Stiffness and natural frequency of a (2PRR)<sup>2</sup>+R planar parallel mechanism

Dong-sheng ZHANG; Yun-dou XU; Jian-tao YAO; Yong-sheng ZHAO

doi:10.3788/OPE.20172511.2904

您当前的位置：

首页 >

文章列表页 >

Stiffness and natural frequency of a (2PRR)²+R planar parallel mechanism

Micro/Nano Technology and Fine Mechanics | 更新时间：2020-07-07

- Stiffness and natural frequency of a (2PRR)²+R planar parallel mechanism
- Optics and Precision Engineering Vol. 25, Issue 11, Pages: 2904-2913(2017)
- 作者机构：
  
  1.燕山大学河北省并联机器人与机电系统实验室, 河北秦皇岛 066004
  2.燕山大学先进锻压成形技术与科学教育部重点实验室, 河北秦皇岛 066004
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20172511.2904
  CLC： TP242
- Received：31 March 2017，
  
  Accepted：22 May 2017，
  
  Published：25 November 2017
- 稿件说明：
移动端阅览
Dong-sheng ZHANG, Yun-dou XU, Jian-tao YAO, et al. Stiffness and natural frequency of a (2PRR)²+R planar parallel mechanism[J]. Optics and precision engineering, 2017, 25(11): 2904-2913.
DOI：

Dong-sheng ZHANG, Yun-dou XU, Jian-tao YAO, et al. Stiffness and natural frequency of a (2PRR)²+R planar parallel mechanism[J]. Optics and precision engineering, 2017, 25(11): 2904-2913. DOI： 10.3788/OPE.20172511.2904.

摘要

基于两移动一转动三自由度平面并联机构构造了一种新型五自由度串并混联机器人并对其并联部分，一具有运动冗余和驱动冗余两种不同模式的平面并联机构（2PRR）

+R进行了运动学分析。首先，建立了三自由度平面并联机构的运动学模型，基于机构的运动学模型推导得到了冗余和非冗余驱动并联机构的刚度矩阵，并且通过求取并联机构各组成构件的等效质量，得到并联机构的质量矩阵；然后，借助系统刚度矩阵和质量矩阵建立的并联机构动力学方程，求得了机构的固有频率方程；最后，通过数值仿真对冗余和非冗余驱动并联机构的刚度及固有频率进行对比分析。结果显示：冗余驱动分支对机构绕

轴方向角刚度和系统的一阶固有频率均值影响最大，其增幅分别为88.46%和31.50%；对

轴方向的线刚度和系统的二阶固有频率均值影响最小，其增幅分别为52.34%和1.90%。因此，冗余驱动分支有助于提高并联机构的整体刚度，改善机构的动态性能。

Abstract

A novel 5-degree-of-freedom (DOF) hybrid serial-parallel manipulator was proposed. The kinematics of Parallel Mechanism (PM) of the 5-DOF hybrid manipulator was analyzed. The PM is a 3-DOF (one translational DOF and two rotational DOFs) metamorphic planar PM (2PRR)

+R with two different types of configurations:actuation redundancy and kinematic redundancy. Firstly

the kinematics model of the 3-DOF planar PM was established. Then

the stiffness matrix of the planar PM was obtained on the basis of kinematics analysis and the mass matrix was obtained by solving each equivalent component mass of the planar PM. Furthermore

the system dynamic equation was established through combining the stiffness matrix and mass matrix

and the natural frequency equation was obtained incidentally based on the dynamic equation. Finally

the stiffnesses and natural frequencies for the redundant and non-redundant planar PMs were analyzed and compared by numerical simulation. The results show that the maximum extend ranges of the stiffness around

-axis and the first-order natural frequency reach 88.46% and 31.50%

respectively; and the minimum extend ranges of the stiffness along

-axis and the second-order natural frequency reach 52.34% and 1.90%

respectively. Thus

the stiffness and natural frequency of the planar PM have been obviously improved by adding actuation redundancy.

关键词

Keywords

references

PATEL Y D, GEORGE P M. Parallel manipulators applications-a survey[J]. Modern Mechanical Engineering, 2012, 2(3):57-64.

曲海波, 梁艺瀚, 方跃法, 等. 4-RRS冗余球面并联机构的静力学与刚度分析[J].机械工程学报, 2015, 51(11):8-15.

QU H B, LIANG Y H, FANG Y F, et al.. Statics and stiffness analysis of 4-RRS redundant spherical parallel mechanism[J]. Journal of Mechanical Engineering, 2015, 51(11):8-15. (in Chinese)

苑飞虎, 赵铁石, 赵延治, 等.并联机构承载能力分析[J].中国机械工程, 2015, 26(7):871-877.

YUAN F H, ZHAO T S, ZHAO Y ZH, et al.. Analysis of load carrying capacity of parallel mechanism[J]. China Mechanical Engineering, 2015, 26(7):871-877. (in Chinese)

陈修龙, 董芳杞, 王清.基于牛顿-欧拉法的4-UPS-UPU并联机构动力学方程[J].光学精密工程, 2015, 23(11):3129-3137.

CHEN X L, DONG F Q, WANG Q. Dynamic equation of 4-UPS-UPU parallel mechanism based on New-Euler approach[J]. Opt. Precision Eng., 2015, 23(11):3129-3137. (in Chinese)

WU G L, BAI S P, KEPLER J. Stiffness characterization of a 3-PPR planar parallel manipulator with actuation compliance[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2015, 229(12):2291-2302.

ZHANG X CH, ZHANG X M, CHEN ZH. Dynamic analysis of a 3-RRR parallel mechanism with multiple clearance joints[J]. Mechanism and Machine Theory, 2014, 78:105-115.

赵磊, 梁超, 张德福, 等.基于3-RRR结构的光学元件柔顺微动调整机构的位姿正解[J].光学精密工程, 2016, 24(6):1373-1381.

ZHAO L, LIANG CH, ZHANG D F, et al.. Forward kinematics of 3-RRR flexure parallel mechanism used in lens micro-adjustment[J]. Opt. Precision Eng., 2016, 24(6):1373-1381. (in Chinese)

LIM H, LEE S H, SO B R, et al.. Design of a new 6-DOF parallel mechanism with a suspended platform[J]. International Journal of Control, Automation and Systems, 2015, 13(4):942-950.

EBRAHIMI I, CARRETERO J A, BOUDREAU R. 3-PRRR redundant planar parallel manipulator:Inverse displacement, workspace and singularity analyses[J]. Mechanism and Machine Theory, 2007, 42(8):1007-1016.

KOTLARSKI J, HEIMANN B, ORTMAIER T. Influence of kinematic redundancy on the singularity-free workspace of parallel kinematic machines[J]. Frontiers of Mechanical Engineering, 2012, 7(2):120-134.

ZHANG D SH, XU Y D, YAO J T, et al.. Kinematics, dynamics and stiffness analysis of a novel 3-DOF kinematically/actuation redundant planar parallel mechanism[J]. Mechanism and Machine Theory, 2017, 116:203-219.

LUCES M, MILLS J K, BENHABIB B. A review of redundant parallel kinematic mechanisms[J]. Journal of Intelligent & Robotic Systems, 2016, 86(2):175-198.

GOSSELIN C, SCHREIBER L T. Kinematically redundant spatial parallel mechanisms for singularity avoidance and large orientational workspace[J]. IEEE Transactions on Robotics, 2016, 32(2):286-300.

牛雪梅, 高国琴, 刘辛军, 等.三自由度驱动冗余并联机构动力学建模与试验[J].农业工程学报, 2013, 29(16):31-41.

NIU X M, GAO G Q, LIU X J, et al.. Dynamics modeling and experiments of 3-DOF parallel mechanism with actuation redundancy[J]. Transactions of the Chinese Society of Agricultural Engineering, 2013, 29(16):31-41. (in Chinese)

LIU H T, HUANG T, KECSKEMÉTHY A, et al.. Force/motion transmissibility analyses of redundantly actuated and overconstrained parallel manipulators[J]. Mechanism and Machine Theory, 2017, 109:126-138.

周鑫, 许允斗, 姚建涛, 等. 5-U(P)S/(P)RPU冗余驱动并联机床完整刚度模型及其刚度特性[J].光学精密工程, 2015, 23(4):1070-1080.

ZHOU X, XU Y D, YAO J T, et al.. Complete stiffness model and stiffness performance of 5-U(P)S/(P)RPU redundantly actuated parallel machine tool[J]. Opt. Precision Eng., 2015, 23(4):1070-1080. (in Chinese)

LI S H, LIU Y M, CUI H L, et al.. Synthesis of branched chains with actuation redundancy for eliminating interior singularities of 3T1R parallel mechanisms[J]. Chinese Journal of Mechanical Engineering, 2016, 29(2):250-259.

李剑锋, 费仁元, 范金红, 等.驱动器布位及冗余驱动对Tricept并联机构性能的影响[J].机械工程学报, 2008, 44(1):31-39.

LI J F, FEI R Y, FAN J H, et al.. Effects of actuator disposition and redundant actuation on performance of the Tricept parallel mechanism[J]. Chinese Journal of Mechanical Engineering, 2008, 44(1):31-39. (in Chinese)

JIANG Y, LI T M, WANG L P. The dynamic modeling, redundant-force optimization, and dynamic performance analyses of a parallel kinematic machine with actuation redundancy[J]. Robotica, 2015, 33(2):241-263.

HARADA T, LIU P D. Internal and external forces measurement of planar 3-DOF redundantly actuated parallel mechanism by axial force sensors[J]. ISRN Robotics, 2013, 2013:593606.

ISAKSSON M, GOSSELIN C, MARLOW K. An introduction to utilising the redundancy of a kinematically redundant parallel manipulator to operate a gripper[J]. Mechanism and Machine Theory, 2016, 101:50-59.

REVELES D, PAMANES G J A, WENGER P. Trajectory planning of kinematically redundant parallel manipulators by using multiple working modes[J]. Mechanism and Machine Theory, 2016, 98:216-230.

GOSSELIN C, LALIBERTÉ T, VEILLETTE A. Singularity-free kinematically redundant planar parallel mechanisms with unlimited rotational capability[J]. IEEE Transactions on Robotics, 2015, 31(2):457-467.

张东胜, 许允斗, 侯照伟, 等.五自由度混联机器人优化设计与运动学分析[J].农业工程学报, 2016, 32(24):69-76.

ZHANG D SH, XU Y D, HOU ZH W, et al.. Optimal design and kinematics analysis of 5-DOF hybrid serial-parallel manipulator[J]. Transactions of the Chinese Society of Agricultural Engineering, 2016, 32(24):69-76. (in Chinese)

WU J, LI T M, WANG J S, et al.. Stiffness and natural frequency of a 3-DOF parallel manipulator with consideration of additional leg candidates[J]. Robotics and Autonomous Systems, 2013, 61(8):868-875.

WU J, CHEN X M, LI T M, et al.. Optimal design of a 2-DOF parallel manipulator with actuation redundancy considering kinematics and natural frequency[J]. Robotics and Computer-Integrated Manufacturing, 2013, 29(1):80-85.

Views

483

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Design and experiments of micro motion platform based on a pair of flexible parallel six-bar linkages

Design and analysis of a novel 3-DOF nanopositioning stage

Computer-Aided Engineering Analysis and Calculation of the Base Structure for the Calibration System on Ship

Optimal design of parameters of the six-hardpoint positioning mechanism for large aperture primary mirror

Variable stiffness control of redundant cable-driven parallel mechanism for on-orbit assembly

Related Author

ZHAO Rong-li

CHEN Xin

LI Ke-tian

SUN Li-ning

RONG Wei-bin

MA Li

Wang Yanfeng

WANG Fuguo

Related Institution

Guangdong Provincial Key Laboratory of Micro-nano Manufacturing Technology and Equipment, Guangdong University of Technology

Robotics Institute, Harbin Institute of Technology

Changchun Institute of Optics and Fien Mechanics, Chinese Acabemy of Sciences

University of Chinese Academy of Sciences

Changchun Institute of Optics，Fine Mechanics and Physics，Chinese Academy of Sciences

AI问答

Address：No.3888 Dong Nanhu Road, Changchun, Jilin, China Postal code：130033
Tel：0431-86176855 Email：gxjmgc@ciomp.ac.cn
Technical support is provided by Beijing Founder electronics co., LTD 吉ICP备11002662号-17 京公网安备11010802024621
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰

Stiffness and natural frequency of a (2PRR)2+R planar parallel mechanism

DOI：10.3788/OPE.20172511.2904

摘要

Abstract

关键词

Keywords

references

Stiffness and natural frequency of a (2PRR)²+R planar parallel mechanism