Analysis and Type Synthesis of Parallel Mechanisms without Parasitic Motion based on Spatial Geometry

doi:10.3901/JME.2021.01.077

Abstract

Abstract: Parasitic motion widely exists in general 1T2R (one translation and two rotations) parallel mechanism, which has a negative influence on motion accuracy and performances of mechanism. To obtain a series of 1T2R parallel mechanisms without parasitic motion, the analysis and type synthesis of parallel mechanisms are conducted based on spatial geometry and screw theory. The condition of rotational axes of parallel mechanism without parasitic motion is analyzed based on spatial geometry theory, then the spatial position relationship between the plane of moving platform and constraint wrenches is explored with screw theory. Branch chains with at least 1T2R degrees of freedom are divided into four types, and positions of constraint wrenches and rotational axes which cause parasitic motions directly are discussed with different [R]-branch chain layouts. The synthesis criteria and geometrical conditions of 1T2R parallel mechanism without parasitic motion are deduced, and 105 kinds of mechanism without parasitic motion are obtained through type synthesis. The kinematics of a new 2RPU-RPRU parallel mechanism without parasitic motion is analyzed to verify the correctness of the method.

Key words: parasitic motion, 1T2R parallel mechanism, screw theory, geometrical conditions

CLC Number:

TH112

CHEN Miao, ZHANG Qing, CHEN Wentao, QIN Xianrong, SUN Yuantao. Analysis and Type Synthesis of Parallel Mechanisms without Parasitic Motion based on Spatial Geometry[J]. Journal of Mechanical Engineering, 2021, 57(1): 77-85.

References

[1] CHAI X X,ZHANG N B,HE L Y,et al. Kinematic sensitivity analysis and dimensional synthesis of a redundantly actuated parallel robot for friction stir welding[J]. Chinese Journal of Mechanical Engineering,2020,33:1. https://doi.org/10.1186/s10033-019-0427-6.
[2] RAMIREZ J,WOLLNACK J. Flexible automated assembly systems for large CFRP-structures[J]. Procedia Technology,2014,15:447-455.
[3] WANG C,FANG Y,GUO S. Multi-objective optimization of a parallel ankle rehabilitation robot using modified differential evolution algorithm[J]. Chinese Journal of Mechanical Engineering,2015,28(4):702-715.
[4] 李剑锋,张凯,张雷雨,等. 并联踝康复机器人的设计与运动性能评价[J]. 机械工程学报,2019,55(9):29-39. LI Jianfeng,ZHANG Kai,ZHANG Leiyu,et al. Design and kinematic performance evaluation of parallel ankle rehabilitation robot[J]. Journal of Mechanical Engineering,2019,55(9):29-39.
[5] MATS I,ANDERS E,SAEID N. Analysis of the inverse kinematics problem for 3-DOF axis-symmetric parallel manipulators with parasitic motion[C]//2014 IEEE International Conference on Robotics and Automation,Piscataway,NJ:IEEE,2014:5736-5743.
[6] 张扬. 无伴随运动对称两转一移并联机构的研究[D].秦皇岛:燕山大学,2016. ZHANG Yang. Study on symmetrical 2R1T parallel mechanism without parasitic motion[D]. Qinhuangdao:Yanshan University,2016.
[7] XU Y D,ZHOU S S,YAO J T,et al. Rotational axes analysis of the 2-RPU/SPR 2R1T parallel mechanism[J]. Mechanisms & Machine Science,2014,22:113-121.
[8] CARRETERO J A,PODHORODESKI R P,NAHON M A,et al. Kinematic analysis and optimization of a new three degree-of-freedom spatial parallel manipulator[J]. Journal of Mechanical Design,2000,122(1):17-24.
[9] ZHAO H,BI S,YU J. A novel compliant linear-motion mechanism based on parasitic motion compensation[J]. Mechanism and Machine Theory,2012,50:15-28.
[10] JHA R,CHABLAT D,BARON L. Influence of design parameters on the singularities and workspace of a 3-RPS parallel robot[J]. Transactions-Canadian Society for Mechanical Engineering,2018,42(1):30-37.
[11] FANG H,XIN B,ZHANG X. Workspace-constrained optimal design of three-degrees-of-freedom parallel manipulators with minimum parasitic motions by integrating interval analysis,region mapping and differential evolution[J]. Engineering Optimization,2015,47(3):407-428.
[12] LI Q,CHEN Z,CHEN Q,et al. Parasitic motion comparison of 3-PRS parallel mechanism with different limb arrangements[J]. Robotics and Computer-Integrated Manufacturing,2011,27(2):389-396.
[13] LI Q,JACQUES M H. 1T2R parallel mechanisms without parasitic motion[J]. IEEE Transactions on Robotics,2010,26(3):401-410.
[14] 陈子明,张扬,黄坤,等. 一种无伴随运动的对称两转一移并联机构[J]. 机械工程学报,2016,52(3):9-17. CHEN Ziming,ZHANG Yang,HUANG Kun,et al. Symmetrical 2R1T parallel mechanism without parasitic motion[J]. Journal of Mechanical Engineering,2016,52(3):9-17.
[15] KANG L,YI B J. Design of two foldable mechanisms without parasitic motion[J]. IEEE Robotics and Automation Letters,2016,1(2):930-937.
[16] 张东胜,姚建涛,许允斗,等. 刚体两次转动姿态描述方法的内在联系[J]. 机械工程学报,2015,51(13):86-94. ZHANG Dongsheng,YAO Jiantao,XU Yundou,et al. The internal relations of the pose description methods of the rigid body after two successive rotations[J]. Journal of Mechanical Engineering,2015,51(13):86-94.
[17] 黄真,赵永生,赵铁石. 高等空间机构学[M]. 北京:高等教育出版社,2014. HUANG Zheng,ZHAO Yongsheng,ZHAO Tieshi. Advanced spatial mechanism[M]. Beijing:Higher Education Press,2014.
[18] 柴馨雪,项济南,李秦川. 2-UPR-RPU并联机构奇异分析[J]. 机械工程学报,2015,51(13):150-157. CHAI Xinxue,XIANG Jinan,LI Qinchuan. Singularity analysis of a 2-UPR-RPU parallel mechanism[J]. Journal of Mechanical Engineering,2015,51(13):150-157.