四连杆膝关节假肢的动力学建模与分析

吕阳; 方虹斌; 徐鉴; 马建敏; 王启宁; 张晓旭

doi:10.6052/0459-1879-20-048

四连杆膝关节假肢的动力学建模与分析

吕阳^*,,
方虹斌^†**††,
徐鉴^†**††,
马建敏^*,
王启宁^***,
张晓旭^{†**††2),}

^*复旦大学航空航天系,上海 200433
^†复旦大学智能机器人研究院,上海 200433
^**上海智能机器人工程技术研究中心,复旦大学,上海 200433
^††智能机器人教育部工程研究中心,复旦大学,上海 200433
^***北京大学工学院,北京 100871

基金项目: 1)国家重点研发计划(2018YFB1307305)

详细信息

通讯作者:
张晓旭

中图分类号: O322
计量
- 文章访问数: 2953
- HTML全文浏览量: 432
- PDF下载量: 334
出版历程
- 收稿日期: 2020-02-14
- 刊出日期: 2020-08-09

DYNAMIC MODELING AND ANALYSIS OF THE LOWER LIMB PROSTHESIS WITH FOUR-BAR LINKAGE PROSTHETIC KNEE

Lü Yang^*,,
Fang Hongbin^†**††,
Xu Jian^†**††,
Ma Jianmin^*,
Wang Qining^***,
Zhang Xiaoxu^{†**††2),}

^*Department of Aeronautics and Astronautics,Fudan University,Shanghai 200433,China
^†Institute of AI and Robotics,Fudan University,Shanghai 200433,China
^**Shanghai Engineering Research Center of AI & Robotics,Shanghai 200433,China
^††Engineering Research Center of AI & Robotics,Ministry of Education,Shanghai 200433,China
^***College of Engineering,Peking University,Beijing 100871,China

摘要

摘要: 相比于单轴式膝关节,四连杆膝关节具有更好的仿生特性和运动安全性,因而在下肢假肢研究中得到广泛关注. 本研究以一款四连杆膝关节被动假肢为研究对象,主要关注足-地交互作用力以及膝关节单边接触力等强非线性因素对下肢假肢步态的影响. 为此,采用 Kelvin-Voigt 模型和库伦模型描述足-地接触力和摩擦力,并采用 Kelvin-Voigt 模型描述膝关节单边接触力,从而基于第一类拉格朗日方程建立假肢动力学模型. 本研究以步态实验测得的髋关节运动数据为模型的驱动信号,针对假肢的步态特征进行了数值分析. 计算结果显示,当膝关节液压阻尼器的刚度较小时,强非线性作用力会使假肢产生显著的亚谐波响应,进而导致步态周期失谐. 进一步研究发现,提胯行为能够避免步态周期失谐,这也为残疾人行走时的提胯等代偿行为提供了一种新的力学解释. 为了评价假肢步态与健康人实测步态的一致性,本研究进一步定义了步态相关系数并分析了膝关节液压阻尼器刚度、阻尼参数对相关系数的影响. 结果表明,通过合理的刚度、阻尼参数设计,两者步态的相关系数可达到 0.9 以上,这为四连杆膝关节被动假肢进一步优化提供了理论支撑.
- 非光滑接触力 /
- 步态实验 /
- 亚谐波响应 /
- 代偿行为 /
- 步态一致性
Abstract: The four-bar linkage prosthetic knee has attracted widespread attention in the study of lower limb prosthesis because it shows a better bionic feature and a higher locomotive safety than the uniaxial joint prosthetic knee. Based on a real four-bar linkage prosthetic knee, this paper mainly studies the strongly nonlinear effects, e.g. the foot-ground interaction force and the unilateral constraint force of knee joint, on the gait of the lower limb prosthesis. For this purpose, firstly, the Kelvin-Voigt contact model is adopted to represent the effect of foot-ground contact force and the unilateral constraint force of the knee joint. The Coulomb model is employed to describe the effect of foot-ground friction force. Then, the Lagrange equations of the first kind are applied to model the dynamics of the prosthesis. Based on this model, the measured hip joint motion of an able-bodied testee is used as the driven signal and the gait characteristics analysis is conducted numerically. The numerical results reveal that if the stiffness of the hydraulic cylinder, which supports the motion of the prosthetic knee joint, is small, the strongly nonlinear effects may lead to the remarkable subharmonic response, which further results in the so-called gait inconformity. Further research shows that the subharmonic response can be avoided by lifting the hip joint, which provides a new insight into the compensatory mechanism such as lifting the hip for the amputee walking from the view of mechanics. In order to evaluate the consistence of the gaits between the prosthesis and the able-bodied testee, this paper further defines the correlation coefficient and analyzes the effects of the hydraulic cylinder's stiffness and damping on this coefficient. The results show that the correlation coefficient of the gaits can be better than 0.9 with proper stiffness and damping design. This discovery provides a solid foundation for further optimization of the four-bar linkage prosthesis.
- non-smooth contact force /
- gait test /
- subharmonic response /
- compensatory mechanism /
- gait consistency

HTML全文

参考文献(1)

[1]	第二次全国残疾人抽样调查主要数据公报(第二号). 时政文献辑览, 2008: 439-442
[2]	Price MA, Philipp B, Frank CS. Design optimization in lower limb prostheses: A review. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2019,27(8):1574-1588
[3]	Breakey JW, Marquette SH. Beyond the Four-Bar Knee. JPO Journal of Prosthetics and Orthotics, 1998,10(3).
[4]	邱海, 方虹斌, 徐鉴. 多稳态串联折纸结构的非线性动力学特性. 力学学报, 2019,51(4):1110-1121
[4]	( Qiu Hai, Fang Hongbin, Xu Jian. Nonlinear characteristics of a multi-stable series Origami structure. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(4):1110-1121 (in Chinese))
[5]	尚昆, 沈力行, 赵改平等. 四连杆膝关节运动学性能仿真软件的实现. 医用生物力学, 2009,24(2):107-111
[5]	( Shang Kun, Shen Lixing, Zhao Gaiping, et al. Realization of kinematics simulation software for four-bar artificial limb knees. Journal of Medical Biomechanics, 2009,24(2):107-111 (in Chinese))
[6]	徐磊. 基于磁流变效应的四连杆假肢膝关节及其构成的下肢假肢的研究. [博士论文]. 重庆:重庆大学, 2016
[6]	( Xu Lei. Magnetroheological effect based four-bar linkage prosthetic knee and the correspondingly constituted lower limb prosthesis. [PhD Thesis]. Chongqing: Chongqing University, 2016 (in Chinese))
[7]	吴波. 基于磁流变阻尼器的动力型智能假肢动力特性分析. [硕士论文]. 哈尔滨: 哈尔滨工业大学, 2015
[7]	( Wu Bo. Dynamic characteristics analysis of active intelligent prosthesis used magnetorheological damper. [Master Thesis]. Harbin: Harbin Institute of Technology, 2015 (in Chinese))
[8]	Quintero D, Martin AE, Gregg RD. Toward unified control of a powered prosthetic leg: A simulation study. IEEE Trans Control Syst Technol, 2018,26(1):305-312
[9]	Huang Y, Wang Q. Torque-stiffness-controlled dynamic walking: analysis of the behaviors of bipeds with both adaptable joint torque and joint stiffness. IEEE Robotics & Automation Magazine, 2016,23(1):71-82
[10]	葛一敏, 袁海辉, 甘春标. 基于步态切换的欠驱动双足机器人控制方法. 力学学报, 2018,50(4):871-879
[10]	( Ge Yimin, Yuan Haihui, Gan Chunbiao. Control method of an underactuated biped robot based on gait transition. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(4):871-879 (in Chinese))
[11]	Skrinjar L, Slavi? J, Bolte?ar M. A review of continuous contact-force models in multibody dynamics. International Journal of Mechanical Sciences, 2018,145(9):171-187
[12]	Hu SW, Guo XL. A dissipative contact force model for impact analysis in multibody dynamics. Multibody System Dynamics, 2015,35(2):131-151
[13]	Carvalho AS, Jorge MM. Exact restitution and generalizations for the Hunt-Crossley contact model. Mechanism and Machine Theory, 2019,139:174-194
[14]	Li B, Wang SM, Makis V, et al. Dynamic characteristics of planar linear array deployable structure based on scissor-like element with differently located revolute clearance joints. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2017: 095440621771027
[15]	Goldsmith W, Frasier JT. Impact: The theory and physical behavior of colliding solids. Journal of Applied Mechanics, 1961,28(4):639
[16]	Mostaghel N, Davis T. Representations of coulomb friction for dynamic analysis. Earthquake Engineering & Structural Dynamics, 1997,26(5):541-548
[17]	Marton L, Lantos B. Modeling, identification, and compensation of stick-slip friction. IEEE Transactions on Industrial Electronics, 2007,54(1):511-521
[18]	Liu L, Wu Z. A new identification method of the Stribeck friction model based on limit cycles. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2014,228(15):2678-2683
[19]	Kamenar E, Zelenika S. Nanometric positioning accuracy in the presence of presliding and sliding friction: Modelling, identification and compensation. Mechanics Based Design of Structures and Machines, 2016,45(1):111-126
[20]	Johanastrom K, Canudas-De-Wit C. Revisiting the LuGre friction model. IEEE Control Systems, 2009,28(6):101-114
[21]	Wang H, Sun Y, Tian Y. Mechanical structure design and robust adaptive integral backstepping cooperative control of a new lower back exoskeleton. Studies in Informatics and Control, 2019,28(2):133-146
[22]	Ikhouane F, Ma?osa V, Pujol G. Minor loops of the Dahl and LuGre models. Applied Mathematical Modelling, 2020,77:1679-1690
[23]	王晓军, 吕敬, 王琪. 含摩擦滑移铰平面多刚体系统动力学的数值算法. 力学学报, 2019,51(1):209-217
[23]	( Wang XiaoJun, Lü Jing, Wang Qi. A numerical method for dynamics of planar multi-rigid-body system with frictional translational joints based on LuGre friction model. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):209-217 (in Chinese))
[24]	Nouri BMY. Friction identification in mechatronic systems. ISA Transactions, 2004,43(2):205-216
[25]	Tjahjowidodo T, Al-Bender F, Brussel HV, et al. Friction characterization and compensation in electro-mechanical systems. Journal of Sound and Vibration, 2007,308(3-5):632-646
[26]	Sun YH, Chen T, Wu CQ, et al. A comprehensive experimental setup for identification of friction model parameters. Mechanism and Machine Theory, 2016,100:338-357
[27]	Zhang X, Xu J, Ji J. Modelling and tuning for a time-delayed vibration absorber with friction. Journal of Sound and Vibration, 2018,424:137-157
[28]	王琪, 庄方方, 郭易圆等. 非光滑多体系统动力学数值算法的研究进展. 力学进展, 2013,43(1):101-111
[28]	( Wang Qi, Zhuang Fangfang, Guo Yiyuan, et al. Advances in the research on numerical methods for non-smooth dynamics of multibody systems. Advances in Mechanics, 2013,43(1):101-111 (in Chinese))
[29]	Zheng X, Wang Q. LCP method for a planar passive dynamic walker based on an event-driven scheme. Acta Mechanica Sinica, 2018,34(3):578-588
[30]	郑鹏, 王琪, 吕敬等. 摩擦与滚阻对被动行走器步态影响的研究. 力学学报, 2020,52(1):162-170
[30]	( Zheng Peng, Wang Qi, Lü Jing, et al. Study on the influence of friction and rolling resistance on the gait of passive dynamic walker. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(1):162-170 (in Chinese))
[31]	段文杰, 王琪, 王天舒. 圆弧足被动行走器非光滑动力学仿真研究. 力学学报, 2011,43(4):765-774
[31]	( Duan Wenjie, Wang Qi, Wang Tianshu. Simulation research of a passive dynamic walker with round feet based on Non-smooth method. Chinese Journal of Theoretical and Applied Mechanics, 2011,43(4):765-774 (in Chinese))
[32]	Ojeda J, Mayo J. A procedure to estimate normal and friction contact parameters in the stance phase of the human gait. Computer Methods in Biomechanics & Biomedical Engineering, 2019: 1-13
[33]	Kadaba MP, Ramakrishnan HK, Wootten ME. Measurement of lower extremity kinematics during level walking. Journal of Orthopaedic Research, 1990,8(3):383-392

施引文献(8)

期刊类型引用(5)

1.	刘东博，陈力. 基于模糊逻辑的双臂空间机器人在轨辅助对接操作变结构力/位控制. 机械工程学报. 2025(01): 60-70 . 百度学术
2.	徐玉龙，王学林，张磊，王鹏，陈昊，赵立德，肖千. 基于干扰观测器的欠驱动手指滑模控制. 齐鲁工业大学学报. 2023(02): 1-7 . 百度学术
3.	宋涛涛，李艳萍，李洪港，韩春雪. 基于改进变结构趋近律的机械臂滑模控制系统. 计算机与现代化. 2023(12): 14-18 . 百度学术
4.	洪梦情，丁萌，顾秀涛，郭毓. 双臂空间机器人的固定时间轨迹跟踪控制. 浙江大学学报(工学版). 2022(06): 1168-1174 . 百度学术
5.	汤万兴，艾海平，陈力. 漂浮基空间机器人固定时间收敛主动容错控制. 福州大学学报(自然科学版). 2022(05): 650-657 . 百度学术