## “Kinematic and Elastostatic Design Optimisation of the 3-DOF Gantry-Tau Parallel Kinematic Manipulator”Authors: Ilya Tyapin and Geir Hovland,
Affiliation: University of Queensland and University of Agder
Reference: 2009, Vol 30, No 2, pp. 39-56. |

**Keywords:**parallel manipulator, statics, design optimisation

**Abstract:**One of the main advantages of the Gantry-Tau machine is a large accessible workspace/footprint ratio compared to many other parallel machines. The Gantry-Tau improves this ration further by allowing a change of assembly mode without internal link collisions or collisions between the links and end-effector. The reconfigurable Gantry-Tau kinematic design obtained by multi-objective optimisation according to this paper gives the following features: 3-D workspace/footprint ratio is more than 3.19, lowest Cartesian stiffness in the workspace is 5N/mu and no link collisions detected. The optimisation parameters are the support frame lengths, the actuator positions and the robot´s arm lengths. The results comparison between the evolutionary complex search algorithm and gradient-based method used for the Gantry-Tau design in the past is also presented in this paper. The detailed statics model analysis of the Gantry-Tau based on a functionally dependency is presented in this paper for the first time. Both the statics model and complex search algorithm may be applied for other 3-DOF Hexapods without major changes. The existing lab prototype of the Gantry-Tau was assembled and completed at the University of Agder, Norway.

PDF (2029 Kb) DOI: 10.4173/mic.2009.2.1

**DOI forward links to this article:**

[1] Alexandr Klimchik, Anatol Pashkevich, Damien Chablat and Geir Hovland (2013), doi:10.1016/j.rcim.2012.09.008 | |

[2] Alexandr Klimchik, Anatol Pashkevich and Damien Chablat (2013), doi:10.1016/j.finel.2013.06.008 | |

[3] Ilya Tyapin and Geir Hovland (2011), doi:10.1007/s11012-010-9394-9 | |

[4] Alexandr Klimchik, Damien Chablat and Anatol Pashkevich (2015), doi:10.1016/j.euromechsol.2014.12.010 | |

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[10] Alexandr Klimchik, Stéphane Caro, Yier Wu, Damien Chablat, Benoit Furet and Anatol Pashkevich (2014), doi:10.1007/978-94-007-7214-4_21 | |

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**References:**

[1] Bi, Z., Lang, S., Zhang, D., Orban, P., Verner, M. (2007). Integrated design toolbox for tripod-based parallel kinematic machines, Journal of Mechanical Design, 129:799-807 doi:10.1115/1.2735340

[2] Brogårdh, T. (2000). Design of high performance parallel arm robots for industrial applications, In Proc. of the Symp. Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball Upon the 100th Anniversary of A Treatise on the Theory on The Screws. University of Cambridge, Trinity College.

[3] Brogårdh, T. Gu, C. (2002). Parallel robot development at ABB, In Proc. 1st Intl. Coll. of the Collaborative Research Centre 562. University of Braunschweig.

[4] Brogårdh, T., Hanssen, S., Hovland, G. (2005). Application-oriented development of parallel kinematic manipulators with large workspace, In Proc. 2nd Intl. Coll. of the Collaborative Research Center 562:Robotic Systems for Handling and Assembly. Braunschweig, Germany, pp. 153-170.

[5] Clavel, R. (1988). Delta, a fast robot with parallel geometry, In Intl. Symp. on Industrial Robots. Lausanne, Switzerland, pp. 91-100.

[6] Coello, C. C. (2002). Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: A survey of the state of the art, Comp. Meth. in Appl. Mech. and Engnrg, 191((11-12)):1245-1287.

[7] Company, O., Pierrot, F., Fauroux, J.-C. (2005). A method for modeling analytical stiffness of a lower mobility parallel manipulator, In IEEE Intl. Conf. on Robotics and Automat. Barcelona, Spain, pp. 3232-3237.

[8] Dashy, A., Yeoy, S., Yangz, G., I.-H.Chery. (2002). Workspace analysis and singularity representation of three-legged parallel manipulators, In Proc. 7th Intl. Conf. in Control, Automat., Robotics And Vision. Singapore, pp. 962-967.

[9] Dimentberg, F. (1965). The screw Calculus and its Applications in Mechanics, Document FTD-HT-23-1632-67, Foreign Technology Division, Wright-Patterson Air Force Base, Ohio, USA.

[10] Eberly, D. H. (2001). 3D game engine design, Morgan Kaufmann, page 561.

[11] El-Khasawneh, B. Ferreira, P. (1999). Computation of stiffness and stiffness bounds for parallel link manipulators, In Int. Journal of Machine Tools and Manufacture. Elsevier Science Ltd., pp. 321-342.

[12] Gosselin, C. (1990). Determination of the workspace of 6-dof parallel manipulators, ASME J. Mech. Des., 112:331-336 doi:10.1115/1.2912612

[13] Gosselin, C. (1999). Stiffness mapping for parallel manipulators, IEEE Transactions on Robotics and Automation, .3:377-382 doi:10.1109/70.56657

[14] Hansen, M. Andersen, T. (2001). A design procedure for actuator control systems using optimization methods, In IEEE The 7th Scandinavian International Conference on Fluid Power. pp. 213-221.

[15] Hansen, M., Andersen, T., Mouritsen, O. (2004). A scheme for handling discrete and continuous design variables in multi criteria design optimization of servo mechanisms, In Mechatronics and Robotics. pp. 234-245.

[16] Hovland, G., Choux, M., Murray, M., Brogårdh, T. (2007). Benchmark of the 3-dof gantry-tau parallel kinematic machine, In IEEE Intl. Conf. on Robotics and Automat. Roma, Italy, pp. 535-542.

[17] Hovland, G., Choux, M., Murray, M., Tyapin, I., Brogårdh, T. (2008). The Gantry-Tau : Summary of latest development at ABB, University of Agder and University of Queensland, In 3rd Intl. Colloquium: Robotic Systems for Handling and Assembly, the Collaborative Research Centre SFB 562. Braunschweig, Germany.

[18] Huang, T. Mei, J. (2001). Stiffness estimation of a tripod-based parallel kinematic machine, In International Conference on Robotics and Automation. Seoul, Korea, pp. 3280-3285.

[19] Li, Y., Chen, S.-F., Kao, I. (2002). Stiffness control and transformation for robotic systems with coordinate and non-coordinate bases, In Intl. Conf. on Roborics and Automat. Washington, USA, pp. 550-555.

[20] Li, Y. Kao, I. (2004). Stiffness control on redundant manipulators: A unique and kinematically consistent solution, In Intl. Conf. on Roborics and Automat. New Orleans, USA, pp. 3956-3961.

[21] Liu, H., Ye, C., Wang, H., Wei, Y. (2007). Stiffness analysis and expirement of a parallel kinematic planer, In Proc. of the IEEE International Conference on Automation and Logistics. Jinan, China.

[22] Lou, Y., Liu, G., Li, Z. (2008). Randomized optimal design of parallel manipulators, IEEE Transactions on Automation Science and Engineering, .2:223-233 doi:10.1109/TASE.2007.909446

[23] Majou, F., Gosselin, C., Wenger, P., Chablat, D. (2004). Parametric stiffness analysis of the orthoglide, In Intl. Symposium on Robotics.

[24] Merlet, J.-P. (2000). Parallel Robots, Kluwer Academic Publisher, Solid Mechanics and its Applications, Vol. 74, Dordrecht, Boston.

[25] Merlet, J.-P. Daney, D. (2006). Leg interference checking of parallel robots over a given workspace trajectory, In Proc. of the IEEE International Conference on Robotics and Automation. Orlando, Florida.

[26] Pashkevich, A., Wenger, P., Chablat, D. (2005). Design strategies for the geometric synthesis of orthoglide-type mechanisms, Journal of Mechanism and Machine Theory, 4.8:907-930 doi:10.1016/j.mechmachtheory.2004.12.006

[27] Pashkevich, A., Wenger, P., Chablat, D. (2007). Kinematic and stiffness analysis of the orthoglide, a PKM with simple, regular workspace and homogeneous performances, In IEEE Intl. Conf. on Robotics and Automat. Roma, Italy, pp. 549-555.

[28] Pierrot, F., Uchiyama, M., Dauchez, P., Fournier, A. (1992). A new design of a 6-dof parallel robot, In Proc. 23rd Intl. Symp. on Industrial Robots. pp. 771-776.

[29] Stamper, R., Tsai, L., Walsh, G. (1997). Optimization of a three dof translational platform for well-conditioned workspace, In Proc. of the Int. Conf. Robotics and Automation. New Mexico, pp. 3250-3255.

[30] Teller, S. (2008). Distance between two line segments in 3D, Geometric tools, http://www.geometrictools.com, 1998-2008.

[31] Tyapin, I. (2009). Multi-objective design optimiation of a class of parallel kinematic machines, In Ph.D Thesis. Brisbane, Queensland, Australia, pp. 1-266.

[32] Uchiyama, M., Iimura, K., Pierrot, F., Dauchez, P., Unno, K., Toyama, O. (1990). A new design of a very fast 6-dof parallel robot, Journal of Robotics and Mechatronics, .4:308-315.

[33] Whitney, D. E. (1969). Optimum step size control for Newton-Raphson solution of nonlinear vector equations, 1.4:572-574.

[34] Williams, I., Hovland, G., Brogårdh, T. (2006). Kinematic error calibration of the gantry-tau parallel manipulator, In IEEE Intl. Conf. on Robotics and Automat. Orlando, pp. 4199-4204.

**BibTeX:**

@article{MIC-2009-2-1,

title={{Kinematic and Elastostatic Design Optimisation of the 3-DOF Gantry-Tau Parallel Kinematic Manipulator}},

author={Tyapin, Ilya and Hovland, Geir},

journal={Modeling, Identification and Control},

volume={30},

number={2},

pages={39--56},

year={2009},

doi={10.4173/mic.2009.2.1},

publisher={Norwegian Society of Automatic Control}

};