一种无汇交轴线对称三转动并联机构的运动分析

摘要/Abstract

摘要： 传统的三自由度转动并联机构（又称球面并联机构）一般都有一个转动中心，且这个中心点往往是分支间多个运动副轴线的汇交点，这种严格的几何条件给机构的加工制造带来很大的难度，制约了这类机构的应用。针对此，提出了一种无汇交轴线的对称三转动并联机构，其三个分支对称布置，分支内及分支间均无汇交轴线。对机构进行了位置反解，得到了机构四种对称的装配构型；从分支运动奇异、平台约束奇异和驱动奇异三个方面对机构进行了奇异分析；最后给定了一组尺寸参数，采用数值搜索的方法得到了机构的姿态工作空间。通过结果可以看出,该机构可以实现三维转动，具有较大的姿态工作空间，而且制造装配相对容易，具有很好的应用前景。

关键词: 三自由度转动, 并联机构, 汇交轴线, 奇异, 姿态工作空间

Abstract: The traditional 3-DOF rotational PMs also called as spherical parallel mechanisms(SPMs) usually had a rotation center which was the intersecting point of multiple revolute joint axes. This strict geometric conditions were very hard to fulfill in the manufacture processes and would restrict further applications of this kind of mechanisms. Thus, a PM with three rotational DOF and no intersecting axes was designed herein. It consisted of three identical limbs distributed symmetrically without intersecting axes in or between limbs. The inverse kinematics was solved and four symmetrical assembly modes were obtained. Then the singularity of the mechanism was analyzed and classified into three types: limb singularity, platform singularity and actuation singularity. At last, its orientation workspace was studied. This mechanism can realize three dimensional rotations with large workspace and is easier for manufacturing and assembly, so it has broad application prospects.

Key words: 3-DOF rotation, parallel mechanism(PM), intersecting axes, singularity, orientation workspace

中图分类号:

TH112

陈子明, 黄坤, 张扬, 丁华锋, 黄真, . 一种无汇交轴线对称三转动并联机构的运动分析[J]. 中国机械工程.

Chen Ziming, , Huang Kun, , Zhang Yang, , Ding Huafeng, Huang Zhen, . Kinematics Analysis of a 3-DOF Symmetrical Rotational Parallel Mechanism without Intersecting Axes[J]. China Mechanical Engineering.

参考文献

[1]Cox D J. The Dynamic Modeling and Command Signal Formulation for Parallel Multi-parameter Robotic Devices[D]. Gainesville, Florida: University of Florida, 1981.

[2]Gosselin C M, Hamei J-F. The Agile Eye: a High-Performance Three-degree-of-freedom Camera-orienting Device[C]// Proceedings of the 1994 IEEE International Conference on Robotics and Automation. San Diego, CA, USA,1994: 781-786.

[3]杭鲁滨, 王彦, 吴俊, 等. 基于拓扑解耦准则的球面并联机构解耦条件研究[J]. 机械工程学报, 2005, 41(9):28-32.

Hang Lubin, Wang Yan, Wu Jun, et al. Decoupling Conditions of Spherical Parallel Mechanism Based on the Topological Decoupling Rules[J]. Chinese Journal of Mechanical Engineering, 2005, 41(9): 28-32.

[4]张立杰, 刘辛军. 球面三自由度并联机器人可达工作空间的研究[J]. 中国机械工程, 2001, 12(10): 1122-1127.

Zhang Lijie, Liu Xinjun. Reachable Workspace Analysis of 3-DOF Spherical Parallel Mechanism [J]. China Mechanical Engineering, 2001, 12(10): 1122-1127.

[5]曾宪菁, 黄田, 曾子平. 3-RRR 型数控回转台的精度分析[J]. 机械工程学报, 2001, 37(11):42-45.

Zeng Xianqing, Huang Tian, Zeng Ziping. Precision Analysis of the 3-RRR NC Rotary Table [J]. Chinese Journal of Mechanical Engineering, 2001, 37(11): 42-45.

[6]Karouia M, Herve J M. A Three-DOF Tripod for Generating Spherical Rotation[C]//Advances in Robot Kinematics.Dordrecht :Springer, 2000: 395-402.

[7]李秦川, 陈欢欢, 李昳, 等. 3 -PC(RR)N 球面三自由度并联机构的运动学分析[J]. 中国机械工程, 2009, 20(11):1280-1285.

Li Qinchuan, Chen Huanhuan, Li Die, et al. Kinematic Analysis of a PC(RR)N 3-DOF Spherical Parallel Mechanism[J]. China Mechanical Engineering, 2009, 20(11):1280-1285.

[8]Di Gregorio R. Singularity Analysis of a Single-loop Underactuated Wrist[C]// International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.Portland, USA,2013: DETC2013-12044.

[9]Di Gregorio R. Position Analysis, Path Planning, and Kinetostatics of Single-loop Ru-(Ns)Pu Wrists[J]. Mechanism and Machine Theory, 2014, 74: 117-133.

[10]Di Gregorio R. Single-loop Wrists Which Generate Triangular Structures[J]. Mechanism and Machine Theory, 2014, 80: 230-245.

[11]Valasek M, Zicha J, Karasek M, et al. Hexasphere-redundantly Actuated Parallel Spherical Mechanism as a New Concept of Agile Telescope[J]. Advances in Astronomy, 2010: 348286.

[12]赵云峰, 程丽, 赵永生. 3-UPS/S并联机构运动学分析及机构优化设计[J]. 机械设计, 2009(1):46-49.

Zhao Yunfeng, Cheng Li, Zhao Yongsheng, et al. Kinematic Analysis of 3-UPS/S Parallel Mechanism and Its Optimization Design[J]. Journal of Mechanical Design, 2009(1): 46-49.

[13]Fang Y, Tsai L-W. Structure Synthesis of a Class of 3-DOF Rotational Parallel Manipulators[J]. IEEE Transactions on Robotics and Automation, 2004, 20(1): 117-121.

[14]Kong X, Gosselin C M. Type Synthesis of 3-Dof Spherical Parallel Manipulators Based on Screw Theory[J]. Journal of Mechanical Design, 2004, 126(1): 101-108.

[15]Enferadi J, Tootoonchi A A. Accuracy and Stiffness Analysis of a 3-RRP Spherical Parallel Manipulator[J]. Robotica, 2011, 29(2): 193-209.

[16]Bonev I A, Chablat D, Wenger P. Working and Assembly Modes of the Agile Eye[C]// Proceedings of the 2006 IEEE International Conference on Robotics and Automation(ICRA 2006) . Orlando, IEEE, 2006: 2317-2322.

[17]Di Gregorio R. Kinematics of a New Spherical Parallel Manipulator with Three Equal Legs: the 3-Urc Wrist[J]. Journal of Robotic Systems, 2001, 18(5): 213-219.

[18]Bonev I A, Gosselin C M. Analytical Determination of the Workspace of Symmetrical Spherical Parallel Mechanisms[J]. IEEE Transactions on Robotics, 2006, 22(5): 1011-1017.

[19]Bai S, Hansen M R, Angeles J. A Robust Forward-Displacement Analysis of Spherical Parallel Robots[J]. Mechanism and Machine Theory, 2009, 44(12): 2204-2216.

[20]Bai S. Optimum Design of Spherical Parallel Manipulators for a Prescribed Workspace[J]. Mechanism and Machine Theory, 2010, 45(2): 200-211.

[21]Zarkandi S. A New Geometric Method for Singularity Analysis of Spherical Mechanisms[J]. Robotica, 2011, 29(7): 1083-1092.

[22]Huang Z, Fang Y. Motion Characteristics and Rotational Axis Analysis of Three DOF Parallel Robot Mechanisms[C]// IEEE International Conference on Systems, Man and Cybernetics.Vancouver, British ,1995: 67-71.

[23]黄真, 方跃法. 三自由度并联角台机构转轴存在的子空间[J]. 东北重型机械学院学报, 1997, 21(2):95-99.

Huang Zhen, Fang Yuefa. Subspace of Existing Rotation Axis of 3-Dof Cubic Parallel Mechanism[J]. Journal of Northeast Heavy Machinery Institute, 1997, 21(2): 95-99.

[24]Huang Z, Chen Z, Liu J, et al. A 3-DOF Rotational Parallel Manipulator without Intersecting Axes[J]. Journal of Mechanisms and Robotics, 2011, 3(2): 021014.

[25]陈子明, 陈谊超, 杨凤霞, 等. 两种三自由度并联角台机构的转动空间分析[J]. 机械工程学报, 2014, 50(5):48-56.

Chen Ziming, Chen Yichao, Yang Fengxia, et al. Rotation Workspace Analysis of Two 3-DOF Cubic Parallel Mechanisms[J]. Chinese Journal of Mechanical Engineering, 2014, 50(5): 48-56.

[26]Chen Z, Cao W, Huang Z. Type Synthesis of 3-Dof Rotational Parallel Mechanisms with No Intersecting Axes[C]// ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.Chicago, 2012: DETC2012-70846.

[27]Fang Y, Tsai L-W. Structure Synthesis of a Class of 4-Dof and 5-Dof Parallel Manipulators with Identical Limb Structures[J]. The International Journal of Robotics Research, 2002, 21(9): 799-810.

[28]Bonev I A, Ryu J. A New Approach to Orientation Workspace Analysis of 6-Dof Parallel Manipulators[J]. Mechanism and Machine Theory, 2001, 36: 15-28.