for the Kinetostatic Synthesis of a Compliant Four-Bar Mechanism, Mechanism and Machine Theory, Vol. 46, No. 8, 2011, pp. 1137–1152.

[25]  Shen, H., Yang, T., Tao, S., Liu, A., and Ma, L. Z., Structure and Displacement Analysis of a Novel Three-Translation Parallel Mechanism, Mechanism and Machine Theory, Vol. 40, 2005, pp. 1181–1194.