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1. 天津大学 机构理论与装备设计教育部重点实验室, 天津 30007;
2. 北京航空航天大学 自动化科学与电气工程学院, 北京 10008;
3. 伦敦大学 国王学院机器人研究中心, 伦敦 WC2R 2LS

Design and modeling of a soft bending actuator
WANG Hua1, KANG Rongjie1, WANG Xingjian2, DAI Jiansheng1,3
1. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 30007;
2. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 10008;
3. Centre for Robotics Research, King's College London, London WC2R 2LS, England
Received: 2016-05-03; Accepted: 2016-06-24; Published online: 2016-07-01 19:30
Foundation item: National Natural Science Foundation of China (51375329); Tianjin Municipal Science and Technology Department Program (14JCYBJC19300); Specialized Research Fund for the Doctoral Program of Higher Education of China (20130032120036)
Corresponding author. KANG Rongjie, E-mail:rjkang@tju.edu.cn
Abstract: Compared with traditional "rigid" robots, soft robots inspired by biology have been of particular interest to the robotic communities due to their inherent compliance and safety. However, the actuation and control of the soft actuators for such soft robotics are still lacking of theoretical investigation. For these issues, a pneumatic actuator was designed to achieve compliant motions for use in soft robots. The mathematical model was then developed based on the analysis of its structure and bending principle utilizing the geometric analysis and the principle of virtual work. The model were finally validated by finite element model and prototype experiments, and can be used for the future design and control of soft robotic actuators.
Key words: soft actuator     pneumatic actuation     bending deformation     mathematical model     finite element analysis

1 软体驱动器设计

 图 1 软体驱动器弯曲原理图 Fig. 1 Diagram of bending principle for soft actuator

 图 2 软体驱动器结构示意图 Fig. 2 Schematic of soft actuator's structure

 参数 数值 长度l0/mm 80 驱动器半径R0/mm 6.5 空腔内径r0/mm 1.5 空腔圆心偏离驱动器中心距离e1/mm 3 不可伸长面与驱动器中心间距离e2/mm 1.5 绕线圈数N 28 绕线螺旋角/(°) 5 质量/kg 0.017

2 软体驱动器建模

2.1 数学模型

1) 硅橡胶材料近似不可压缩。

2) 驱动器在弯曲过程中几何形状均圆柱。

3) 驱动器在弯曲过程中均保持常曲率弯曲。

4) 绕线不可伸长，而且与驱动器外表面始终保持接触。

2.1.1 材料模型

 (1)

 (2)

2.1.2 驱动器模型

 (3)

 图 3 变形前后的驱动器尺寸 Fig. 3 Size of actuator before and after deformation

 (4)
 (5)
 图 4 弯曲驱动器的几何形状 Fig. 4 Geometry of bending actuator

 (6)

 图 5 未变形驱动器几何形状 Fig. 5 Geometry of undeformed actuator

 (7)
 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

 (15)

 (16)

 图 6 偏心距对驱动器弯曲角θ的影响 Fig. 6 Influence of eccentric distance on bending angle θ of actuator

 (17)

2.2 有限元模型

 图 7 有限元模型中P=80 kPa下驱动器状态 Fig. 7 State of actuator in finite element model at P=80 kPa
3 实验验证 3.1 实验平台搭建

 图 8 实验测量平台 Fig. 8 Experimental measurement platform
 图 9 控制系统流程图 Fig. 9 Flowchart of control system
3.2 实验数据分析

 图 10 不同气压下软体驱动器末端位移 Fig. 10 Tip displacement of soft actuator in different pressure

4 结论

1) 本文以所设计的新型软体驱动器样机为基础，利用虚功原理和几何方法建立了适用于该类型软体驱动器的数学模型，可用于预测软体驱动器在不同气压下的弯曲位置。

2) 借助有限元软件建立了有限元模型，不仅验证了数学模型的有效性，而且对驱动器的应力、应变等进行了观察，对将来进一步分析软体驱动器参数对弯曲性能的影响具有指导作用。

3) 通过仿真分析和原理样机实验验证了数学模型，并展示了其良好的弯曲能力。

4) 该软体驱动器具有良好的柔顺性、适应性与安全性，可用于驱动软体机器人在非结构环境中工作，如深腔探测、空间操作、医疗手术等。此外，在康复陪护、家政服务等具有较高安全性要求的场合，该驱动器及其驱动的机器人系统也有良好的应用潜力。

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#### 文章信息

WANG Hua, KANG Rongjie, WANG Xingjian, DAI Jiansheng

Design and modeling of a soft bending actuator

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(5): 1053-1060
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0364