Kineto-static analysis of a novel high-speed parallel manipulator with rigid-flexible coupled links

Abstract

A novel high-speed parallel kinematic machine (PKM) named Delta-S parallel manipulator is proposed, which consists of a fixed base connected to a moving platform through three limbs with identical topology. Each limb is composed of one driving arm and one follower arm, herein, the latter includes two strings and one middle rod, all located in a same plane. Compared with similar manipulators with uniform parameters, the novel and unique topology as well as the addition of two strings of Delta-S manipulator can remove the clearance of the spherical joints, reduce the inertial load of components further, improve the positioning accuracy and dynamic performance, and so on. In order to formulate the kineto-static model of Delta-S manipulator, the kineto-static analyses and models of the driving arm, the generalized follower and the moving platform can be carried out by the D’ALEMBERT principle. For the sake of obtaining the force analytic results of strings, the deformation compatibility condition of strings and the middle rod are determined. Furthermore, in virtue of the assumption of small deformation and the linear superposition principle, the minimal pre-tightening force of the strings is calculated. The main results include that the loads of the strings and the middle rod must be larger than “zero” and the pre-tightening force over the workspace must be larger than the minimal pre-tightening force at any time within the workspace, which lay the foundation for the dynamic analysis and the prototype manufacture of the Delta-S manipulator.

Keywords

parallel kinematic machines (PKMs) / Delta-S manipulator / kineto-static analysis / deformation compatibility condition / pre-tightening force

References

[1] TlustyJ., ZiegertJ., RidgewayS.. Fundamental comparison of the use of serial and parallel kinematics for machine tools [J]. CIRP Annals-Manufacturing Technology, 2002, 48(1): 351-356

[2] WeckM., StaimerD.. Parallel kinematic machine tools-current state and future potentials [J]. CIRP Annals-Manufacturing Technology, 2002, 51(2): 671-683

[3] CorbelD., CompanyO., PierrotF.. Optimal design of a 6-dof parallel measurement mechanism integrated in a 3-dof parallel machine-tool [C]. Proceedings of 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2008, Nice, France, IEEE Press: 1970-1976

[4] ZhuS. J., HuangZ., ZhaoM. Y.. Singularity analysis for six practicable 5-DoF fully-symmetrical parallel manipulators [J]. Mechanism and Machine Theory, 2009, 44: 710-725

[5] LuY., ShiY., HuangZ., YuJ.-p., LiS.-h., TianX.-bin.. Kinematics/statics of a 4-DOF over-constrained parallel manipulator with 3 legs [J]. Mechanism and Machine Theory, 2009, 44: 1497-4506

[6] SunT., SongY.-m., LiY.-g., ZhangJun.. Stiffness estimation for the 4-DOF hybrid module of a novel reconfigurable robot [C]. Proceedings of 2009 ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, 2009, London, UK, IEEE Press: 565-571

[7] TsaiL.W., JoshiS. A.. Kinematics and optimization of a spatial 3-UPU parallel manipulator [J]. Journal of Mechanical Design ASME, 2000, 122: 439-446

[8] HuangT., LiM., LiZ.-x., ChetwyndD. G., WhitehouseD. J.. Optimal kinematic design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index [J]. IEEE Transactions on Robotics and Automation, 2004, 20(3): 538-542

[9] CLAVEL R. Device for the movement and positioning of an element in space: US 4976582 [P]. 1990-12-11.

[10] PierrotF., DauchezP., FournierA.. HEXA: A fast six-DoF fully-parallel robot [C]. Proceedings of 5th International Conference on Advanced Robotics (ICAR), 1991, Pisa, Italy, IEEE Press: 1158-1163

[11] MillerK.. Synthesis of a manipulator of the new UWA robot [C]. Proceedings of Australian Conference on Robotics and Automation, 1999, Brisbane, Australia, QLD Press: 228-233

[12] BehzadipourS., KhajepourA., DekkerR., ChanE.. DeltaBot: A new cable-based Ultra high speed robot [J]. ASME Dynamics Systems and Control Division (Publication) DSC, 2003, 72(1): 533-537

[13] BehzadipourS., KhajepourA.. Stiffness of cable-based parallel manipulators with application to stability analysis [J]. ASME Journal of Mechanical Design, 2006, 128(1): 303-310

[14] HUANG Tian, LI Zhan-xian, LI Meng. 2-DOF translational parallel robot with rotational joints: CHN, CN1355087A [P]. 2002-06-26. (in Chinese)

[15] HuangT., LiZ.-x., LiMeng.. Conceptual design and dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations [J]. ASME Journal of Mechanical Design, 2004, 126(3): 449-455

[16] HUANG Tian, LIU Hai-tao, Zhao Xue-man. Spatial three translational parallel mechanism with parallelogram link: CHN, CN1785607 [P]. 2006-06-14. (in Chinese)

[17] O’BrienT. W.. General soultion of suspended cable problem [J]. ASCE Journal of Structural Division, 1967, 93(1): 1-26

[18] IrvineH. M.. Static of suspended cable [J]. ASCE Journal of Structural Division, 1975, 90(3): 89-123

[19] RaidK.. Some modeling aspects in the nonlinear finite element analysis of cable supported bridges [J]. Computers and Structures, 1999, 71(4): 397-412

[20] RussellJ. C., LardnerT. J.. Statics experiments on an elastic catenary [J]. ASCE Journal of Structural Division, 1997, 123(12): 1322-1324