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

doi:10.1007/s11465-016-0389-7

Front. Mech. Eng.

2016, Vol. 11

Issue (2) : 135-143 https://doi.org/10.1007/s11465-016-0389-7

RESEARCH ARTICLE

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

Fugui XIE(

),Xin-Jun LIU(

)

The State Key Laboratory of Tribology & Institute of Manufacturing Engineering, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China; Beijing Key Laboratory of Precision/Ultra-precision Manufacturing Equipment and Control, Tsinghua University, Beijing 100084, China

Download: PDF(762 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

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

Corresponding Author(s): Fugui XIE,Xin-Jun LIU

Online First Date: 25 May 2016 Issue Date: 29 June 2016

Cite this article:

Fugui XIE,Xin-Jun LIU. Analysis of the kinematic characteristics of a high-speed parallel robot with Schönflies motion: Mobility, kinematics, and singularity[J]. Front. Mech. Eng., 2016, 11(2): 135-143.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-016-0389-7
https://academic.hep.com.cn/fme/EN/Y2016/V11/I2/135

Fig.1 CAD model of the spatial parallel robot: (a) Overview and (b) bottom view

Fig.2 Kinematic scheme of the parallel robot presented in Fig. 1

Tab.1 Basic elements and their meanings

Fig.3 Relationship among line vectors

Fig.4 Relationship between line vector and couple

Fig.5 Relationship among couples

Fig.6 Motion line graph in the third chain and the corresponding constraint line graph

Fig.7 Constraint line graph of the mobile platform

Fig.8 Motion line graph of the mobile platform

Fig.9 Input transmission singularity: (a) RR(Pa)RR kinematic chain and (b) PRR kinematic chain

Fig.10 Sample case for output transmission singularity

Fig.11 Distribution of the output transmission singularity indices

Fig.12 Singular loci in the plane z = −1.8 and z = −2.4 when φ ∈ ( − 45 ° , 45 ° )

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 https://doi.org/10.1016/j.rcim.2007.02.022
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 https://doi.org/10.1115/1.4006743
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 https://doi.org/10.1177/0278364905054655
6	Pierrot F, Reynaud C, Fournier A. Delta: A simple and efficient parallel robot. Robotica, 1990, 8(02): 105–109 https://doi.org/10.1017/S0263574700007669
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 https://doi.org/10.1115/1.3066659
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 https://doi.org/10.1109/AIM.1999.803222
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 https://doi.org/10.1109/IROS.2005.1545143
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 https://doi.org/10.1016/j.mechmachtheory.2012.04.004
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 https://doi.org/10.1016/j.mechmachtheory.2013.03.001
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 https://doi.org/10.1115/1.4005336
15	Zhao Y. Singularity, isotropy, and velocity transmission evaluation of a three translational degrees-of-freedom parallel robot. Robotica, 2013, 31(02): 193–202 https://doi.org/10.1017/S0263574712000197
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 https://doi.org/10.1115/1.4007410
17	White N L. Grassmann-cayley algebra and robotics. Journal of Intelligent & Robotic Systems, 1994, 11(1-2): 91–107 https://doi.org/10.1007/BF01258296
18	Merlet J P. Singular configurations of parallel manipulators and Grassmann geometry. The International Journal of Robotics Research, 1989, 8(5): 45–56 https://doi.org/10.1177/027836498900800504
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 https://doi.org/10.1177/02783640122067426
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 https://doi.org/10.1109/TRO.2009.2017132
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 https://doi.org/10.1177/0278364908095918
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 https://doi.org/10.1115/1.1582878
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 https://doi.org/10.1109/TRA.2003.820853
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 https://doi.org/10.1115/1.4004123
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 https://doi.org/10.1115/1.4007004
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 https://doi.org/10.1016/j.rcim.2013.07.002
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

[1]	Qizhi MENG, Fugui XIE, Xin-Jun LIU. Conceptual design and kinematic analysis of a novel parallel robot for high-speed pick-and-place operations[J]. Front. Mech. Eng., 2018, 13(2): 211-224.
[2]	Gang HAN, Fugui XIE, Xin-Jun LIU. Evaluation of the power consumption of a high-speed parallel robot[J]. Front. Mech. Eng., 2018, 13(2): 167-178.
[3]	Guizhong XIE,Dehai ZHANG,Jianming ZHANG,Fannian MENG,Wenliao DU,Xiaoyu WEN. Implementation of sinh method in integration space for boundary integrals with near singularity in potential problems[J]. Front. Mech. Eng., 2016, 11(4): 412-422.
[4]	Girish Sudhir MODAK,Manmohan Manikrao BHOOMKAR. Innovative stair climber using associated wheels[J]. Front. Mech. Eng., 2016, 11(3): 299-310.
[5]	Ruiming LI,Yan-An YAO. Eversible duoprism mechanism[J]. Front. Mech. Eng., 2016, 11(2): 159-169.
[6]	Saeed ABDOLSHAH,Erfan SHOJAEI BARJUEI. Linear quadratic optimal controller for cable-driven parallel robots[J]. Front. Mech. Eng., 2015, 10(4): 344-351.
[7]	S. SHANKAR GANESH,A.B. KOTESWARA RAO. Stiffness of a 3-degree of freedom translational parallel kinematic machine[J]. Front. Mech. Eng., 2014, 9(3): 233-241.
[8]	Abdelhak KHECHAI,Abdelouahab TATI,Abdelhamid GUETTALA. Finite element analysis of stress concentrations and failure criteria in composite plates with circular holes[J]. Front. Mech. Eng., 2014, 9(3): 281-294.
[9]	Mahdi BAMDAD. Analytical dynamic solution of a flexible cable-suspended manipulator[J]. Front Mech Eng, 2013, 8(4): 350-359.
[10]	Juan Carlos JáUREGUI, Eusebio E. HERNáNDEZ, Marco CECCARELLI, Carlos LóPEZ-CAJúN, Alejandro GARCíA. Kinematic calibration of precise 6-DOF stewart platform-type positioning systems for radio telescope applications[J]. Front Mech Eng, 2013, 8(3): 252-260.
[11]	Alin STOICA, Doina PISLA, Szilaghyi ANDRAS, Bogdan GHERMAN, Bela-Zoltan GYURKA, Nicolae PLITEA. Kinematic, workspace and singularity analysis of a new parallel robot used in minimally invasive surgery[J]. Front Mech Eng, 2013, 8(1): 70-79.
[12]	Josef SCHADLBAUER, Manfred L. HUSTY, Stéphane CARO, Philippe WENGERY. Self-motions of 3-RPS manipulators[J]. Front Mech Eng, 2013, 8(1): 62-69.
[13]	Jens KOTLARSKI, Bodo HEIMANN, Tobias ORTMAIER. Influence of kinematic redundancy on the singularity-free workspace of parallel kinematic machines[J]. Front. Mech. Eng., 2012, 7(2): 120-134.
[14]	Po-Chih LEE, Jyh-Jone LEE. Singularity and workspace analysis of three isoconstrained parallel manipulators with schoenflies motion[J]. Front Mech Eng, 2012, 7(2): 163-187.
[15]	Fengfeng XI, Yuwen LI, Hongbo WANG. Module-based method for design and analysis of reconfigurable parallel robots[J]. Front Mech Eng, 2011, 6(2): 151-159.

Viewed

Full text

Abstract

Cited

Shared

Discussed