Abstract—The paper carries out finite element analysis and lightweight design of the lower extremity exoskeleton of a gait rehabilitation training robot. PRO/E is used to model and assemble the whole machine of the lower extremity exoskeleton. ANSYS Workbench is used to build the finite element model of the lower extremity exoskeleton. The intensity and rigidity of critical components of the lower extremity exoskeleton are checked. The rigidity of bulk structure of the lower extremity exoskeleton is analyzed, and the integral rigidity characteristic is obtained. At the same time, the first ten natural frequencies and the mode shapes of the lower extremity exoskeleton are obtained by modal analysis, which provides the important modal parameter and avoids resonance. From the above analytic results, the lower extremity exoskeleton has plenty of space to optimize and improve its structure. The structure of the drive connection block is improved when the physical model appears the looseness. The incompact physical model structure causes laterality of the lower extremity exoskeleton, so the paper puts forward the optimization scheme of the lower extremity exoskeleton which has the compact structure of joints. In order to make it reach the lightweight design of the lower extremity exoskeleton under the condition of meeting the request for the intensity, rigidity, vibration characteristics and rehabilitation training.

I. INTRODUCTION ower extremity exoskeleton is a new type of the mechanical device which can be wearable. From the

theoretical viewpoint of man-machine integrated and intelligent system, it is a man-machine integrated system of human host and machine assistant [1]. At present, typical robots of the lower extremity exoskeleton in abroad are BLEEX [2], LOKOMAT [3] and XOS [4] developed by SARCOS company. The robot of lower body rehabilitation training developed by our laboratory is used to help people who are gait disorder or similar patients to do rehabilitation training, it is consist of the lower extremity exoskeleton, a

This work was supported in part by the Natural Science Foundation of

China (NSFC 50975165, 51275282), Program of Shanghai Subject Chief Scientist (PSSCS 10XD1401900) and Innovation Group Project from Shanghai Education Commission.

Baijun Ding is with the Laboratory of Intelligent Machine and System School of Mechatronics Engineering and Automation, Shanghai University, phone: +86-137-0169-4830, China; (e-mail:baijunding_22@126.com).

Jinwu Qian, corresponding author, is with the Laboratory of Intelligent Machine and System School of Mechatronics Engineering and Automation, Shanghai University, phone: +86-021-56331783, fax: +86-021-56331783, China; (e-mail: jwqian@shu.edu.cn).

Linyong Shen is with the Laboratory of Intelligent Machine and System School of Mechatronics Engineering and Automation, Shanghai University, phone: +86-021-56331783, fax: +86-021-56331783, China; (e-mail: shenlycn@163.com).

Yanan Zhang is with the Laboratory of Intelligent Machine and System School of Mechatronics Engineering and Automation, Shanghai University, phone: +86-021-56331783, fax: +86-021-56331783, China; (e-mail: ynzhang@mail.shu.edu.cn).

weight loss device, a treadmill and the control system. BLEEX and XOS are a kind of lower extremity exoskeleton robot which can improve the function of human body, their objects are normal people, rather than patients, and don’t need the treadmill to participate in work. The lower limb exoskeleton robot developed by our laboratory is used to assist patients to do rehabilitation training like the LOKOMAT. But it has the difference with the LOKOMAT, the lower limb exoskeleton robot developed by our laboratory has more an ankle freedom than the LOKOMAT, which is more accord with the law of human walking. The lower extremity exoskeleton is an important part of the lower body rehabilitation training robot, its intensity and rigidity of good or bad not only affect their working performance, useful life, but also affect the effect of rehabilitation of patients. Reasonably optimizing the lower extremity exoskeleton structure to ensure the sufficient intensity, rigidity and good dynamic characteristics, and ultimately to achieve the lightweight design. Therefore, the finite element analysis about stress, deformation and vibration characteristics of the lower extremity exoskeleton has important and practical significance.

The paper applies the method of the finite element analysis, ANSYS Workbench (hereinafter referred to as AWE) is used to create the finite element model of the lower extremity exoskeleton and calculate the intensity and rigidity of key parts of the lower extremity exoskeleton, the maximum stress and the total deformation displacement are obtained, in order to check the intensity and rigidity of the key parts; The rigidity of bulk structure of the lower extremity exoskeleton is analyzed, and the integral rigidity characteristic is obtained; The natural frequencies and mode shapes of the lower extremity exoskeleton are obtained by modal analysis, in order to avoid resonance; From the above analytic results, the lower extremity exoskeleton has plenty of space to optimize and improve its structure. The structure of the drive connection block is improved when the physical model appears the looseness. The incompact physical model structure causes laterality of the lower extremity exoskeleton, so the paper puts forward the optimization scheme of the lower extremity exoskeleton which has the compact structure of joint. In order to make it reach the lightweight design of lower extremity exoskeleton under the condition of meeting the request for the intensity, rigidity, vibration characteristics and rehabilitation training.

II. BUILD FINITE ELEMENT MODEL

A. Build the CAD Model In this paper, the lower extremity exoskeleton have two

mechanical legs, each mechanical leg has three rotational degrees of freedom. Each joint has one degree of freedom.

Finite element analysis and optimized design of exoskeleton for lower extremity rehabilitation training

Baijun Ding, Jinwu Qian, Linyong Shen, Yanan Zhang Shanghai University

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978-1-4673-2127-3/12/$31.00 © 2012 IEEE 1397

Proceedings of the 2012 IEEEInternational Conference on Robotics and Biomimetics

December 11-14, 2012, Guangzhou, China

Owing to two mechanical legs are completely symmetrical, so the single leg is modeled and analyzed. In this article, the primary parts of the lower extremity exoskeleton are modeled and assembled by using the powerful 3D modeling software PRO/E. Due to analyze the bulk structure, taking into account a number of small features which have little effect on the performance of the overall structure. Therefore, based on the Saint-Venant principle, the paper properly simplifies the part’s local features, such as the thread, the chamfer, screw holes and so on [5]. At the same time, in order to balance the calculation accuracy and the computational time of AWE, the paper omits the connecting accessories (screws, nuts) which have little effect of the overall rigidity and the vibration frequency. The single leg of the lower extremity exoskeleton is shown in Fig. 1. After utilizing the dedicated seamless interface with AWE, the whole lower extremity exoskeleton is imported into AWE, paying particularly attention to the consistency of units. This method utilizes the specialized interface to combine with PRO/E and AWE, which achieves the seamless connection. Therefore elements are not basically lost in the model transferring process.

Fig. 1. The single leg of exoskeleton

B. Finite Element Modeling After the model of lower extremity exoskeleton is

imported into AWE, taking into account the consistency of the actual model materials. Besides the material of the shoe is selected the plastic, the remaining parts are selected LY12 aluminum alloy, and its performance parameters are shown in Table I.

TABLE I PERFORMANCE PARAMETERS OF LY12

Parameters Numerical Value

Modulus of elasticity Poisson's ratio

Density Tensile strength

Yield strength

AWE will automatically detects the assemble relation of

the lower extremity exoskeleton. Therefore, it selects the default binding connection in the contact setting. This paper uses the Solid187 and Solid45 mixed unit when the lower extremity exoskeleton is automatically meshed, which consists of 127352 nodes and 61177 units.

C. Determination of Constraint and Load In view of the whole robot system, the lower extremity

exoskeleton is fixed on a parallelogram mechanism, which can only move up and down with the body's center of gravity in the vertical direction. Moreover, the hip rod is fixed in the

sagittal plane and direction relative to the parallelogram mechanism. Therefore, the hip fixed rod’s rear end face is added the fixed constraint; Because the patients are fixed with the mechanical leg in the rehabilitation process, therefore, three forces are simulated instead of the thigh, the shank and the foot; And as a result of the analysis object is the whole structure of the mechanical leg and the drive, therefore, without considering the driving forces which operate the external skeleton in the analysis of the static intensity and rigidity. The finite element model of the lower extremity exoskeleton is established as shown in Fig. 2, which includes the grid model and the condition of constraint and load.

Fig. 2. The finite element model of exoskeleton

III. ANALYSIS OF THE STATIC INTENSITY AND RIGIDITY At present, for the general machinery manufacturing, the

safety factor of thermoplastic materials is desirable: under the static loads. Because LY12 is a

thermoplastic material, this article only studies the forces when the lower extremity exoskeleton is static, so take

. For plastic materials which have not obvious yield limit, they can produce 0.2% plastic strain stress as the yield guideline [6], so

In the form of yield failure, carbon steel, copper, aluminum and other plastic materials should adopt the maximum shear stress theory (the third strength theory) and the distortion energy density theory (the fourth strength theory) to check [7].

(1)

(2)

A. Check the Intensity and Rigidity of Key Parts Due to the lower extremity exoskeleton has more parts, in

terms of components not received the driving force, its intensity and rigidity are fully consistent with the requirements. Therefore, this article selects several key parts which are directly functioned to check its intensity and rigidity. The mesh partition units of parts adopt the tetrahedral unit solid187 and the Patch Conforming Method.

Fig. 3. The grid model and constraint load of the hip drive suspension block

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The grid model and the constraint load of the hip drive suspension block is shown in Fig. 3, through the calculation of AWE’s analysis module to obtain a series of corresponding stress, deformation and displacement.

By adding the Shear Stress and the Equivalent Stress, AWE can respectively calculate the shear stress and the equivalent stress value. They are referred to above the third and the fourth strength theory value. Accordingly there is no need to calculate three major principal stress. All kinds of the cloudy images of the hip drive suspension block are shown in Fig. 4, the analytic result is shown in table II. represent the maximum shear stress, represent the maximum equivalent stress, represent the maximum total deformation, represent the minimum safety factor, locations are unsafe when it is less than 1.

Fig. 4. The cloudy images of the hip drive suspension block

TABLE II

ANALYTIC RESULT OF THE HIP DRIVE SUSPENSION BLOCK

Parameters Result

Satisfy the third strength Satisfy the fourth strength

Satisfy rigidity Safety

All kinds of cloudy images of the hip drive connection

block are shown in Fig. 5, the analytic result is shown in table III.

Fig. 5. The cloudy images of the hip drive connection block

TABLE III

ANALYTIC RESULT OF THE HIP DRIVE CONNECTION BLOCK

Parameters Result

Satisfy the third strength Satisfy the fourth strength

Satisfy rigidity Safety

All kinds of cloudy images of the ankle drive connection

block are shown in Fig. 6. The analytic result is shown in table IV.

Fig. 6. The cloudy images of the ankle drive connection block

TABLE IV

ANALYTIC RESULT OF THE ANKLE DRIVE CONNECTION BLOCK

Parameters Result Satisfy the third strength

Satisfy the fourth strength

Satisfy rigidity

Safety

By analyzing the key parts of the lower extremity

exoskeleton we know that the various components are accorded with the requirement of the intensity and rigidity. Moreover, the maximum equivalent stress doesn’t far reach the maximum yield limit, the maximum total deformation is very small, that are completely under the condition of deformation range. So it has more space to optimize and improve its structure in the next optimization design, and ultimately to achieve the lightweight design of the lower extremity exoskeleton.

B. Rigidity Analysis of External Skeleton By analyzing the intensity and rigidity of the lower

extremity exoskeleton’s various parts, we can draw the conclusion that exoskeleton’s components have good rigidity. But this is not sufficient to explain the exoskeleton structure has good rigidity, so this article analyzes the rigidity of the bulk structure of the lower extremity exoskeleton. According to the above finite element analytic model, the cloudy images of the whole structure’s deformation displacement are calculated by the analysis module of AWE, as shown in Fig. 7.

From the chart we can see that the maximum displacement appears on the shoe, this is because of the hip fixed rod’s rear end face is added the fixed constraint. From the whole model, the mechanical leg is equivalent to a free hanging rod. Table V shows the overall deformation result of the lower extremity exoskeleton. represent the maximum total deformation, represent the maximum deformation of X direction, represent the maximum deformation of Y direction, represent the maximum deformation of Z direction.

From the analytic result, we can see that the whole deformation of the lower extremity exoskeleton’s shoe end is very small, the deformation is under the withstand deformation range. Therefore, from the overall deformation we can draw the conclusion that the lower extremity exoskeleton has the sufficient static rigidity, it has plenty of space to optimize and improve its structure.

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Fig. 7. The cloudy images of exoskeleton’s whole deformation

TABLE V

ANALYTIC RESULT OF EXOSKELETON’S WHOLE STRUCTURE

Symbol Deformation (mm) Description of Deformation

0.91719 Fluctuant and lateral swing 0.61404 X direction to lateral swing

0.28701 0.65410

Y direction to swing Z direction to fluctuant swing

IV. MODAL ANALYSIS OF THE WHOLE EXOSKELETON According to the vibration theory, multiple degrees of

freedom system with a certain natural frequency vibration presents the vibration form, which is called the mode. The displacement of the system exist certain proportional relation, called the natural mode of vibration. The core of modal analysis is to ascertain and describe the dynamic parameters of the structural system. For the vibrational coefficient of N degrees of freedom, its un-damped free vibration equation can be expressed as:

(3) Among them, represent the mass matrix, represent the rigidity matrix, represent the response vector. Due to the free vibration can be decomposed into a series of simple harmonic vibration, so it can be expressed as a formula:

(4) In the formula 4, represent the natural frequency of the simple harmonic vibration, represent the amplitude column vector of the node displacement. Formula 4 is enclosed into formula 3, by eliminating the factor we can have:

(5) By formula 5, we can calculate N eigenvalues:

and the corresponding N eigenvectors: . The square root of characteristic value:

represent the i modal shape of structure. All of constitute the natural mode of matrix [8].

The modal analysis of structure generally needn’t to calculate all the inherent frequency and the vibration model, conversely should consider the frequency when the system is working. Usually only the low order natural frequency may cause system’s resonance. In this paper, the result of the static intensity and rigidity is regarded as the prestressed condition of the modal analysis [9] [10], the calculated result is more close to the actual natural frequency. The first ten

order natural frequencies of the overall exoskeleton structure are calculated as shown in table VI. Fig. 8 shows the vibration effect of first two modes by amplifying.

TABLE VI

THE FIRST TEN ORDER NATURAL FREQUENCIES OF EXOSKELETON

Order Frequency (Hz) Mode Description

1 13.029 Lateral swing of leg, maximum displacement of shoe:14.934mm

2 14.439 Swing back and forth, maximum displacement of shoe: 16.751mm

3 4

5 6

7 8 9

10

43.064 50.484

58.178 62.200

90.730 106.79 109.22

119.85

Lateral bending deformation of leg Vertical direction rotation, lateral and up and

down swing slightly Up and down vibration of leg

Vertical direction rotation, lateral swing slightly

Forward and back rotation around the knee Lateral bending deformation of leg

Lateral bending deformation, slightly larger than the eighth amplitude

Lateral bending deformation around the knee

Fig. 8. The vibration effect of first two modes

Table VI shows that the natural frequencies of the lower extremity exoskeleton are relatively low, especially the first two order natural frequencies. From the Fig. 8 we see that the modes of the lower extremity exoskeleton are the overall vibration mode, it indicates the overall structure of exoskeleton have good rigidity. But in the rehabilitation training process, the exoskeleton is prone to resonance if the frequencies of the treadmill and other external environment are close to the natural frequency of the lower extremity exoskeleton, and the vibration frequency of the treadmill is about 50Hz, Therefore the first two order natural frequencies of exoskeleton keep away from the frequency of the treadmill, which avoids the resonance. From the vibration figure we see that the structure vibration of the lower extremity exoskeleton is more stable, which reduces and ensures the rehabilitation effect of patients in the rehabilitation process. Thus, understanding each order natural frequency is advantageous to fundamentally avoid resonance.

Through the modal analysis, it provides the important modal parameters for the overall lower extremity exoskeleton, it provides the theoretical basis for optimization design of the lower extremity exoskeleton, it also lays the foundation for safety and deeply studying of the vibration of the lower extremity exoskeleton, it provides the reference basis for experimental verification. Therefore, in the next optimization design, as long as the first two order natural

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vibration frequencies of the optimized exoskeleton avoid the vibration frequency of the treadmill.

V. THE SCHEME OF OPTIMIZATION DESIGN From the result of the static intensity and rigidity and the

modal analysis, we see that the exoskeleton has a large space for the optimization and improvement of structure. In view of the existing model, because of the driving force is larger when the system is doing gait movement, the hanging block used to mount drive appears looseness when it is fixed on the thigh and the shank. So the drive suspension block is not completely fixed on the structure of the thigh and the shank. It will affect the uncertainty of rehabilitation training and arouse negative effect, therefore, this structure was optimized and improved. The optimized and un-optimized drive suspension block structures are shown in Fig. 9.

Fig. 9. Optimized and un-optimized drive suspension block structures Compared with the un-optimized structure, the optimized

structure is added a thickened part between the leg and the drive suspension block. At the same time, it is also added the contacted wall thickness of the suspension block, which is used to increase the depth of the screw thread between the screw and the thigh, and avoid suspension block’s looseness when the driving force is larger. In the condition of loading the same constraint and load, the maximum equivalent stress of the optimized structure is reduced by 10.972MPa, which avoids the looseness of the connection part.

As a result of the hip, the knee and the ankle of the existing model have a certain gap, and the mechanical leg below the thigh is suspended on the hip axis, its diameter is 14mm. Taking into account the whole exoskeleton has a certain length, so the ankle end of the mechanical leg has a larger lateral displacement caused by the strain of the hip in the actual training process. For the actual model, the drive connection block is separately fixed on the leg, so the mechanical structure of the joint is not compact enough and weighting the exoskeleton of the mechanical leg. Therefore, to optimize the structure of the joint, the paper focuses on optimizing and improving the mechanical structure of the drive connection block, not only regarded as the drive connection block, but also skillfully acted as the important part of the joint used to connect the thigh, the shank and the foot structure, it plays a dual role and enhances the overall stiffness of joints. Then the paper puts forward the optimization scheme of the lower extremity exoskeleton which has the compact joint structure, to achieve lightweight design [11].

Compared with the existing structure of the mechanical leg, the exoskeleton of the optimization scheme is in the premise of keeping the overall structure constant. Because the stiffness requirement of the joint is higher, therefore, the thigh parts at the joint junction is thickened, which improves the overall stiffness of the mechanical leg joint and reduces the lateral displacement; Taking into account the shafts of

the hip, the knee and the ankle are very fine in the existing model, the stiffness of the joint is not satisfactory. As above said, the ankle end of the mechanical leg has a larger lateral displacement caused by the strain of the hip, so the shafts of the hip, the knee and the ankle are bolded, especially bold the shaft of the hip. At the same time, bearings and other shafting parts are changed.

Because of the whole large volume of the original drive weights the lower extremity exoskeleton. Therefore, the paper also optimizes and improves the structure of the drive. Compared with the original drive structure, one of the sleeve and the motor bracket are made more substantial changes, which narrows nearly one-third smaller than the volume of the original drive. Meanwhile, the synchronous belt pulleys are made corresponding improvements, which simplifies the internal structure of the drive. The overall structure of the drive appears even more succinct. By modeling and assembling in PRO/E, the optimization scheme of the lower extremity exoskeleton which has the compact joint structure is shown in Fig. 10. After giving the materials and without considering the connecting part, such as the bolt and screws, the quality of the single leg before and after optimization is shown in table VII.

Fig. 10. The optimized single leg of exoskeleton

TABLE VII

COMPARISON OF THE QUALITY OF THE SINGLE LEG

Optimized process Mass of Single Leg

(kg) Falling Extent

Before optimization 12.20 10%

After optimization 10.98

After establishing the optimized finite element model of the lower extremity exoskeleton, the cloudy images of the optimized exoskeleton’s deformation displacement are calculated by the analytic module of AWE, as shown in Fig. 11. The overall deformation result of the optimized exoskeleton is shown in table VIII.

Fig. 11. The cloudy images of deformation displacement

of the optimized exoskeleton

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TABLE VIII THE OVERALL DEFORMATION RESULT OF OPTIMIZED EXOSKELETON

Symbol Deformation (mm) Description of Deformation

1.37610 Fluctuant and lateral swing 0.71070 X direction to lateral swing

0.64338 1.06400

Y direction to swing Z direction to fluctuant swing

From the Fig. 11, we can see that the maximum

displacement appears on the shoe, the maximum total amount of deformation is under the withstand deformation range. Therefore, the optimization scheme of the lower extremity exoskeleton which has the compact joint structure meets the rigidity requirement.

In addition, by the modal analysis of the lower extremity exoskeleton which has the compact joint structure, the first ten order natural frequencies of the overall structure are calculated as shown in table IX. Fig. 12 shows the vibration effect of first two modes by amplifying.

TABLE IX

THE FIRST TEN ORDER NATURAL FREQUENCIES OF THE IMPROVED EXOSKELETON

Order Frequency (Hz) Mode Description

1 12.582 Lateral swing of leg, maximum displacement of shoe: 15.934mm

2 15.840 Swing back and forth, maximum displacement of shoe: 18.790mm

3 4 5 6

7

8

9 10

35.739 38.533 47.208 52.238

79.025

89.214

101.05 112.27

Up and down vibration of leg Up and down and lateral swing of leg

Vertical direction rotation Lateral bending deformation with small

amplitude Vertical direction rotation, slightly larger than

the fifth amplitude Forward and back bending deformation

around the knee Lateral bending deformation around the knee

Forward and back bending deformation around the knee

From the table IX, we see that the first two order natural

frequencies of the optimized exoskeleton keep away from the frequency of the treadmill (50Hz), which avoids the resonance. Therefore, the optimization scheme of the lower extremity exoskeleton which has the compact joint structure accords with the design requirement of the vibration characteristics.

Fig. 12. The vibration effect of first two modes of

the optimized exoskeleton

VI. CONCLUSION Through the use of AWE simulation software, the paper

analyzes the static intensity and rigidity of the lower extremity exoskeleton, it can judge the exoskeleton meets the requirement of the intensity and the rigidity or not. The modal analysis of the whole structure can obtain its own dynamic characteristics, which avoids the resonance. Combined with the analysis result and the laterality caused by the incompact physical model structure, the paper puts forward the optimization scheme of the lower extremity exoskeleton which has the compact joint structure. In order to make it reach the lightweight design under the condition of meeting the request for the intensity, rigidity, vibration characteristics and rehabilitation training. The weight of the optimized exoskeleton is reduced by 10%.

In addition, in the follow-up of the optimization process, the key parts of the lower extremity exoskeleton can be automatically optimized for size by the optimization module of AWE.

ACKNOWLEDGMENT This research is jointly sponsored by Natural Science

Foundation of China (Grant No. 50975165, 51275282), Program of Shanghai Subject Chief Scientist (PSSCS 10XD1401900) and Innovation Group Project from Shanghai Education Commission.

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