Design and analysis of three-degree-of-freedom large-stroke flexible tip-tilt stage driven by voice coil motor

doi:10.3785/j.issn.1006-754X.2025.04.108

Chinese Journal of Engineering Design

2025, Vol. 32

Issue (1): 82-91 DOI: 10.3785/j.issn.1006-754X.2025.04.108

Robotic and Mechanism Design

Design and analysis of three-degree-of-freedom large-stroke flexible tip-tilt stage driven by voice coil motor

Zhihao XU¹(

),Xiaowei LU²,Yuxin XIE¹,Leijie LAI¹(

)

^1.School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China
^2.Holley Technology Ltd. , Hangzhou 310023, China

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Abstract

In order to solve the problem that the traditional piezoelectric-driven tip-tilt stage cannot adapt to many millimeter-level large-stroke application scenarios due to its small stroke, a three-degree-of-freedom large-stroke flexible tip-tilt stage driven by voice coil motor is designed, and its compliance modeling and performance testing are carried out. Firstly, the structural configuration of the three-degree-of-freedom large-stroke flexible tip-tilt stage was introduced, which included three sets of 120° uniformly arranged vertical driving chains, and the motion decoupling of each driving chain and the linear guidance of the motor rotor were achieved by using flexible spherical hinges and parallelogram mechanisms. At the same time, the kinematics equation of the dynamic platform of the tip-tilt stage was established according to the geometric relationship of each driving chain. Then, the compliance matrix method was used to derive the compliance analytical models for the flexible spherical hinge, the driving chain and the overall tip-tilt stage. Subsequently, the accuracy of the derived compliance analytical model was verified through the statics finite element simulation analysis for the tip-tilt stage. Finally, a tip-tilt stage testing system was built to measure its maximum stroke, as well as the translational compliance along the Z-axis and the rotational compliance around the X and Y axes, so as to verify the effectiveness and rationality of the structural design of the tip-tilt stage and the derived compliance analytical model. The results showed that the relative error between the calculation results of the compliance analytical model and the finite element simulation results, as well as the experimental results, was within 10%. The maximum stroke range of the tip-tilt stage was ±0.054 3 rad×±0.047 2 rad×±4.45 mm, which had the advantages of large-stroke and compact structure. The designed tip-tilt stage can be used in various situations that require large-stroke spatial positioning, demonstrating broad application prospects.

Key words： tip-tilt stage large-stroke compliance voice coil motor flexible spherical hinge finite element simulation

Received: 30 January 2024 Published: 04 March 2025

CLC:

TH 112

Corresponding Authors: Leijie LAI E-mail: hankxu99@163.com;lailj@sues.edu.cn

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Cite this article:

Zhihao XU,Xiaowei LU,Yuxin XIE,Leijie LAI. Design and analysis of three-degree-of-freedom large-stroke flexible tip-tilt stage driven by voice coil motor. Chinese Journal of Engineering Design, 2025, 32(1): 82-91.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2025.04.108 OR https://www.zjujournals.com/gcsjxb/Y2025/V32/I1/82

音圈电机驱动的三自由度大行程柔性偏摆台设计与分析

为解决传统压电驱动偏摆台因行程较小而无法适应诸多毫米级大行程应用场景的问题，设计了一种音圈电机驱动的三自由度大行程柔性偏摆台，并对其进行了柔度建模与性能测试。首先，介绍了三自由度大行程柔性偏摆台的结构构型，该构型包含3组呈120°均匀排布的垂直驱动支链，并利用柔性球铰和平行四边形机构实现各驱动支链的运动解耦和电机动子的直线导向；同时，根据各驱动支链的几何关系建立了偏摆台动平台的运动学方程。然后，利用柔度矩阵法推导了柔性球铰、驱动支链和整个偏摆台的柔度解析模型。接着，通过对偏摆台进行静力学有限元仿真分析，验证了所推导的柔度解析模型的准确性。最后，通过搭建偏摆台测试系统来测量偏摆台的最大行程以及沿Z轴的平移柔度和绕X、Y轴的旋转柔度，验证了偏摆台结构设计以及所推导柔度解析模型的有效性和合理性。结果表明：柔度解析模型计算结果与有限元仿真结果、实测结果的相对误差均在10%以内；偏摆台的最大行程范围为±0.054 3 rad×±0.047 2 rad×±4.45 mm，具有行程大、结构紧凑等优点。所设计的偏摆台适用于多种需要大行程空间定位的场景，具有广阔的应用前景。

关键词： 偏摆台, 大行程, 柔度, 音圈电机, 柔性球铰, 有限元仿真

Fig.1 Structure of three-degree-of-freedom large-stroke flexible tip-tilt stage

Fig.2 Guiding principle of parallelogram mechanism

Fig.3 Deformation principle of reed-type flexible spherical hinge

Fig.4 Mechanism schematic and kinematics model of tip-tilt stage

Fig.5 Schematic diagram of reed beam under force

Fig.6 Section structure and structural parameters of flexible spherical hinge

Table 1 Values of structural parameters of flexible spherical hinge

Fig.7 Connection relationship and local coordinate system of each reed beam in flexible spherical hinge

Fig.8 Structural parameters of driving chain

Table 2 Values of structural parameters of driving chain

Fig.9 Overall compliance calculation model of tip-tilt stage

Fig.10 Statics finite element simulation results of tip-tilt stage

对比项

$C δ Z$ /

(mm/N)

$C θ X$ /

［rad/(N·m)］

$C θ Y$ /

［rad/(N·m)］

相对误差/%

2.64

7.84

5.10

计算值

0.044 76

0.006 70

仿真值

0.043 61

0.007 27

0.007 06

Table 3 Comparison between calculated and simulated values of compliance of tip-tilt stage

Fig.11 Prototype of tip-tilt stage

Fig.12 Connection schematic of various components of tip-tilt stage testing system

Fig.13 Relationship curve between force/torque and pose of dynamic platform of tip-tilt stage

对比项

$C δ Z$ /

(mm/N)

$C θ X$ /

［rad/(N·m)］

$C θ Y$ /

［rad/(N·m)］

相对误差/%

8.88

1.76

3.32

计算值

0.044 76

0.006 70

实测值

0.041 11

0.006 82

0.006 93

Table 4 Comparison between calculated and measured values of compliance of tip-tilt stage


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