光电工程

Connecting rod/i	$ {\alpha }_{i} $/(°)	$ {a}_{i} $/mm	$ {d}_{i} $/mm	$ {\theta }_{i} $/(°)
1	90	0	$ {d}_{1} $	$ {\theta }_{1} $
2	90	0	$ {d}_{2} $	$ {\theta }_{2} $
3	0	$ {a}_{3} $	0	$ {\theta }_{3} $+90

Connecting rod/i	$ {\alpha }_{i} $/(°)	$ {a}_{i} $/mm	$ {d}_{i} $/mm	$ {\theta }_{i} $/(°)
1	90	0	$ {d}_{1} $	$ {\theta }_{1} $
2	90	0	$ {d}_{2} $	$ {\theta }_{2} $
3	0	$ {a}_{3} $	0	$ {\theta }_{3} $+90

Name	Composition	Location	Function
Thigh	Thighbone	From the hip upwards, and from the knee downwards	Support and propel the body
Lower leg	Tibia and fibula	From the knees down to the ankles up	Stabilize and support the body
Foot	Heel, sole, heel of foot, toe region	Below the ankle	Supporting weight, walking, running

Name	Composition	Location	Function
Thigh	Thighbone	From the hip upwards, and from the knee downwards	Support and propel the body
Lower leg	Tibia and fibula	From the knees down to the ankles up	Stabilize and support the body
Foot	Heel, sole, heel of foot, toe region	Below the ankle	Supporting weight, walking, running

Name	Construction	Function
Thigh	Exoskeleton structure, bandage fixation	Improve stability and expand the scope of application
Lower leg	Exoskeleton structure, bandage fixation	Improve stability and expand the scope of application
Foot	Frame structure, cork, bandage fixation	Improve stability and expand the scope of application

Name	Construction	Function
Thigh	Exoskeleton structure, bandage fixation	Improve stability and expand the scope of application
Lower leg	Exoskeleton structure, bandage fixation	Improve stability and expand the scope of application
Foot	Frame structure, cork, bandage fixation	Improve stability and expand the scope of application

	The first point/nm	The second point/nm
Foot	1546	1550
Lower leg	1548	1550
Thigh	1546	1550

	The first point/nm	The second point/nm
Foot	1546	1550
Lower leg	1548	1550
Thigh	1546	1550

Corresponding point	Right leg
The first part of the foot	13.6	0.9963	13.4	0.9967
The second part of the foot	13.9	0.9984	13.5	0.9991
The first part of the lower leg	10.1	0.9962	10.1	0.9946
The second part of the lower leg	10.1	0.9989	10.2	0.9965
The first part of the thigh	9.9	0.9977	10.2	0.9954
The second part of the thigh	10.1	0.9991	10.0	0.9906

Corresponding point	Right leg
The first part of the foot	13.6	0.9963	13.4	0.9967
The second part of the foot	13.9	0.9984	13.5	0.9991
The first part of the lower leg	10.1	0.9962	10.1	0.9946
The second part of the lower leg	10.1	0.9989	10.2	0.9965
The first part of the thigh	9.9	0.9977	10.2	0.9954
The second part of the thigh	10.1	0.9991	10.0	0.9906

	Right foot	Right lower leg	Right thigh	Left foot	Left lower leg	Left thigh
$ \mu $	0.34	0.59	0.62	0.55	0.76	0.71
$ \sigma $	0.01	0.01	0.01	0.01	0.01	0.01

	Right foot	Right lower leg	Right thigh	Left foot	Left lower leg	Left thigh
$ \mu $	0.34	0.59	0.62	0.55	0.76	0.71
$ \sigma $	0.01	0.01	0.01	0.01	0.01	0.01

Angle/(°)	Theoretical step pitch/cm	Theoretical step high/cm	Actual step pitch/cm	Actual step high/cm	Step pitch error/%	Step high error/%
0	0	0	0	0	0	0	0	0
5	3.5	9.3	11.33	0.64	11.01	0.59	2.8	7.8
10	8.9	18.2	21.11	2.69	20.5	2.61	2.9	3.0
15	14.1	13.4	28.83	3.62	27.8	3.88	3.6	6.7
20	18.8	3.4	30.71	5.01	31.2	5.12	1.6	2.2

Angle/(°)	Theoretical step pitch/cm	Theoretical step high/cm	Actual step pitch/cm	Actual step high/cm	Step pitch error/%	Step high error/%
0	0	0	0	0	0	0	0	0
5	3.5	9.3	11.33	0.64	11.01	0.59	2.8	7.8
10	8.9	18.2	21.11	2.69	20.5	2.61	2.9	3.0
15	14.1	13.4	28.83	3.62	27.8	3.88	3.6	6.7
20	18.8	3.4	30.71	5.01	31.2	5.12	1.6	2.2

	Foot	Lower leg	Thigh	Average
J	0.9374	0.9228	0.9534	0.9379

	Foot	Lower leg	Thigh	Average
J	0.9374	0.9228	0.9534	0.9379

光纤光栅下肢外骨骼步态监测方法

PDF下载

闫希研 ¹^,² , 冯艳 ¹^,²^,^*^,^* , 马智恒 ¹ , 张华 ¹^,²

光电工程 | 研究论文 2026,53(1): 250124-1

收起

光电工程 |研究论文 2026 , 53 (1) : 250124 -1

光纤光栅下肢外骨骼步态监测方法

全屏

闫希研¹^,², 冯艳¹^,²^,^*^,^*, 马智恒¹, 张华¹^,²

作者信息

¹上海工程技术大学机械与汽车工程学院机器人研究所，上海 201620

²上海大型构件智能制造机器人技术协同创新中心，上海 201620

通讯作者:

冯艳，xmfy0833@sina.com。

作者简介:

作者贡献

闫希研：研究资料的收集、分析，论文写作；冯艳：指导论文选题，论文修改；马智恒：协助实验数据采集；张华：基金项目资金支持，实验指导。

闫希研(1999-)，男，陕西汉中人，硕士研究生，主要从事光纤智能感知的研究。E-mail：15029492776@163.com 15029492776@163.com

冯艳(1976-)，女，江西南昌人，博士，教授，主要研究方向为光纤光栅传感、智能机器人触觉感知等。E-mail：xmfy0833@sina.com xmfy0833@sina.com

Lower extremity exoskeleton gait monitoring method based on fiber Bragg grating

Xiyan Yan¹^,², Yan Feng¹^,², Zhiheng Ma¹, Hua Zhang¹^,²

Affiliations

¹Robotics Institute, School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China

²Shanghai Large-Scale Component Intelligent Manufacturing Robot Technology Collaborative Innovation Center, Shanghai 201620, China

Corresponding Author:

xmfy0833@sina.com

出版时间: 2026-01-25 doi: 10.12086/oee.2026.250124

文章导航

摘要

收起

步态信息对下肢康复医疗具有重要意义，因此设计了一款基于光纤光栅(FBG)传感单元的下肢外骨骼监测装置。通过理论推导和仿真分析，验证了外骨骼结构的合理性，揭示了下肢步态参数(步高、步距)影响FBG中心波长变化的规律，并提出了步态节奏的评价指标。对FBG传感单元的12个监测点进行力标定实验，结果表明每个监测点位的平均力灵敏度大于9.9 pm/N。志愿者穿戴好外骨骼装置后进行步态监测实验。实验结果表明，实际步距-步高对比理论模型的误差低于10%。步态节奏为0.9379，这证明了理论模型的合理性，表明光纤光栅下肢外骨骼步态监测装置运动稳定，能够有效监测下肢运动。

关键词

光纤光栅传感单元 / 下肢外骨骼 / 步高 / 步距 / 步态节奏

Abstract

收起

Objective

In recent years, various devices for monitoring lower limb movement have emerged. Electrical sensors are susceptible to electromagnetic interference, while visual signals are affected by light intensity. Fiber Bragg Grating (FBG) sensors, on the other hand, have been widely adopted due to their excellent linearity, high sensitivity, flexibility, and strong anti-interference characteristics. During lower limb movement, the forces on the toes and heels of the foot continuously change, and the forces on the calf and thigh also fluctuate. However, research on the integrated monitoring of foot, calf, and thigh movements remains limited. Therefore, the development of a lower limb exoskeleton monitoring device is significant.

Methods

This study first established a theoretical model based on kinematics and verified its feasibility through theoretical analysis and simulation. Subsequently, a lower limb exoskeleton and its monitoring sensor unit were designed. Calibration experiments were conducted on the lower limb sensor unit using a tensile testing machine. The force sensitivities of all sensing units were obtained above 9.9 pm/N, and the goodness of fit values were all above 0.9906, demonstrating that the sensing units possess excellent monitoring performance. The exoskeleton provides support for the wearer, and the sensor unit integrated within it successfully monitors lower limb movements. After the volunteer wore the exoskeleton, motion monitoring experiments were conducted. The resulting data showed periodic changes, consistent with the conclusions drawn from the theoretical model and simulation analysis. The device features a simple power system that provides a certain level of assistance. Furthermore, the system includes an upper-level computer to analyze the monitored data and provide warning feedback based on the movement state.

Results and Discussions

In the theoretical model, as the angles of the three segments of the lower limb increase, the wavelength of the corresponding sensor units either increases or decreases. The relationship between step length and step height in the simulation analysis aligns with theoretical predictions. Additionally, dynamic analysis of the simplified structure further verified the accuracy of the step length-step height relationship. Finally, experimental data from the volunteer wearing the exoskeleton exhibited periodic changes, with stable mean values and standard deviations for the lower limb regions. The error between the theoretical and actual step length-step height was approximately 10%. The average value of the lower limb gait rhythm index (J) was 0.9379. These results confirm that the lower limb exoskeleton monitoring device meets monitoring requirements without negatively impacting the monitoring process and can accurately track the volunteer's lower limb movements. From a technical perspective, this study has made significant progress in sensing unit design and system integration. The advantages of FBG sensors lie not only in their high sensitivity and anti-interference capability but also in their suitability for multi-point synchronous monitoring due to their distributable embeddability and wavelength-encoding characteristics. In this system, by arranging sensing units at corresponding positions on the sole, ankle joint, knee joint, and thigh, a monitoring network covering key lower limb movement nodes was constructed. This distributed layout can capture the biomechanical changes during various phases of the gait cycle, providing multidimensional data for gait analysis and motor dysfunction assessment. In terms of system integration, the exoskeleton structure not only serves as a carrier for the sensing units but its mechanical design also fully considers ergonomics and movement adaptability. Lightweight hinge structures are used at the joints to reduce movement constraints while ensuring support stiffness. The power system employs lightweight electric actuators that primarily provide assistive torque during the gait propulsion phase, reducing the wearer's walking energy expenditure. When gait abnormalities (such as foot dragging or excessively high left-right asymmetry) or sudden force changes are detected, the system can provide alerts through sound or interface flashes, possessing preliminary gait anomaly warning capabilities.

Conclusions

Looking at the application prospects, this FBG-based lower limb exoskeleton monitoring device holds potential not only for motion analysis or assistance in healthy populations but also, and more importantly, in the field of rehabilitation medicine. It can provide objective and continuous gait parameter monitoring for patients after lower limb surgery or those with post-stroke sequelae, helping rehabilitation therapists quantitatively assess recovery progress. Furthermore, it could potentially integrate with functional electrical stimulation or robotic-assisted training to form an intelligent rehabilitation training system. Additionally, in specialized operational fields (such as firefighting or loaded marching), this technology could be used to monitor operators' fatigue states and prevent sports injuries. In summary, this study successfully designed and validated a lower limb exoskeleton monitoring device integrated with FBG sensing technology. The device achieves synchronous, anti-interference monitoring of multi-part lower limb movements with reliable data, while the exoskeleton structure provides a certain level of assistance during monitoring. The experimental results confirm their effectiveness, laying a solid foundation for subsequent research. Future work will focus on algorithm optimization, system lightweighting and portability, as well as clinical validation and functional expansion for specific application scenarios, aiming to ultimately transition the device from a laboratory prototype to a practical product.

Key words

fiber Bragg grating sensing unit / lower limb exoskeleton / step height / step length / gait rhythm

引用本文

闫希研, 冯艳, 马智恒, 张华. 光纤光栅下肢外骨骼步态监测方法. 光电工程, 2026 , 53 (1) : 250124 -1 . DOI: 10.12086/oee.2026.250124

Xiyan Yan, Yan Feng, Zhiheng Ma, Hua Zhang. Lower extremity exoskeleton gait monitoring method based on fiber Bragg grating[J]. Opto-Electronic Engineering, 2026 , 53 (1) : 250124 -1 . DOI: 10.12086/oee.2026.250124

正文

收起

1　引　言

收起

步态信息对下肢康复医疗具有重要意义，下肢步态监测装置的需求量不断上升^[1-2]。监测下肢运动有二类方法^[3-4]。第一类为电信号、视觉监测。2023年北京交通大学^[5]提出了使用平移倾斜变焦摄像机进行视频直播的远程康复信息系统。2023年Yu等^[6]提出了基于健侧表面肌电信号的肢体康复机器人控制系统。2023年Fischer等^[7]提出了一种采用形状记忆合金和电容力传感的主动外骨骼界面柔顺执行器。然而电信号、视觉信号监测不便，容易受到外界干扰。

第二类为光纤光栅监测。其主要监测足部和其他肢体的运动。监测足部的运动主要有：2022年Zhang等^[8]提出了一种用于足底压力中心(center of pressure, COP)测量的光纤布拉格光栅(fiber Bragg grating sensor, FBG)压力垫。2023年Mahmud等^[9]提出了基于光纤光栅的智能鞋垫，能够测量足底压力和温度。2023年Lavarda等^[10]提出了基于FBG集成于复合材料和自适应模糊控制器的智能足部。2024年Mishra等^[11]提出了基于FBG的足底应变和步态分析装置的设计。监测其他肢体的运动主要有：2023年Pires-Junior等^[12]提出了光纤嵌入式智能人工肌腱的设计变形监测。2023年Zheng等^[13]提出了用于实时监测人体姿势和运动状态的高灵敏度双包层光纤光栅传感器，用于识别人体姿态和运动状态。2025年Alhussein等^[14]提出了基于光纤光栅的步态识别。2024年Pulcinelli等^[15]提出了基于FBG的膝关节监测。2024年Leal-Junior等^[16]提出了光电智能家居：异质光学传感器方法和人工智能在远程监控中的新范式，利用光学传感器进行人体运动监测。2024年Rocha等^[17]提出了基于光纤布拉格光栅的智能医疗室内定位。2024年Wang等^[18]提出了高精度大量程的FBG人体膝关节角度可穿戴测量机制。2024年Rohan等^[19]对FBG在生物医学中的应用进行了系统性的总结与分析。光信号监测具有稳定、长期的特点，且光纤传感器线性度好、灵敏度高，适合依附于外骨骼对人体进行长期监测。

监测下肢的装置不能影响正常人的运动，且需要具有一定的动力辅助患者监测。2024年Duan等^[20]提出了基于中心模式发生器的下肢外骨骼步态生成策略，所设计的系统可以克服台式下肢外骨骼固定训练模式的局限性，能够适应各种用户独特的步态特征，便于步态定制。2024年Kapsalyamov等^[21]提出了一种用于个体化步态康复的新型欠驱动机器人矫形器，经过分析发现该外骨骼可以提供适合康复目的人体运动。

相较于之前的研究，本研究将12支FBG传感器融入到下肢的运动监测中，根据FBG传感器的特点，融合材料和机械结构设计出了隔绝人体温度的传感器单元(隔绝了人体温度对监测传感单元的影响)、所设计外骨骼具有辅助行走的作用、该下肢外骨骼尺寸可调节，适合不同体型的人使用。本文基于FBG传感单元研制了一种适合于不同体型(身高为165~185 cm，脚码为37~45码)的人穿戴的下肢步态监测外骨骼装置，通过理论分析和仿真分析验证了其监测步态的可行性。采用机构学D-H参数法建立下肢步态模型理论并构建了步态分析方法，揭示了下肢步态参数(步高、步距)影响FBG中心波长变化的规律。实验研究结果表明，该下肢外骨骼监测装置可以监测人体步态参数，具有一定的助力功能，可在上位机实现其监测反馈情况，并做出预警反馈。

2　监测结构的设计和原理

收起

2.1　FBG原理

FBG传感器用于监测物理量，如应力、温度、压力等^[22-23]。

$ \lambda_{\mathrm{B}}=2 n_{{\mathrm{e f f}}} \varLambda \;,$

(1)

式中：

$ {\varLambda } $

是相位掩模光栅的周期；

$ {n}_{{\mathrm{eff}}} $

是光纤纤芯针对自由空间中心波长的折射率。当光纤布拉格光栅受到外界应力和温度的作用时，受弹光效应和热光效应的影响，光纤光栅的有效折射率和光栅周期都会发生变化，因此反射的布拉格波长

$ {{\lambda }}_{{\mathrm{B}}} $

的变化公式^[24-25]可以表示为

$ \frac{\Delta \lambda_{\mathrm{B}}}{\lambda_{\mathrm{B}}}=k_{\varepsilon} \Delta \varepsilon+k_T \Delta T\;, $

(2)

式中：

${\Delta }{\lambda }_{{\mathrm{B}}} $

为中心波长偏移量；

$ {k}_{\varepsilon }=1-{P}_{{\mathrm{e}}} $

为应力作用下波长应变灵敏度系数，其中

$ {P}_{{\mathrm{e}}} $

为有效弹光系数；

$ {k}_{T}=\alpha +\xi $

为光纤光栅温度传感的灵敏度系数，其中

$ \alpha $

为热膨胀系数，

$ \xi $

为热光系数；

$ \mathrm{\Delta }\varepsilon $

为轴向应变变化量；

$ \mathrm{\Delta }T $

为温度变化量。中心波长1550 nm的FBG传感器如图1所示，

$ {k}_{\varepsilon }=1.2\;{\mathrm{pm}}/\varepsilon $

，

$ {k}_{T}=10.5\;{\mathrm{pm}}/^\circ{\mathrm{C}} $

。

2.2　监测结构的设计及原理

监测部位有脚、小腿、大腿如图2所示，通过监测这些部位得到运动情况。

2.2.1　足底压力监测结构的设计及原理

考虑到脚尖和脚跟受力最大，将两支传感器分别设计在这两个位置。足底压力监测结构长31 cm，第一监测点和第二监测点相距21 cm，可以得知该足底压力监测结构可以监测脚码为37 (脚长约23.5 cm)至45 (脚长约29 cm)的人群。

足底压力监测结构使用软木结构-隔热(软木导热性能差，保证人体温度无法影响FBG传感器)、缓冲(使用UV胶将FBG固定在两层软木之间-监测脚部运动)。如图3所示，

$ \theta $

表示足底监测结构受到外力之后，结构表面改变的角度，

$ {a}_{1} $

表示足底监测结构的高度，

$ {b}_{1} $

表示足底监测结构的长度。

因为

$ \mathrm{\Delta }T=0 $

，根据式(2)和应变原理可得式(3)。

$ \frac{\mathrm{\Delta }{\lambda }_{{\mathrm{B}}}}{{\lambda }_{{\mathrm{B}}}}={k}_{\varepsilon }\frac{F}{E{a}_{1}\mathrm{\Delta }{b}_{1}}\;, $

(3)

式中：F是下肢运动时传递给FBG的力；E是弹性模量。

长度的改变伴随着角度的变化，根据式(3)可得式(4)。

$ \frac{\mathrm{\Delta }\lambda }{\lambda }={K}_{\varepsilon }\left(\frac{{b}_{1}}{\mathrm{cos}\mathrm{\Delta }\theta }-{b}_{1}\right)\frac{F}{E{a}_{1}}\;. $

(4)

根据式(3)可知，传感器波长变化与鞋垫变形呈线性关系。根据式(4)可知，随着角度改变，传感器波长随之改变。

2.2.2　肢体监测结构的设计及原理

该下肢外骨骼长75 cm，小腿和大腿都可以调节长度(各自可调节10 cm)，因此其最长为95 cm，最短为75 cm。下肢大约占身高的45%~47%，因此可知该外骨骼可以监测身高为165 cm至185 cm的人群。

考虑到小腿和大腿前后位置受力变化明显，将四支FBG传感器分别设计在这四处位置。肢体监测结构由TPU材料(该材料导热性能较差，可以保护FBG传感器单元不受人体温度的影响)制作：中间一个凹槽放置FBG栅区(保护和固定)，FBG用502胶、UV胶(保护FBG栅区)固定，之后将其固定在绷带上，绷带受力会紧贴监测者腿部。监测原理如图4所示。

当下肢绷紧时，FBG受到拉应力，中心波长变长；反之，拉应力减小，中心波长变短。监测原理与2.2.1节一致。

本研究的实验是在室温情况下进行的，并且下肢不同点位的监测传感单元已经进行了温度隔绝的措施，并不会受到人体温度的影响，因此不需要对FBG传感器进行温度补偿。

2.3　下肢监测康复装置的设计与分析

2.3.1　下肢装置的运动分析

图5为右腿运动分析示意图，表1列出了D-H参数，下肢外骨骼结构的右腿和左腿分析原理一致。

表示正运动学：在标准D-H参数法中，d_i表示两Z轴之间的垂直距离，相邻连杆坐标系{i-1}与{i}之间的齐次变换矩阵

$ {}_{i+1}{}^{i}{\boldsymbol{T}} $

可表示为

$ {{}_{i+1}{}^{i}{\boldsymbol{T}}=\left[ \begin{array}{cccc}\cos{\theta }_{i} & -\cos{\alpha }_{i}\sin{\theta }_{i} & \sin{\alpha }_{i}\sin{\theta }_{i} & {\alpha }_{i}\cos{\theta }_{i}\\\sin{\theta }_{i}& \cos{\alpha }_{i}\cos{\theta }_{i}& -\sin{\alpha }_{i}\cos{\theta }_{i}& {\alpha }_{i}\sin{\theta }_{i}\\0& \sin{\alpha }_{i}& \cos{\alpha }_{i}& {d}_{i}\\ 0& 0& 0& 1\end{array} \right]\;.} $

(5)

利用表1中数据和式(5)得到外骨骼各关节间的齐次变换矩阵，由此可以得到外骨骼的位姿变换矩阵：

$ { }_3^0 {\boldsymbol{T}}={ }_1^0 {\boldsymbol{T}} \cdot{ }_2^1 {\boldsymbol{T}} \cdot{ }_3^2 {\boldsymbol{T}}=\left[\begin{array}{cccc}n_x & o_x & a_x & p_x \\n_y & o_y & a_y & p_y \\n_{\textit{z}} & o_{\textit{z}} & a_{\textit{z}} & p_{\textit{z}} \\0 & 0 & 0 & 1\end{array}\right]\;, $

(6)

$ \left\{\begin{array}{l}{n}_{x}=\sin{\theta }_{1}-\cos{\theta }_{1}\cos{\theta }_{2}\sin{\theta }_{3}-\cos{\theta }_{1}\cos{\theta }_{2}\sin{\theta }_{3}\\ {n}_{y}=-\cos{\theta }_{1}-\cos{\theta }_{2}\sin{\theta }_{1}\sin{\theta }_{3}-\cos{\theta }_{3}\sin{\theta }_{1}\sin{\theta }_{2}\\ {n}_{\textit{z}}=\cos({\theta }_{2}+{\theta }_{3})\\ {o}_{x}=\cos({\theta }_{2}+{\theta }_{3})\cos{\theta }_{1}\\ {o}_{y}=\cos\left({\theta }_{2}+{\theta }_{3}\right)\sin{\theta }_{1}\\ {o}_{\textit{z}}=\sin\left({\theta }_{2}+{\theta }_{3}\right)\\ {a}_{x}=-\sin{\theta }_{1}-\cos{\theta }_{1}\cos{\theta }_{2}\sin{\theta }_{3}-\cos{\theta }_{1}\cos{\theta }_{3}\sin{\theta }_{2}\\ {a}_{y}=\cos{\theta }_{1}-\cos{\theta }_{2}\sin{\theta }_{1}\sin{\theta }_{3}-\cos{\theta }_{3}\sin{\theta }_{1}\sin{\theta }_{2}\\ {a}_{\textit{z}}=\cos({\theta }_{2}+{\theta }_{3})\\ {p}_{x}=-{a}_{2}\cos{\theta }_{1}\sin{\theta }_{2}-{a}_{3}\cos{\theta }_{1}\cos{\theta }_{2}\sin{\theta }_{3}\\ \qquad -{a}_{3}\cos{\theta }_{1}\cos{\theta }_{3}\sin{\theta }_{2}\\ {p}_{y}=-{a}_{2}\sin{\theta }_{1}\sin{\theta }_{2}-{a}_{3}\cos{\theta }_{2}\sin{\theta }_{1}\sin{\theta }_{3}\\ \qquad -{a}_{3}\cos{\theta }_{3}\sin{\theta }_{1}\sin{\theta }_{2}\\ {p}_{\textit{z}}={a}_{2}\cos{\theta }_{2}+{a}_{3}\cos{\theta }_{2}\cos{\theta }_{3}+{d}_{1}\end{array}\right.\;, $

(7)

$ \left\{\begin{split} &{\boldsymbol{p}}=\left[\begin{array}{l}{p}_{x}\\ {p}_{y}\\ {p}_{\textit{z}}\end{array}\right]\;\\&{\boldsymbol{R}}=\left[\begin{array}{ccc}{n}_{x}& {o}_{x}& {a}_{x}\\ {n}_{y}& {o}_{y}& {a}_{y}\\ {n}_{\textit{z}} & {o}_{\textit{z}}& {a}_{\textit{z}}\end{array}\right]\end{split}\right.\;. $

(8)

逆运动学：

$ \left\{\begin{array}{l}{\theta }_{1}=-{\mathrm{arctan}}\left(\dfrac{{p}_{y}-{a}_{2}{n}_{y}}{{a}_{2}{n}_{x}-{p}_{x}}\right)\\{\theta }_{2}=0.5{\mathrm{arctan}}\left(\dfrac{{o}_{\textit{z}}}{\cos{\theta }_{1}{o}_{x}+\sin{\theta }_{1}{o}_{y}}\right)\\{\theta }_{3}={\mathrm{arctan}}\left(\dfrac{\sin{\theta }_{1}{n}_{x}-\cos{\theta }_{1}{n}_{y}}{\cos{\theta }_{1}{a}_{y}-\sin{\theta }_{1}{a}_{x}}\right)\end{array}\right.\;, $

(9)

式中：

$ {\theta }_{1} $

、

$ {\theta }_{2} $

、

$ {\theta }_{3} $

∈[−20°, 20°]。

2.3.2　下肢装置的结构分析

下肢的组成和作用如表2所示，设计的下肢外骨骼特点如表3所示。

使用ANSYS分析软件对主要支撑结构进行受力分析(应变分析)，如图6所示。

通过对下肢外骨骼装置进行受力分析可知下肢外骨骼不会明显变形(以标定实验50 N为仿真的施加力)。

2.4　下肢装置的步态分析

人体运动的步态如图7、图8所示。

人体运动可以通过步态参数-步距、步高进行判断。

通过上述理论可以得到步距L、步高H参数公式如式(10)所示。

$ \left\{\begin{array}{l}{L}_{1}\mathrm{sin}{\theta }_{1}+{L}_{2}\mathrm{sin}{\theta }_{2}+{L}_{3}\mathrm{sin}{\theta }_{3}=L\\ \left({L}_{1}+{L}_{2}+{L}_{3}\right)-\big({L}_{1}\mathrm{cos}{\theta }_{1}+{L}_{2}\mathrm{cos}{\theta }_{2}\\\qquad \qquad\quad\;\; +{L}_{3}\mathrm{cos}{\theta }_{3}\big)=H\end{array}\right.\;. $

(10)

根据式(10)可得式(11)：

$ \left\{\begin{array}{l}{L}_{i}=\displaystyle{\sum} _{i=1}^{+\infty }{L}_{i}\;(i\in {\mathrm{Z}})\\ \left({L}_{1}+{L}_{2}+{L}_{3}\right)-\big({L}_{1}\mathrm{cos}{\theta }_{1}+{L}_{2}\mathrm{cos}{\theta }_{2}\\\qquad \qquad\quad\;\;+{L}_{3}\mathrm{cos}{\theta }_{3}\big)=H\end{array}\right.\;. $

(11)

脚长为30 cm，小腿长为42 cm，大腿长为45 cm，运动过程中脚、小腿、大腿转动范围为[0°, 30°]。假设脚、小腿、大腿的旋转角度一次改变1° (图9(b)横坐标取三个角度的平均值)，同时增大或者减小，三个初始角度为0°。根据式(10)，进行理论步距-步高的仿真，如图9所示。

根据图9(a)数据可知，建立的该步距-步高理论模型可以反馈出正常的下肢运动情况。根据图9(b)可知，随着角度的变化，步高在升高，反之，角度减小，步高降低。将下肢简化为如图9(c)所示的下肢简化模型，对其进行运动学仿真确定下肢运动时，步高的变化情况，根据图9(d)步高仿真数据可知，大腿质心的高度随时间变化，呈周期性变化。

随着下肢各个部位的角度增大，肢体传递给监测装置的力增大，其变化角度增大，反之减小。则根据式(10)得到式(12)：

$ {\mathrm{arccos}}\frac{\left({L}_{1}+{L}_{2}+{L}_{3}\right)-\left({L}_{3}\mathrm{cos}{\theta }_{3}+{L}_{2}\mathrm{cos}{\theta }_{2}\right)-H}{{L}_{1}}={\theta }_{1}\;, $

(12)

$ \mathrm{\Delta }\theta ={K}_{\theta }{\theta }_{1}\;. $

(13)

脚、小腿、大腿的角度变化和监测装置的形变角度存在一定的线性关系，

$ {K}_{\theta } $

取决于每个人的下肢情况。

根据式(4)、(12)、(13)可知脚第一点位如式(14)所示；同理可得小腿、大腿第一点位如式(15)和式(16)所示。

可知，随着脚、小腿、大腿的运动角度增大，波长的变化增大。式(14)~式(16)分别针对下肢三个部位的第一点位。第二点位刚好相反，如式(17)所示。

根据式(4)、(12)、(17)可得脚、小腿、大腿第二点位的关系式，如式(18)~式(20)所示。

根据式(18)、(19)、(20)可知，第二点位的传感器波长随着角度的增大而减小。

$ \dfrac{{\mathrm{\Delta }\lambda }_{1}}{{\lambda }_{1}}={K}_{\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}{K}_{\theta }{\theta }_{1}}-{b}_{1}\right)\dfrac{F}{E{a}_{1}}={K}_{\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}\left({K}_{\theta }{\mathrm{arccos}}({\left({L}_{1}+{L}_{2}+{L}_{3}\right)-\left({L}_{1}\mathrm{cos}{\theta }_{1}+{L}_{2}\mathrm{cos}{\theta }_{2}\right)-H})/{{L}_{3}}\right)}-{b}_{1}\right)\dfrac{F}{E{a}_{1}}\;, $

(14)

$ \dfrac{{\mathrm{\Delta }\lambda }_{3}}{{\lambda }_{3}}={K}_{\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}{K}_{\theta }{\theta }_{3}}-{b}_{1}\right)\dfrac{F}{E{a}_{1}}={K}_{\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}\left({K}_{\theta }{\mathrm{arccos}}({\left({L}_{1}+{L}_{2}+{L}_{3}\right)-\left({L}_{1}\mathrm{cos}{\theta }_{1}+{L}_{3}\mathrm{cos}{\theta }_{3}\right)-H})/{{L}_{2}}\right)}-{b}_{1}\right)\dfrac{F}{E{a}_{1}} \;,$

(15)

$ \dfrac{{\mathrm{\Delta }\lambda }_{5}}{{\lambda }_{5}}={K}_{\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}{K}_{\theta }{\theta }_{5}}-{b}_{1}\right)\dfrac{F}{E{a}_{1}}={K}_{\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}\left({K}_{\theta }{\mathrm{arccos}}({\left({L}_{1}+{L}_{2}+{L}_{3}\right)-\left({L}_{2}\mathrm{cos}{\theta }_{2}+{L}_{3}\mathrm{cos}{\theta }_{3}\right)-H})/{{L}_{1}}\right)}-{b}_{1}\right)\dfrac{F}{E{a}_{1}} \;,$

(16)

$ \mathrm{\Delta }\theta =\frac{{\theta }_{1}}{{K}_{\theta }}\;, $

(17)

$ \dfrac{{\mathrm{\Delta }\lambda }_{2}}{{\lambda }_{2}}={K_\varepsilon} {\left(\dfrac{{b}_{1}}{\mathrm{cos}({{\theta }_{2}}/{{K}_{\theta }})}-{b}_{1}\right)\dfrac{F}{E{a}_{1}}=}{K_\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}\left(({{\mathrm{arccos}}({\left({L}_{1}+{L}_{2}+{L}_{3}\right)-\left({L}_{1}\mathrm{cos}{\theta }_{1}+{L}_{2}\mathrm{cos}{\theta }_{2}\right)-H})/{{L}_{3}}})/{{K}_{\theta }}\right)}-{b}_{1}\right)\dfrac{F}{E{a}_{1}}\;, $

(18)

$ \dfrac{{\mathrm{\Delta }\lambda }_{4}}{{\lambda }_{4}}={K}_{\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}({{\theta }_{4}}/{{K}_{\theta }})}-{b}_{1}\right)\dfrac{F}{E{a}_{1}}={K}_{\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}\left(({{\mathrm{arccos}}({\left({L}_{1}+{L}_{2}+{L}_{3}\right)-\left({L}_{1}\mathrm{cos}{\theta }_{1}+{L}_{3}\mathrm{cos}{\theta }_{3}\right)-H})/{{L}_{2}}})/{{K}_{\theta }}\right)}-{b}_{1}\right)\dfrac{F}{E{a}_{1}}\;, $

(19)

$ \dfrac{{\mathrm{\Delta }\lambda }_{6}}{{\lambda }_{6}}={K}_{\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}({{\theta }_{6}}/{{K}_{\theta }})}-{b}_{1}\right)\dfrac{F}{E{a}_{1}}={K}_{\varepsilon }\left(\dfrac{{b}_{1}}{\mathrm{cos}\left(({{\mathrm{arccos}}({\left({L}_{1}+{L}_{2}+{L}_{3}\right)-\left({L}_{3}\mathrm{cos}{\theta }_{3}+{L}_{2}\mathrm{cos}{\theta }_{2}\right)-H})/{{L}_{1}}})/{{K}_{\theta }}\right)}-{b}_{1}\right)\dfrac{F}{E{a}_{1}}\;. $

(20)

2.5　下肢监测助力单元的设计

下肢监测装置中的步进电机为其提供动力，在踝关节和膝关节设置了两个42电机，根据之前监测的情况设定参数进行驱动辅助(电机电源为12 V电池，实验者通过手动操作电机控制器让电机正向旋转或者反向旋转，对实验者提供抬腿和收腿的助力)。下肢外骨骼装置如图10所示，LABVIEW上位机界面如图11所示。

上位机读取到数据进行分析并展示在上位机界面上。图12是下肢外骨骼的整体监测系统。其中信息模块是对步态状况评价方法的设计，该设计根据实际情况设定。

使用LABVIEW上位机界面展示康复情况。将3组监测数据综合分析，如果数值超过阈值，指示灯亮起，说明志愿者下肢存在问题，反之则没有问题。

$ ({{x}_{1}+{x}_{3}+{x}_{5}})/{3} $

为下肢数据分析系统的纵坐标，横坐标为时间。

$ 0.9{\mathrm{C}} $

是阈值(根据2.4节的分析，

$ J\geqslant 0.9 $

属于强相关，表明步伐间隔具有规律性、步态稳定、脚步落地和起步的配合非常好。因此选择0.9作为C的系数)。文中给出的评价指标是单一分析得出的，针对不同病情和要求可以将其阈值进行贴合实际的计算确定。C是常数，因为志愿者是正常人，因此取任意常数如256作为C值(

$ 256\times 0.9=230.4 $

)。

$ \left\{\begin{array}{l}{\lambda }_{\max1}-{\lambda }_{\min1}=\Delta {\lambda }_{1}\\{x}_{1}=\dfrac{230.4({\lambda }_{\max1}-{\lambda }_{1})}{\mathrm{\Delta }{\lambda }_{1}}\end{array}\right.\;, $

(21)

式中：

$ {\lambda }_{\max1} $

是右脚第一点位的第一周期的最长波长(对应

$ 230.4 $

)；

$ {\lambda }_{\min1} $

是右脚第一点位的第一周期的最短波长(对应0)；

$ {\lambda }_{1} $

是实际监测的波长；

$ {x}_{1} $

是右脚第一点位的数值。对应右小腿第一点位和右大腿第一点位的数值

$ {x}_{3} $

、

$ {x}_{5} $

推导与其一致。根据式(21)可得式(22)。

$ \left\{\begin{array}{l}\dfrac{{x}_{1}+{x}_{3}+{x}_{5}}{3} \gt 230.4\;(出现问题)\\ \dfrac{{x}_{1}+{x}_{3}+{x}_{5}}{3}\leqslant 230.4\;(没有问题)\end{array}\right.\;. $

(22)

3　实验研究

收起

FBG传感器初始中心波长如表4所示。左下肢和右下肢对应的监测点位的FBG中心波长一致，每个光纤光栅的栅区长度为10 mm，反射率大于90%，3 dB带宽≤0.25 nm。实验中光纤光栅解调仪的型号为HB-FBG-1000-8，以35 Hz频率进行FBG中心波长数据的保存。

3.1　标定实验

对足底压力监测结构和腿部运动监测结构进行“加载”和“卸载”的力标定，使用电子拉伸机(C65.102)，范围为[0 N，50 N]，每5 N监测一次，如图13所示。得到监测数据如图14、表5所示。

传感单元的力灵敏度都在9.9 pm/N以上，拟合优度都在0.9906上。

3.2　下肢运动监测实验

使用下肢康复外骨骼监测装置进行监测，实验者为一名25岁的男子，其身高为175 cm，体重为72 kg。如图15所示，纵坐标为FBG中心波长的改变量。

下肢第一点位在开始是波长上升，第二点位在开始是波长下降。随着志愿者的运动，所有点位的波长随时间周期性变化。实际监测的下肢各个点位的波形变化情况与2.4节中的式(14)、(15)、(16)、(18)、(19)、(20)的分析一致。根据式(23)、(24)可以得到下肢监测数据的均值和标准差。

$ \mu =\frac{1}{n}\sum _{i=1}^{n}{x}_{i}\;, $

(23)

$ \sigma=\sqrt{\frac{1}{N}\sum_{i=1}^n(x_i-\mu)^2}\; ， $

(24)

式中：

$ {x}_{i} $

是下肢运动引起的FBG中心波长变量；N是监测数据的总量。

由表6可知，下肢左右腿的步态数据较为稳定。

3.3　实验对比分析

该节的实验者与3.2节的实验者为同一人。

下肢外骨骼右腿装置的脚、小腿和大腿处放置了三个IMU传感器，用于监测角度的变化，右腿上升和下降各监测五个点(以大腿角度为基准)。根据式(11)可得理论步距-步高，对比实际步距-步高(以右脚监测装置的中心为点监测-该点用红色标记)，如图16、表7所示。

根据表7数据可知，实际步距-步高对比理论步距-步高的模型的误差低于10%，误差在合理范围内。证明了监测装置具有良好的监测性能，也再次验证了理论模型的合理性以及2.2节监测数据的准确性。

3.4　步态数据分析

步态正常与否的判断可以由步态节奏(J)进行分析确定。

步态节奏是指步伐间隔的规律性、步态周期的稳定性、脚步落地和起步的配合。皮尔逊相关性分析方法可以求得数据之间的规律、周期性。使用皮尔逊分析方法对其进行表征(皮尔逊相关系数大于0.9时，属于强相关)，如式(25)所示。

$ J=\frac{n(\sum xy)-(\sum x\left)\right(\sum y)}{\sqrt{[n\sum {x}^{2}-(\sum {x)}^{2}\left]\right[n\sum {y}^{2}-(\sum {y)}^{2}]}}\;, $

(25)

式中：n是数据点的数量；x是右下肢相应监测点的FBG传感器的波长变量；y是左下肢相应监测点的FBG传感器的波长变量(对应右下肢的监测点)。

$ J\geqslant 0.9 $

属于强相关，表明步伐间隔具有规律性、步态稳定、脚步落地和起步的配合非常好。

将监测得到的数据(3.2节)利用判别方法进行判别，如图17所示。

根据表8可知，相应点位是强相关的，证明下肢步伐的间隔具有规律性、脚步落地和起步的配合较好。

4　结　论

收起

通过理论和仿真分析可知，光纤光栅下肢外骨骼的步态监测装置可适用于不同体型(身高为165~185 cm，脚码为37~45码)的人群。利用机构学建立了下肢监测模型，经理论仿真和运动学仿真分析, 揭示了步距和步高参数影响FBG中心波长变化的规律。志愿者穿戴好下肢外骨骼之后进行步态实验，得到监测点位的波长变化符合正常步态变化，与2.4节中的理论模型(式(14)、(15)、(16)、(18)、(19)、(20))分析一致，对应数据的均值和标准差也反映了监测的步态数据具有一定的稳定性。理论模型的步高-步距与实际步高-步距的误差在10%以内，证明了该模型具有一定的合理性。实验研究结果表明，下肢步态节奏为0.9379，可以监测出正常志愿者的步态，且该装置具有一定的助力功能。结合上位机可以对监测数据进行预警反馈。

参考文献

收起

文献

收起

参考文献引证文献

排序方式：

Wu Q C, Wang Z J, Chen Y, et al. Barrier Lyapunov function-based fuzzy adaptive admittance control of an upper limb exoskeleton using RBFNN compensation[J]. IEEE/ASME Trans Mech, 2025, 30(1): 3−14.

Zou C B, Peng Z N, Zhang L, et al. Optimization-based adaptive assistance for lower limb exoskeleton robots with a robotic walker via spatially quantized gait[J]. IEEE Trans Autom Sci Eng, 2025, 22: 2806−2818.

Belal M, Alsheikh N, Aljarah A, et al. Deep learning approaches for enhanced lower-limb exoskeleton control: a review[J]. IEEE Access, 2024, 12: 143883−143907.

Chmielewski P P, Data K, Strzelec B, et al. Human Aging and age-related diseases: from underlying mechanisms to pro-longevity interventions[J]. Aging Dis, 2024, 16: 1853−1877.

Darmawan S A, Arifin A, Hermawan N. Information systems for remote rehabilitation with live video streaming using A pan tilt zoom camera[C]//Proceedings of 2023 International Seminar on Intelligent Technology and Its Applications (ISITIA), Surabaya, 2023: 399–404. https://doi.org/10.1109/ISITIA59021.2023.10221109.

Yu S Q, Guo J, Guo S X, et al. Design of control system for lower limb rehabilitation robot on the healthy side sEMG signal[C]//Proceedings of 2023 IEEE International Conference on Mechatronics and Automation (ICMA), Harbin, 2023: 1038–1043. https://doi.org/10.1109/ICMA57826.2023.10215624.

Fischer N, Alagi H, Beigl M, et al. A compliant actuator-sensor unit using a shape memory alloy and capacitive force sensing for active exoskeleton interfaces[C]//Proceedings of 2023 IEEE-RAS 22nd International Conference on Humanoid Robots (Humanoids), Austin, 2023: 1–7. https://doi.org/10.1109/Humanoids57100.2023.10375226.

Zhang J, Wei Q. An 8-FBGs pressure pad for COP measurement of plantar[C]//Proceedings of 2022 IEEE 10th International Conference on Information, Communication and Networks (ICICN), Zhangye, 2022: 460–464. https://doi.org/10.1109/ICICN56848.2022.10006437.

Mahmud S, Khandakar A, Chowdhury M E H, et al. Fiber Bragg gratings based smart insole to measure plantar pressure and temperature[J]. Sens Actuators A: Phys, 2023, 350: 114092.

Lavarda M D, Gomes D F, Paes T, et al. Smart foot based on FBG integrated in composite material and adaptive fuzzy controller[J]. IEEE Sens Lett, 2023, 7(9): 5001004.

Mishra M, Sahu P K, Datta M. Design of an enhanced spatial resolution indoor plantar strain and gait analysis setup for biomedical applications[J]. Eng Res Express, 2024, 6(2): 025332.

Pires-Junior R, Frizera A, Leal-Junior A. Design of an optical fiber embedded smart artificial tendon for deformation monitoring[J]. Opt Fiber Technol, 2023, 80: 103464.

Zheng J J, Zhang S, Liu Y X, et al. High-sensitive double-clad fiber Bragg grating sensors for real-time monitoring of body posture and movement state[J]. IEEE Sens J, 2023, 23(16): 18579−18586.

Alhussein G, Chi H R, Alberto N, et al. Gait-based user identification for smart home: when machine learning meets FBG accelerometers[J]. IEEE Trans Consumer Electron, 2025, 71(1): 2332−2341.

Pulcinelli M, Presti D L, Massaroni C, et al. Wearable elastic band based on 3D-printed fiber Bragg grating sensor for knee joint monitoring[C]//Proceedings of 2024 IEEE International Workshop on Metrology for Industry 4. 0 & IoT (MetroInd4. 0 & IoT), Firenze, 2024: 597–602. https://doi.org/10.1109/MetroInd4.0IoT61288.2024.10584188.

Leal-Junior A, Avellar L, Blanc W, et al. Opto-electronic smart home: heterogeneous optical sensors approaches and artificial intelligence for novel paradigms in remote monitoring[J]. IEEE Internet Things J, 2024, 11(6): 9587−9598.

Rocha M, Nepomuceno A C, Chi H R, et al. Indoor localization using fiber Bragg grating-based accelerometers for smart healthcare[J]. IEEE Trans Consumer Electron, 2024, 70(1): 68−77.

Wang K F, Tian A F, Hao Y P, et al. Development of a high-precision and large-range FBG-based sensor inspired by a crank-slider mechanism for wearable measurement of human knee joint angles[J]. IEEE Trans Med Robot Bionics, 2024, 6(4): 1688−1698.

Rohan R, Venkadeshwaran K, Ranjan P. Recent advancements of fiber Bragg grating sensors in biomedical application: a review[J]. J Opt, 2024, 53(1): 282−293.

Duan W, Chen W H, Wang J H, et al. Gait-generation strategy for lower limb exoskeleton based on central pattern generator[J]. IEEE/ASME Trans Mechatron, 2024, 29(6): 4191−4202.

Kapsalyamov A, Hussain S, Brown N A T, et al. A novel underactuated robotic orthosis for individualized gait rehabilitation[J]. IEEE Trans Med Robot Bionics, 2024, 6(1): 213−223.

Koyama S, Yoda T, Yamamoto M, et al. Verification of optimal installation point of FBG sensor for pulsation strain measurement[J]. IEEE Sens J, 2023, 23(16): 18183−18192.

李群, 陆云才, 邵剑, 等. 基于EpoCore胶裹覆的FBG传感器温度敏感性研究[J]. 光电工程, 2024, 51(12): 240228.

Li Q, Lu Y C, Shao J, et al. Research on temperature sensitivity of FBG sensor based on EpoCore adhesive coated[J]. Opto-Electron Eng, 2024, 51(12): 240228.

曾川, 童杏林, 李泽恺, 等. 基于线型光纤光栅阵列传感的引气管道泄漏研究[J]. 激光技术, 2025, 49(2): 271−277.

Zeng C, Tong X L, Li Z K, et al. A research on the leakage of aircraft duct based on linear fiber grating array[J]. Laser Technol, 2025, 49(2): 271−277.

茶映鹏, 蔡建军, 彭星玲. 基于FBG的薄板空间形状重构误差分析[J]. 光通信研究, 2025, 51(5): 240164.

Cha Y P, Cai J J, Peng X L. Error analysis of spatial shape reconstruction of FBG-based thin plate[J]. Study Opt Commun, 2025, 51(5): 240164.

2026年第53卷第1期

PDF下载

引用本文

BibTeX

文章信息

doi: 10.12086/oee.2026.250124

接收时间：2025-04-27
首发时间：2026-10-22
出版时间：2026-01-25

补充材料

相关文章

文章信息

作者

出版历史

收稿日期：2025-04-27
修回日期：2025-06-21
录用日期：2025-06-25

基金

作者信息

¹上海工程技术大学机械与汽车工程学院机器人研究所，上海 201620

²上海大型构件智能制造机器人技术协同创新中心，上海 201620

通讯作者:

冯艳，xmfy0833@sina.com。

参考文献

分享链接

https://castjournals.cast.org.cn/joweb/oee/CN/10.12086/oee.2026.250124

分享至

全文二维码

扫描看全文

引用本文

BibTeX

本文的引用情况

2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

关闭全屏

BibTeX
EndNote
RefWorks
TxT

Connecting rod/i	$ {\alpha }_{i} $/(°)	$ {a}_{i} $/mm	$ {d}_{i} $/mm	$ {\theta }_{i} $/(°)
1	90	0	$ {d}_{1} $	$ {\theta }_{1} $
2	90	0	$ {d}_{2} $	$ {\theta }_{2} $
3	0	$ {a}_{3} $	0	$ {\theta }_{3} $+90

Connecting rod/i

$ {\alpha }_{i} $

/(°)

$ {a}_{i} $

/mm

$ {d}_{i} $

/mm

$ {\theta }_{i} $

/(°)

$ {d}_{1} $

$ {\theta }_{1} $

$ {d}_{2} $

$ {\theta }_{2} $

$ {a}_{3} $

$ {\theta }_{3} $

+90

Name	Composition	Location	Function
Thigh	Thighbone	From the hip upwards, and from the knee downwards	Support and propel the body
Lower leg	Tibia and fibula	From the knees down to the ankles up	Stabilize and support the body
Foot	Heel, sole, heel of foot, toe region	Below the ankle	Supporting weight, walking, running

Name

Composition

Location

Function

Thigh

Thighbone

From the hip upwards, and from the knee downwards

Support and propel the body

Lower leg

Tibia and fibula

From the knees down to the ankles up

Stabilize and support the body

Foot

Heel, sole, heel of foot, toe region

Below the ankle

Supporting weight, walking, running

Name	Construction	Function
Thigh	Exoskeleton structure, bandage fixation	Improve stability and expand the scope of application
Lower leg	Exoskeleton structure, bandage fixation	Improve stability and expand the scope of application
Foot	Frame structure, cork, bandage fixation	Improve stability and expand the scope of application

Name

Construction

Function

Thigh

Exoskeleton structure, bandage fixation

Improve stability and expand the scope of application

Lower leg

Exoskeleton structure, bandage fixation

Improve stability and expand the scope of application

Foot

Frame structure, cork, bandage fixation

Improve stability and expand the scope of application

	The first point/nm	The second point/nm
Foot	1546	1550
Lower leg	1548	1550
Thigh	1546	1550

The first point/nm

The second point/nm

Foot

1546

1550

Lower leg

1548

1550

Thigh

1546

1550

Corresponding point	Right leg
The first part of the foot	13.6	0.9963	13.4	0.9967
The second part of the foot	13.9	0.9984	13.5	0.9991
The first part of the lower leg	10.1	0.9962	10.1	0.9946
The second part of the lower leg	10.1	0.9989	10.2	0.9965
The first part of the thigh	9.9	0.9977	10.2	0.9954
The second part of the thigh	10.1	0.9991	10.0	0.9906

Corresponding point

Right leg

Left leg

Sensitivity/(pm/N)

R²

Sensitivity/(pm/N)

R²

The first part of the foot

13.6

0.9963

13.4

0.9967

The second part of the foot

13.9

0.9984

13.5

0.9991

The first part of the lower leg

10.1

0.9962

10.1

0.9946

The second part of
the lower leg

10.1

0.9989

10.2

0.9965

The first part of the thigh

9.9

0.9977

10.2

0.9954

The second part of the thigh

10.1

0.9991

10.0

0.9906

	Right foot	Right lower leg	Right thigh	Left foot	Left lower leg	Left thigh
$ \mu $	0.34	0.59	0.62	0.55	0.76	0.71
$ \sigma $	0.01	0.01	0.01	0.01	0.01	0.01

Right foot

Right lower leg

Right thigh

Left foot

Left lower leg

Left thigh

$ \mu $

0.34

0.59

0.62

0.55

0.76

0.71

$ \sigma $

0.01

Angle/(°)	Theoretical step pitch/cm	Theoretical step high/cm	Actual step pitch/cm	Actual step high/cm	Step pitch error/%	Step high error/%
0	0	0	0	0	0	0	0	0
5	3.5	9.3	11.33	0.64	11.01	0.59	2.8	7.8
10	8.9	18.2	21.11	2.69	20.5	2.61	2.9	3.0
15	14.1	13.4	28.83	3.62	27.8	3.88	3.6	6.7
20	18.8	3.4	30.71	5.01	31.2	5.12	1.6	2.2

Angle/(°)

Theoretical step
pitch/cm

Theoretical step
high/cm

Actual step
pitch/cm

Actual step
high/cm

Step pitch
error/%

Step high
error/%

Thigh

Lower leg

Foot

3.5

9.3

11.33

0.64

11.01

0.59

2.8

7.8

8.9

18.2

21.11

2.69

20.5

2.61

2.9

3.0

14.1

13.4

28.83

3.62

27.8

3.88

3.6

6.7

18.8

3.4

30.71

5.01

31.2

5.12

1.6

2.2

	Foot	Lower leg	Thigh	Average
J	0.9374	0.9228	0.9534	0.9379

Foot

Lower leg

Thigh

Average

0.9374

0.9228

0.9534

0.9379