A Novel Not-fully Symmetrical 3T1R PM with Low Coupling-degrees and Its Kinematics

Abstract

Abstract: By using topological structure synthesis theory and method based on POC equation，a novel 4-DOF 3T1R not-fully-symmetrical PM 2-RPaRSS with low coupling degrees was presented.Firstly，the coupling degree of the PM was calculated(κ=1).The modeling method and the numerical solutions for forward position kinematics of the PM were established based on ordered single-open-chain (SOC) units. Then the correctness of the forward solutions was verified by the inverse solutions and a numerical example. Furthermore，the total shape and size as well as Z-section shape of the workspace of the PM were analyzed. Further，the singularity of the PM was also analyzed，and three kinds of singular conditions were obtained. Lastly，the 3D model for the prototype of the manipulator was designed. This work shows that 2-RPaRSS manipulator is simple in structure and the workspace and the rotation ability of moving platform of the PM is larger than that of H4, I4R and Cross-Ⅳ.

Key words: not-fully-symmetrical parallel manipulator(PM)；position and orientation characteristic(POC) equation；coupling degree；three-translation and one rotation(3T1R), forward position solution

摘要： 根据基于方位特征（POC）方程的并联机构拓扑设计理论和方法，分析了一种可实现三平移一转动输出运动的新型低耦合度的非全对称四自由度并联机械手2-RPaRSS，并完成其运动学建模与分析。首先，分析计算出该机构的耦合度(κ=1)，给出了基于序单开链（SOC）的机构位置正解的建模方法及其数值解；其次，通过导出机构位置反解及算例，验证了正反解求解的正确性；再次，分析了该机构位置工作空间的形状大小及工作空间Z向各截面形状；然后，对机构的奇异位形进行了分析，得到其发生三类奇异的条件；最后，设计了该机械手样机的三维CAD模型。研究结果表明，2-RPaRSS机械手比H4、I4R、Cross-Ⅳ结构简单，且具有更大的工作空间和更好的动平台转动能力。

关键词: 非全对称并联机构, 方位特征方程, 耦合度, 三平移一转动, 正向位置

CLC Number:

TP273

SHEN Huiping;SHAO Guowei;DENG Jiaming;MENG Qingmei;YANG Tingli. A Novel Not-fully Symmetrical 3T1R PM with Low Coupling-degrees and Its Kinematics[J]. China Mechanical Engineering.

沈惠平;邵国为;邓嘉鸣;孟庆梅;杨廷力. 一种新型低耦合度非全对称三平移一转动并联机械手及其运动学分析[J]. 中国机械工程.

References

[1]BOURI M, CLAVEL R. The Linear Delta: Developments and Applications[C]// Robotics（ISR），2010 41st International Symposium on and 2010 6th German Conference on Robotics. Munich,2010:1-8.
[2]REY L, CLAVEL R. The Delta Parallel Robot[M]// London：Parallel Kinematic Machines,1999:401-417.
[3]PIERROT F, COMPANY O. H4: a New Family of 4-DOF Parallel Robots[C]// IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Altlanta,1999:508-513.
[4]KRUT S, COMPANY O, BENOIT M, et al. I4: a New Parallel Mechanism for Scara Motions
[C]// IEEE International Conference on Robotics & Automation. Taipei,2008:1875-1880.
[5]KRUT S, NABAT V, COMPANY O, et al. A High-speed Parallel Robot for Scara Motions [C]// IEEE International Conference on Robotics & Automation. New Orleans, LA,2004:4109-4115.
[6]NABAT V, RODRIGUEZ M D L O, COMPANY O, et al. Par4: Very High Speed Parallel Robot for Pick-and-place[C]// IEEE/RSJ International Conference on Intelligent Robots and Systems. Edmonton,2005:553-558.
[7]LDINGHAUSEN M V, MIURA M, WRZLER N. Heli4: a Parallel Robot for Scara Motions with a Very Compact Traveling Plate and a Symmetrical Design[C]// Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on. Beijing,2006:1656-1661.
[8]李玉航，梅江平，刘松涛,等. 一种新型4自由度高速并联机械手动力尺度综合[J]. 机械工程学报，2014,50(19):32-40.
LI Yuhang, MEI Jiangping, LIU Songtao, et al. Dynamic Dimensional Synthesis of a 4-DOF High-speed Parallel Manipulator[J]. Journal of Mechanical Engineering,2014,50(19):32-40.
[9]KONG Xianwen，GOSSELIN C M. Type Synthesis of 3T1R 4-DOF Parallel Manipulators Based on Screw Theory[J]. IEEE Transactions on, Robotics and Automation，2005,22(10)：535-547.
[10]罗玉峰，刘卓，石志新,等. 三平移一转动并联机构型综合及分类[J]. 机械设计与研究，2010，26(5):40-43.
LUO Yufeng, Liu Zhuo, Shi Zhixin, et al. Structural Synthesis and Classification of 3-translational and 1-rotation Parallel Manipulator[J].Journal of Machine Design and Research,2010,26(5):40-43.
[11]金琼，杨廷力，刘安心,等. 基于单开链单元的三平移一转动并联机器人机构型综合及分类[J]. 中国机械工程，2001,12(9):1038-1043.
JIN Qiong, YANG Tingli, LIU Anxin, et al. Structural Synthesis and Classification of the 4-DOF(3T-1R) Parallel Robot Mechanisms Based on the Units of Single-opened-chain[J].China Mechanical Engineering，2001,12(9):1038-1043.
[12]XIE Fugui，LIU Xinjun. Design and Development of a High-speed and High-rotation Robot with Four Identical Arms and a Single Platform[J]. Journal of Mechanisms & Robotics，2015，7(4):041015.1-12.
[13]LI Zhibin，LOU Yunjiang，ZHANG Yongsheng，et al.Type Synthesis，Kinematic Analysis，and Optimal Design of a Novel Class of Schnflies-motion Parallel Manipulators[J]. IEEE Transactions on Automation Science & Engineering，2013,10(3):674-686.
[14]GOGU G. Structural Synthesis of Fully-isotropic Parallel Robots with Schnflies Motions Via Theory of Linear Transformations and Evolutionary Morphology[J]. European Journal of Mechanics-A/Solids，2007，26(2):242-269.
[15]SALGADO O, ALTUZARRA O, PETUYA V, et al. Synthesis and Design of a Novel 3T1R Fully-parallel Manipulator[J]. Journal of Mechanical Design,2008,130(4):137-139.
[16]ANCUTA A, COMPANY O, PIERROT F. Design of Lambda-quadriglide: a New 4-DOF Parallel Kinematics Mechanism for Schnflies Motion[C]// ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Montreal, Quebec,2010:1131-1140.
[17]RICHARD P L,GOSSELIN C M, KONG Xianwen. Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator [J]. Journal of Mechanical Design,2006，129(6):611-616.
[18]王进戈,范丽华,徐礼钜. 3-RPS并联平台机构的位置正解与奇异构形分析的数值-符号解[J]. 机械设计,2005,22(5):15-19.
WANG Jinge, FAN Lihua, XU Liju.Positional Forward Solution and Numeric-symbolic Solution of Singular Configuration Analysis for 3-RPS Parallel Platform Mechanism[J].Journal of Machine Design,2005,22(5):15-19.
[19]杨廷力，刘安心，罗玉峰，等. 机器人机构拓扑结构设计[M]. 北京：科学出版社，2012.
YANG Tingli，LIU Anxin， LUO Yufeng，et al. Theory and Application of Robot Mechanism Topology[M]. Beijing: Sicence Press,2012.
[20]沈惠平，杨廷力，朱小蓉，等，一种三平移一转动并联机器人：中国，201510564382.5[P].2015-09-08.
SHEN Huiping，YANG Tingli，ZHU Xiaorong，et al.A Parallel Mechanism with Three Translations and One Rotation：China，201510564382.5[P].2015-09-08.
[21]沈惠平，杨廷力，李云峰，等，一种三平移一转动并联机器人抓放器：中国，201510648948.2[P].2015-10-09.
SHEN Huiping，YANG Tingli，LI Yunfeng，et al. A Parallel Robot Picker with Three Translations and One Rotation：China，201510648948.2[P].2015-10-09.
[22]沈惠平，杨廷力，邵国伟，等，一种三平移一转动并联机构机械手：中国，201510640394.X[P].2015-10-09.
SHEN Huiping，YANG Tingli，SHAO Guowei，et al.A Parallel Robot Hand with Three Translations and One Rotation：China，201510640394.X[P].2015-10-09.
[23]YANG Tingli，LIU Anxin，SHEN Huiping，et al. Topological Structure Synthesis of 3T1R Parallel Mechanism Based on POC Equations[C]//Lecture Notes in Computer Science,Proceedings of 9th International Conference on Intelligent Robotics and Applications. Hachioji, 2016:147-161.
[24]沈惠平，尹洪波，王振，等.基于拓扑结构分析的求解6-SPS并联机构位置正解的研究[J].机械工程学报,2013,49(21)：70-80.
SHEN Huiping, YIN Hongbo, WANG Zhen, et al. Research on Forward Position Solutions for 6-SPS Parallel Mechanisms Based on Topology Structure Analysis[J]. Journal of Mechanical Engineering,2013,49(21):70-80.

[25]于晖，孙立宁，刘品宽，等.新型6-HTRT 并联机器人工作空间和参数研究[J].机器人,2002,24(4):293-298.
YU Hui, SUN Lining, LIU Pinkuan, et al. Study on the Workspace and Parameter of Novel 6-HTRT Parallel Robot[J]. Robot,2002,24(4):293-298.

[26]刘平松. I4R型并联机器人全域性能及其优化研究[D]. 南京：南京理工大学，2013.
LIU Pingsong. Study on Global Performance and Optimization of I4R Parallel Robot[D].Nanjing:
Nanjing University of Science and Technology,2013.

[27]GOSSELIN C, ANGELES J. Singularity Analysis of Closed-loop Kinematic Chains[J]. IEEE Transactions on Robotics & Automation,1990,6(3):281-290.