Forward kinematics of 3-RRR flexure parallel mechanism used in lens micro-adjustment

ZHAO Lei; LIANG Chao; ZHANG De-fu; DONG Li-jian; PENG Hai-feng

doi:10.3788/OPE.20162406.1373

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Forward kinematics of 3-RRR flexure parallel mechanism used in lens micro-adjustment

Micro/Nano Technology and Fine Mechanics | 更新时间：2020-08-13

- Forward kinematics of 3-RRR flexure parallel mechanism used in lens micro-adjustment
- Optics and Precision Engineering Vol. 24, Issue 6, Pages: 1373-1381(2016)
- 作者机构：
  
  1. 中国科学院长春光学精密机械与物理研究所应用光学国家重点实验室超精密光学工程研究中心,吉林长春,130033
  2. 长春理工大学经济管理学院, 吉林长春 130022
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20162406.1373
  CLC： TH703;TN305.7
- Received：12 November 2015，
  
  Revised：15 December 2015，
  
  Published：25 June 2016
- 稿件说明：
移动端阅览
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 Lei, LIANG Chao, ZHANG De-fu etc. Forward kinematics of 3-RRR flexure parallel mechanism used in lens micro-adjustment[J]. Editorial Office of Optics and Precision Engineering, 2016,24(6): 1373-1381
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 DOI： 10.3788/OPE.20162406.1373.

ZHAO Lei, LIANG Chao, ZHANG De-fu etc. Forward kinematics of 3-RRR flexure parallel mechanism used in lens micro-adjustment[J]. Editorial Office of Optics and Precision Engineering, 2016,24(6): 1373-1381 DOI： 10.3788/OPE.20162406.1373.

摘要

针对光刻投影物镜中光学元件

X／Y／θ

微动调整的工程需求，研制了一种基于3-RRR结构的光学元件柔顺微动调整机构，并对其位姿正解进行了研究。建立了3-RRR柔顺并联机构的伪刚体模型，并采用矢量代数法理论推导了该机构的位姿正解，得到了它的理论雅克比矩阵。然后，在NASTRAN中建立了3-RRR柔顺并联机构的有限元模型，得到了仿真环境下该机构的位姿正解和雅克比矩阵。最后，对研制的3-RRR柔顺并联机构进行了实验研究，得到了该机构真实的位姿正解和雅克比矩阵。实验结果表明，实验雅克比矩阵的各项系数分别为0.577 7、-0.304 0、-0.283 3、0.002 1、0.524 6、-0.516 5、1.402 6、1.481 9、1.435 3，而理论雅克比矩阵相对应的各项系数分别为0.612 9、-0.306 5、-0.306 5、0、0.530 8、-0.530 8、1.444 6、1.444 6、1.444 6，得到的数据表明：采用矢量代数法能够理论推导出该机构正确的位姿正解公式。提出的3-RRR柔顺微动调整机构位姿正解方法为微动调整机构的研制提供了设计依据。

Abstract

To meet the requirements of

X/Y/θ

adjustment in a lithography projection lens

a 3-RRR flexure parallel mechanism used in lens micro-adjustment was developed and its forward kinematics was researched. Firstly

the pseudo-rigid body model of the 3-RRR flexure parallel mechanism was established

the forward kinematic solution of the 3-RRR parallel mechanism was derived based on vector mathematical theory

and its theoretical Jacobian matrix was obtained. Then

the Finite Element Model(FEM) of the 3-RRR parallel mechanism was established in NX NASTRAN environment

and the FEM forward kinematic solution and the FEM Jacobian matrix were obtained. Finally

according to the experiment of the 3-RRR flexure parallel mechanism

the actual forward kinematic solution and the actual Jacobian matrix were acquired. The experiment results show that: the parameters of the actual Jacbian matrix are 0.5777

-0.304 0

-0.283 3

0.002 1

0.524 6

-0.516 5

1.402 6

1.481 9

1.435 3

while the parameters of the theoretical Jacbian matrix are 0.612 9

-0.306 5

0.530 8

-0.530 8

1.444 6

respectively. The experiment results demonstrate that the forward kinematics can be exactly derived by the vector mathematical theory. The forward kinematic equation method for the 3-RRR flexure parallel mechanism is feasible when designing micro-motion mechanisms.

关键词

Keywords

references

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