Sensitivity Analysis of a Planar Parallel Manipulator with Kinematic Redundancy

doi:10.3901/JME.2020.23.045

Abstract

Abstract: The error sensitivity of a planar kinematically redundant parallel manipulator which has a closed-loop chain is analysed. The inverse kinematics and forward kinematics of the manipulator are analysed. Based on the matrix method, the error model of the manipulator is established. The error model is verified by combining inverse kinematics with forward kinematics. Based on the error model, the index of error sensitivity of the manipulator is obtained, and the contour map of each index in the workspace is drawn. Based on the error sensitivity index, the low error sensitive workspace is defined and the distribution of the low error sensitive workspace in the workspace is drawn. The error sensitivity is compared with that of the planar 3-RRR parallel manipulator. The results show that the low error sensitive workspace of the planar kinematically redundant parallel manipulator is large, and the low error sensitive workspace can be continuously expanded by adjusting the kinematically redundant chain, so that the manipulator can maintain low error sensitivity in a large range of the workspace.

Key words: planar parallel manipulator, kinematic redundancy, error modeling, error sensitivity

CLC Number:

TH112

LI Guanming, QU Haibo, GUO Sheng. Sensitivity Analysis of a Planar Parallel Manipulator with Kinematic Redundancy[J]. Journal of Mechanical Engineering, 2020, 56(23): 45-57.

References

[1] 张英,魏世民,李端玲,等.平面并联机构正运动学分析的几何建模和免消元计算[J].机械工程学报,2018,54(19):27-33. ZHANG Ying,WEI Shimin,LI Duanling,et al. Geometric modeling and free-elimination computing method for the forward kinematics analysis of planar parallel manipulators[J]. Journal of Mechanical Engineering,2018,54(19):27-33.
[2] LI Q,XIANG J,CHAI X,et al. Singularity analysis of a 3-RPS parallel manipulator using geometric algebra[J]. Chinese Journal of Mechanical Engineering,2015,28(6):1204-1212.
[3] GOSSELIN C,SCHREIBER L. Redundancy in parallel mechanisms:A review[J]. Applied Mechanics Reviews,2018,70(1):10802.
[4] QU H,GUO S,ZHANG Y. A novel relative degree-of-freedom criterion for a class of parallel manipulators with kinematic redundancy and its applications[J]. Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2016,231(22):4227-4240.
[5] ZHAN Z,ZHANG X,ZHANG H,et al. Unified motion reliability analysis and comparison study of planar parallel manipulators with interval joint clearance variables[J]. Mechanism and Machine Theory,2019,138:58-75.
[6] DING J,LYU S,DA T,et al. Error space estimation of three degrees of freedom planar parallel mechanisms[J]. Journal of Mechanisms and Robotics,2019,11(3):1-16.
[7] 姚蕊,李庆伟,孙京海,等. FAST望远镜馈源舱精度分析研究[J].机械工程学报,2017,53(17):36-42. YAO Rui,LI Qingwei,SUN Jinghai,et al. Accuracy analysis on focus cabin of FAST[J]. Journal of Mechanical Engineering,2017,53(17):36-42.
[8] 王娜,张涛,王秋红. 3UPS-PU并联机构的运动学误差建模与验证[J].机械传动,2020,44(7):113-118. WANG Na,ZHANG Tao,WANG Qiuhong. Modeling and verification of kinematics error of 3UPS-PU parallel mechanism[J]. Journal of Mechanical Transmission,2020,44(7):113-118.
[9] CHEN Y,XIE F,LIU X,et al. Error modeling and sensitivity analysis of a parallel robot with SCARA (selective compliance assembly robot arm) Motions[J]. Chinese Journal of Mechanical Engineering,2014,27(04):693-702.
[10] 谢福贵,刘辛军,陈禹臻.一种新型虚拟中心并联机构的误差灵敏度分析[J].机械工程学报,2013,49(17):85-91. XIE Fugui,LIU Xinjun,CHEN Yuzhen. Error sensitivity analysis of novel virtual center mechanism with parallel kinematics[J]. Journal of Mechanical Engineering,2013,49(17):85-91.
[11] 赵延治,宋晓鑫,杨建涛,等.基于虚设运动副的并联机器人静态误差建模与标定[J].中国机械工程,2017,28(18):2189-2197. ZHAO Yanzhi,SONG Xiaoxin,YANG Jiantao,et al. Static error modelling and calibration for parallel robots based on virtual joint pairs[J]. China Mechanical Engineering,2017,28(18):2189-2197.
[12] CHEBBI A H,CHOUAIBI Y,AFFI Z,et al. Sensitivity analysis and prediction of the orientation error of a three translational parallel manipulator[J]. Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2018,232(1):140-161.
[13] 丁高鹏,李开明.三平动冗余驱动并联机床误差分析及标定方法的研究[J].机床与液压,2018,46(21):24-28. DING Gaopeng,LI Kaiming. Study on error analysis and calibration method for parallel machine tool with three translational DOF redundant drive[J]. Machine Tool& Hydraulics,2018,46(21):24-28.
[14] 沈丹峰,叶国铭,王贯超,等.二自由度平面冗余并联机构杆件长度的误差分析[J].机械设计,2017,34(5):65-70. SHEN Danfeng,YE Guoming,WANG Guanchao,et al. Error analysis of rods length on 2-DOF planar redundant parallel mechanism[J]. Journal of Machine Design,2017,34(5):65-70.
[15] 石则昌,刘深厚.机构精确度[M].北京:高等教育出版社,1995. SHI Zechang,LIU Shenhou. Mechanism accuracy[M]. Beijing:Higher Education Press,1995.
[16] QU H,GUO S. Kinematics analysis of a novel planar parallel manipulator with kinematic redundancy[J]. Journal of Mechanical Science and Technology,2017,31(4):1927-1935.
[17] ZHANG D,XU Y,YAO J,et al. Analysis and optimization of a spatial parallel mechanism for a new 5-DOF hybrid serial-parallel manipulator[J]. Chinese Journal of Mechanical Engineering,2018,31(3):60-68.
[18] BINAUD N,CARO S,WENGER P. Sensitivity comparison of planar parallel manipulators[J]. Mechanism and Machine Theory,2010,45:1477-1490.
[19] 李雨桐,王玉新.并联机构奇异构型运动稳定性与其动力学参数[J].机械工程学报,2017,53(13):75-81. Li Yutong,WANG Yuxin. Motion stability at singular configurations related to kinematic parameters of a parallel manipulator[J]. Journal of Mechanical Engineering,2017,53(13):75-81.
[20] ZHAN Z,ZHANG X,JIAN Z,et al. Error modelling and motion reliability analysis of a planar parallel manipulator with multiple uncertainties[J]. Mechanism and Machine Theory,2018,124:55-72.
[21] WU G,BAI S,KEPLER J A,et al. Error modeling and experimental validation of a planar 3-PPR parallel manipulator with joint clearances[J]. Journal of Mechanisms and Robotics,2012,4(4):1.
[22] CARO S,BINAUD N,WENGER P. Sensitivity analysis of 3-RPR planar parallel Manipulators[J]. Journal of Mechanical Design,2009,131(23):121005.
[23] 邹琦,曲海波,郭盛.一种三自由度可重构并联机构优化设计及性能分析[J].中国机械工程,2018,29(10):1172-1178. ZOU Qi,QU Haibo,GUO Sheng. Optimal design and performance analysis of a 3-DOF reconfigurable parallel mechanism[J]. China Mechanical Engineering,2018,29(10):1172-1178.