Analysis of the kinematic characteristics of a high-speed parallel robot with Schönflies motion: Mobility, kinematics, and singularity

Abstract

This study introduces a high-speed parallel robot with Schönflies motion. This robot exhibits a promising prospect in realizing high-speed pick-and-place manipulation for packaging production lines. The robot has four identical limbs and a single platform. Its compact structure and single-platform concept provides this robot with good dynamic response potential. A line graph method based on Grassmann line geometry is used to investigate the mobility characteristics of the proposed robot. A generalized Blanding rule is also introduced into this procedure to realize mutual conversion between the line graphs for motions and constraints. Subsequently, the inverse kinematics is derived, and the singularity issue of the robot is investigated using both qualitative and quantitative approaches. Input and output transmission singularity indices are defined based on the reciprocal product in screw theory and the virtual coefficient by considering motion/force transmission performance. Thereafter, the singular loci of the proposed robot with specific geometric parameters are derived. The mobility analysis, inverse kinematics modeling, and singularity analysis conducted in this study are helpful in developing the robot.

Keywords

parallel robot / mobility / inverse kinematics / singularity / transmission performance

References

[1] Yang T, Sun D. A general degree of freedom formula for parallel mechanisms and multiloop spatial mechanisms. Journal of Mechanisms and Robotics, 2012, 4(1): 011001 doi:10.1115/1.4005526

[2] Rahman T, Krouglicof N, Lye L. Kinematic synthesis of nonspherical orientation manipulators: Maximization of dexterous regular workspace by multiple response optimization. Journal of Mechanical Design, 2012, 134(7): 071009 doi:10.1115/1.4006830

[3] Xu Q, Li Y. An investigation on mobility and stiffness of a 3-DOF translational parallel manipulator via screw theory. Robotics and Computer-Integrated Manufacturing, 2008, 24(3): 402–414

[4] Liu S, Huang T, Mei J, . Optimal design of a 4-DOF SCARA type parallel robot using dynamic performance indices and angular constraints. Journal of Mechanisms and Robotics, 2012, 4(3): 031005

[5] Huang Z, Cao Y. Property identification of the singularity loci of a class of Gough-Stewart manipulators. The International Journal of Robotics Research, 2005, 24(8): 675–685

[6] Pierrot F, Reynaud C, Fournier A. Delta: A simple and efficient parallel robot. Robotica, 1990, 8(02): 105–109

[7] Adept Quattro S650H.

[8] Altuzarra O, Hernandez A, Salgado O, . Multiobjective optimum design of a symmetric parallel Schönflies-motion generator. Journal of Mechanical Design, 2009, 131(3): 031002

[9] Pierrot F, Company O. H4: A new family of 4-DOF parallel robots. In: Proceedings of 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. New Jersey: IEEE, 1999, 508–513

[10] Nabat V. de la ORodriguez M, Company O, . Par4: Very high speed parallel robot for pick-and-place. In: Proceedings of 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems. New Jersey: IEEE, 2005, 553–558

[11] An Articulated Traveling Plate.

[12] Ruggiu M, Kong X. Mobility and kinematic analysis of a parallel mechanism with both PPR and planar operation modes. Mechanism and Machine Theory, 2012, 55: 77–90

[13] Bohigas O, Manubens M, Ros L. Singularities of non-redundant manipulators: A short account and a method for their computation in the planar case. Mechanism and Machine Theory, 2013, 68: 1–17

[14] Amine S, Tale Masouleh M, Caro S, . Singularity conditions of 3T1R parallel manipulators with identical limb structures. Journal of Mechanisms and Robotics, 2012, 4(1): 011011

[15] Zhao Y. Singularity, isotropy, and velocity transmission evaluation of a three translational degrees-of-freedom parallel robot. Robotica, 2013, 31(02): 193–202

[16] Yu J J, Dong X, Pei X, . Mobility and singularity analysis of a class of two degrees of freedom rotational parallel mechanisms using a visual graphic approach. Journal of Mechanisms and Robotics, 2012, 4(4): 041006

[17] White N L. Grassmann-cayley algebra and robotics. Journal of Intelligent & Robotic Systems, 1994, 11(1-2): 91–107

[18] Merlet J P. Singular configurations of parallel manipulators and Grassmann geometry. The International Journal of Robotics Research, 1989, 8(5): 45–56

[19] Monsarrat B, Gosselin C M. Singularity analysis of a three-leg six-degree-of-freedom parallel platform mechanism based on Grassmann line geometry. The International Journal of Robotics Research, 2001, 20(4): 312–328

[20] Kanaan D, Wenger P, Caro S, . Singularity analysis of lower mobility parallel manipulators using Grassmann-Cayley algebra. IEEE Transactions on Robotics, 2009, 25(5): 995–1004

[21] Ben-Horin P, Shoham M. Application of Grassmann-Cayley algebra to geometrical interpretation of parallel robot singularities. The International Journal of Robotics Research, 2009, 28(1): 127–141

[22] Bonev I A, Zlatanov D, Gosselin C M. Singularity analysis of 3-DOF planar parallel mechanisms via screw theory. Journal of Mechanical Design, 2003, 125(3): 573–581

[23] Kong X W, Gosselin C M. Type synthesis of 3T1R 4-DOF parallel manipulators based on screw theory. IEEE Transactions on Robotics and Automation, 2004, 20(2): 181–190

[24] Yu J, Li S, Su H, . Screw theory based methodology for the deterministic type synthesis of flexure mechanisms. Journal of Mechanisms and Robotics, 2011, 3(3): 031008

[25] Liu X J, Wu C, Wang J S. A new approach for singularity analysis and closeness measurement to singularities of parallel manipulators. Journal of Mechanisms and Robotics, 2012, 4(4): 041001

[26] Xie F G, Liu X J, You Z, . Type synthesis of 2T1R-type parallel kinematic mechanisms and the application in manufacturing. Robotics and Computer-Integrated Manufacturing, 2014, 30(1): 1–10

[27] Blanding D L. Exact Constraint: Machine Design Using Kinematic Processing. New York: ASME Press, 1999

[28] Amine S, Kanaan D, Caro S, . Constraint and singularity analysis of lower-mobility parallel manipulators with parallelogram joints. In: Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. New York: ASME Press, 2010, 1317–1326

[29] Xie F G, Liu X J. Design and development of a high-speed and high-rotation robot with four identical arms and a single platform. Journal of Mechanisms and Robotics, 2015, 7(4): 041015

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