International Conference on Control, Automation and Systems 2010 Oct. 27-30, 2010 in KINTEX, Gyeonggi-do, Korea

1. INTRODUCTION

Nowadays, many neurological diseases such as stroke are continually increasing. These are commonly caused by certain unhealthy lifestyles such as consuming too much high-cholesterol foods, not having enough exercises and also due to age factor. Currently, one of the major cause of death in Korea is cerebrovascular accident (CVA) which is also referred as stroke. In addition, the number of tendency of people who get the paretic disease caused by CVA is progressively increasing, even at younger ages [1]. The reason of CVA is the sudden death of a number of brain cells due to lack of oxygen. This can be caused by impaired blood flow to the brain as a result of blockage or rupture of an artery. CVA can also occur by severe stress, rapidly changing temperature, physical shock and so on.

As a consequence, stroke patients may lose lots of body functions because of injury in brain, including the walking ability. After stroke, the patient may get immediate recovery treatment like remedial surgery or by other means. Subsequently, if spontaneous recovery is not possible, the patent will undergo into the rehabilitation phase of the treatment to recover his/her physical ability [2]. This part of the treatment can take long time with immense efforts, along with very high treatment costs. Thus, it requires tremendous spirit of the patient and the therapist as well as the supporting family.

Usually, the pattern of paretics gait is stiff knee gait (SKG) [3]. To support patients activities and reduce the social costs, reciprocating gait orthoses (RGO) are commonly used for the rehabilitation purposes for such patients in these days. It is an assistance device aimed commonly for patients who are suffering from the paralysis as a consequence of stroke or other neurological diseases. An RGO can help stiff knee gait

of paretic by using locking mechanism of the RGOs knee part so that it can support the moment generated by patients weight. These devices can be helpful through the extra support even if the paretic is not able to control the muscle activities sufficiently enough. However, such devices can cause asymmetry during gait as a result of the irregular and sudden impulsive compulsion support. Therefore, it is very important to develop an active type RGO to provide smoother supporting forces/torques for improved gait of the patient. In this study we proposed a novel kinematic design towards developing an active knee orthosis which can sustain the variety of lower limb movements. The design of the knee orthosis is based on biomechanical structure of human musculoskeletal system of lower extremities. It emulates almost identical movements of the knee joint and the muscle structures around it. The proposed design principally aims for supporting the lack of muscle forces vicariously as the patient needs to make movement of lower limb. In the following sections, we will introduce the biomechanical structure of humans lower limb and the proposed kinematic design of the active knee orthosis that uses hybrid-actuating system with two actuators.

2. THE MECHANICAL STRUCTURE OF LOWER LIMB AND THE GAIT

2.1 The musculoskeletal structure of lower limb

At first, it will be important to understand the musculoskeletal structure of lower limb to illustrate the proposed design configuration for this research. Fig. 1 represents how the muscles attach to the lower limb skeleton system. First, we need to understand and distinguish the muscles applying the governing forces to the knee joint that predominantly provides necessary torques to support the human body weight and rotations

A Novel Design for Lower Extremity Gait Rehabilitation Exoskeleton Inspired by Biomechanics

Sang-Hun Pyo, Abdullah zer and Jungwon Yoon*

School of Mechanical and Aerospace Engineering and ReCAPT, Gyeongsang National University, Jinju, Korea

(Tel : +82-55-751-6693; Fax: +82-55-762-0227; E-mail: jwyoon@gnu.ac.kr) *Corresponding author

Abstract: The use of robotic assistive devices and exoskeletons to supply movement therapy for the rehabilitation of patients following variety of diseases is noticeably growing presently. In order to provide consistent therapy as well as walking assistance, we are developing a wearable lower-limb exoskeleton robot with an adaptive foot device for better walking ability and enhanced stability. In this paper, we focus on the mechanical design of an active knee orthosis. The proposed kinematic design is inspired by the knee biomechanics. Therefore, it is expected that the proposed configuration will help to provide more natural gait during theraphy sessions of patients or in daily use as a sophisticated system. It is based on efficiently controlling the knee motions with hybrid actuations. The two actuators will be implemented with the proposed design; one as hamstring and the other as quadriceps. It is anticipated that the new system will offer an enhanced walking capacity for the patients. Keywords: Human body dynamics, Bio-mechanics, Gait Rehabilitation, Exoskeleton

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of the knee joint in sagittal plane. This will be important to us in design procedures to understand the leg movements and its relation to knee joint rotations physically. As shown in the figure, the hamstring is attached between the pelvis and the tibia near back side of the knee joint. In addition, the length of hamstring is the longest muscle within the part of lower limb. The position of hamstring, however, is not very crucial in generating the torque at knee joint to support the body weight but provides fast angular velocity during swing phase.

Fig. 1 The illustration of musculoskeletal system about

humans lower limb.

The quadriceps is found between the middle part of femur and the front side of tibia near knee joint. The behavior of quadriceps is different as compared with the hamstring as shown by Fig.2.

Fig. 2 Compressive force of patella.

The moment that is generated by the weight of human

body is controlled by the compressive force of this muscle mainly. These significant forces are generated by means of the contraction of quadriceps. When the contraction of quadriceps occur at knee joint, a reaction force by the patella ligament is produced, which generates a compression at the knee. Hence, the reason of the folding out at the knee joint against the bodyweight is the resultant force at quadriceps muscle chiefly. It should be noted here that the existence of the patella is crucial as it provides both connection between muscles and a support point to limit the extensions. This

feature of the quadriceps bio-mechanics is considered in our mechanical design motivation which will be demonstrated in following sections.

Fig. 3 Different type illustration of bio-mechanics modeling.

As mentioned earlier, the quadriceps plays an

important role of fixing the angle of knee joint under body weight. The mechanical functioning of these muscles resembles to linear actuation type movements as can be seen from the figures. Hence, these muscles can be mechanically represented identical as linear actuator as shown in Fig.3. In addition, it can be recognized that it determines the angle between the femur and the tibia with the contraction of quadriceps.

The mechanical structure of knee joint is also important in the analysis. The placement of patella is between the quadriceps tendon and the patella tendon. The roll of patella is transmitting force which is produced by quadriceps contraction. The force is tranferred form patella to tibia by sliding motion of femur on the knee joint.

The two tendons of knee joint can be represented as equivalent springs [4]. In addition, we can see the four-bar mechanism in center of knee joint. This signify us that knee joint can not be solely represented as revolute joint in a simple way [5]. 2.2 The analysis of human gait cycle During the stage of development of an assistive gait device, it is evidently necessary to analyze the gait cycles to make clear design motivations. According to the research of human gait cycle [6], human gait is defined by continuative process of heel-strike and foot off alternately as shown by Fig.4. The initial condition (IC) is defined by the moment of heel-strike at the calcaneal. After the IC the stance phase starts as shown in Fig. 4. The stance phase constitutes 60% of the gait cycle.

The stance phase can be divided to several sub phases. The following phase of IC is the mid-stance

Fig. 4 The illustration of gait cycle [6]. (MST). When the gait cycle is in the mid-stance, the

body weight is transferred to the sole of foot and the balance of body is controlled by the dorsiflexion of

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ankle. After the phase of MST, the next phase of gait cycle is the terminal stance (TST) that is toe-off with the ground by the calf muscle. The final stage of the stance is the pre-swing (PS) phase. After the stance phase is finished, the gait cycle is changed to the swing phase. The first sequence is initial swing (IS). When the gait cycle is on the IS, the foot is in the air by the contraction of hamstring muscle and calf muscle. The following to sequence is mid-swing (MSW). Next to the sequence is the terminal swing (TSW) preparing to contact with the ground. Subsequently, the cycle of gait is completed at last when the sequence of gait is just before the hill-strike.

The phase of IC and TST which take approximately 10% of the total gait cycle each, support the body by two legs. Therefore, the phase of heel-strikes as the starting point of stance and toe-off as the starting point of swing consume the largest muscle forces in a short time. Particularly, the transition states of gait cycle like IC that is the end point of swing phase and the PS that is next to TST and the end point of stance phase are difficult to the patient. These phases not only require power but also necessitate another capacity to attempt the heel-strike and the toe-off for the continuation of walk. Hence, the proposed active type RGO as an active knee orthosis design is thought to be of assistance for patients who lost partially their power and walking abilities. These concerns generally cause the patient difficulty in walking. 2.3 The analysis of knee joint on the gait cycle

It is also needed to understand the knee joint kinematics and torque requirements of the process during the design stage and synthesis of the active knee orthosis. Firstly, we can design the basis of robot control to support the gait by analyzing the knee joint on the gait cycle. Consequently, the analysis of inconsistent lower limb motions from the gait analysis of a normal person can be restored for the use of a patient, [6][7].

The Fig.5 is the graph which is showing the angle of knee and adduction torque with each cycle of general person (sex: male, height: 1.70 m, weigh: 68kg). Thus, for example, we can know that the knee joint angle and adduction torque relationship in time of a gait period.

Meanwhile, the maximum adduction torque (MAT) by quadriceps in regular gait velocity is represent by

M.A.T 2.13% Body weight Height= ~

3.37% Body weight Height . (1)

Fig. 5 The knee analysis of gait cycle.

The maximum adduction torque is generated at the

cycle of LR and TST. And torque is generated by the contraction of quadriceps mainly [8]. The ISW is the processing of toe-off from ground by the contraction of hamstring. The torque of knee by the hamstring is shown by Fig.6 [3].

Fig. 6 The flexion torque for swing phase.

In the research of human gait, the flexion torque tend to be increased when the gait velocity is increasing. Consequently, it means the angular velocity of knee joint is also bigger than before when the flexion angle is increased. [6],[9].

3. THE KNEE ORTHOSIS DESIGN 3.1 The conceptual design of knee orthosis The conceptual design of the proposed active knee othosis has been realized by taking into account the considerations of humans bio-mechanics as explained in previous sections.

With the proposed design, it is attempted to contain the unique kinematic structure of lower limb and knee arrangement with their characteristics. Fig.7 shows the active knee orthosis design for use of patients to support gait cycle and variable lower limb movement in the real life or in rehabilitation practice.

The proposed design works to support patients lower limb movement including climbing slope and walking, resembling the humans musculoskeletal system. The patients who suffered from paralysis will have difficulty to control the muscle by themselves. Hence, the RGO equipped with knee actuators system will supply desired external force to substitute the lack of muscle forces and

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induce the knee angle for gait cycles accurately.

Fig.7 The conceptual design of developed knee orthosis. 3.2 The kinematics of knee orthosis The developed knee orthosis can be divided into two parts as shown in Fig.7. One part is the linear actuator as hamstring and the other part is the actuator as quadriceps and the structure as patella. With this design, it is expected to obtain improved competence as compared to solely revolute joint actuation designs at the knee joint. Nevertheless, the proposed design corresponds more closely to the biomechanical structure of lover limp and muscle-knee compound. First, we define hamstring system in terms of kinematics. The input is the actuators displacement and the output is the angle of tibia. As a result, we need to define the kinematic relation on each parameter of the knee orthosis as shown by Fig.8.

Fig. 8. The mechanism of proposed model

and the kinematics model for hamstring system. The kinematic relation for the mechanism can be

written as a function of coordinate x as ( )f xq = . (2)

where x is the displacement of actuator as hamstring. From the figure it can be analytically written as

: cos( ) cos( ) sin( ),: sin( ) sin( ) cos( ).

p

p

X l x l dY x l d

f q qf q q

- + = -= +

rr (3)

After some arrangements we can obtain the theta angle as the function of sliding distance of the actuator as

2 2 21 1

2 2tan sin

2

p p

p

l x l d ld l l d

q - - - - - = - - +

. (4)

Next, we refer to Fig.9 to analyze the mechanism of quadriceps system.

Fig. 9 The mechanism of proposed model.

The degree of freedom (DOF) of quadriceps system

can be found by using Grbler-Kutzbach criterion shown below as

1 23( 1) 2m n j j= - - - . (5) Here, m is the DOF of mechanism, n is the number of

linkage, j1 and j2 are the relevant joints with applicable DOF. By using this relation, we can identify the DOF of quadriceps system at each circumstance depending on contact or non-contact condition. When the quadriceps system is under the non- contact condition, the DOF of quadriceps will be two as shown by Fig.10.

Fig. 10 The redundancy of quadriceps system under

the non-contact condition.

The other circumstance is when the quadriceps system is under the contact state. In this condition the system will have one DOF assuming it is as if pinned at contact point. The quadriceps system which was designed with the conformity of the biomechanical structure of muscle-knee compound can be represented in a simpler way as shown by the model in Fig. 10.

Fig. 11 shows the kinematic model of the quadriceps

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system. The kinematic relations for the analysis will first be obtained assuming the patella part is in contact and virtually constrained to only rotation at this point. In this case, the quadriceps system can be considered to have one degree of freedom. In order to maintain the contact condition of this state, it will be necessary to apply a torque (T) acting around the knee and this can be generated by the hamstring part of the mechanism. To represent this actuation, or in other words to control the contact state, an actuator symbol is placed in the figure to the contact point which in fact does not exist. Consequently, the quadriceps system of Fig. 9 can be represented with the kinematic model shown in Fig. 11 when quadriceps system is under the contact condition. The kinematics of quadriceps can be represented by

( )f sq = . (6) where s is the displacement of actuator as quadriceps andq is the angle of tibia. After using calculations with virtual displacements and kinematic relations we can compute theta for quadriceps as

2 2 2 21 1

2 2tan sin

2k b

k

c d l ld

c l c dq - -

+ + -= +

+

. (7)

Fig.11 The kinematics model of the quadriceps system.

Here,

1 2sin cos(90 )barc l s ql y y= - - + - - , (8)

1 2sin sin(90 )legd l s ql y y= - - - - , (9) where y and y can be computed from

11 2 2

cos ,( cos ) ( sin )bar leg

r wl s l s

yl l

- + = + + -

(10)

12 2 2

sinsin

( cos ) ( sin ).leg

bar leg

l s

l s l s

l

l ly -

-=

+ + -

(11)

As a result, we can know the relationship between the displacement of quadriceps actuator and the angle tibia if we compute the equations 7 to 11. The result is shown by Fig.12 after computing the above equations. Each of the parameters is substituted from the design value for

the conceptual design of knee orthosis. In conclusion, we can identify that when the actuators displacement is decreased under the contact condition, the angle of tibia (q ) tend to be decreased proportionally.

The upper region of graph in Fig.12 represents impossible (or unfeasible) area in terms of mechanical design. The lower area means that quadriceps system with 2 DOF under non-contact condition. The graph line indicate the hybrid system of two actuators and also means the system has 1 DOF when the patella part is in contact as a limiter with the circular structure of knee orthosis.

Fig. 12 The relation between quadriceps actuator and knee angle.

4. THE PECULIARITY AND INTERACTION

Fig.13 illustrates the support phases with actuations of a paralysis patient by using proposed active knee orthosis. The Table underneath the figure displays the DOF of quadriceps system corresponding to the each gait phase during supporting a patient. When the knee orthosis assists a paralysis patient in swing phase, the quadriceps system has redundancy with having two DOF. In this phase, the hamstring system provides the swing motion effortlessly. On the other hand, the quadriceps system works with the hamstring system under the contact state intermittently when the gait cycle is on the stance phase as illustrated in Fig. 13. The permanent support for the patient simply depends on the hamstring system with its freely adjustable actuator stroke when the gait cycle is on the stance phase. In the stance state, hamstring provide the concact of patella so as to provide sufficient backing forces against the human weight. As mentioned above, system works along with the quadriceps system. This necessitates higher actuator force capability at the quadriceps system specifically as compared to the hamstring system. Therefore, in this state, the two actuators consistently in combination actuate the knee orthosis and the DOF becomes one for the quadriceps.

The adduction torque is supported by the quadriceps system entirely as shown by Fig.13. Therefore, the actuator used as quadriceps must be able to create

Fig. 13 The movement of exoskeleton robot

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strong force to match the need for supporting the body weight with the adduction torque given in Fig.5 during the stance phase and under the contact condition as given by Fig.12. On the other hand, the specification of the hamstring system will just require to support the weight of the tibia part. The hamstring system can have independent movement by increasing the x displacement coordinate with the linear actuator of hamstring system. The hamstring part of the mechanism therefore will not necessitate high power. However, it must have high velocity response competence to provide timely displacement so as to track accurately for the desired gait cycle as inspired by the biomechanics. Hence, the size of this actuator will be relatively smaller.

With the proposed design proposal, it can be possible to reduce the systems weight by using different reduction gears with two actuators. Even if small-sized actuators are used, it is still possible with the proposed design to produce the torques and angular velocities matching with the desired stance phase and swing phase altogether.

ACKNOWLEDGEMENT

This work was supported by 2nd stage BK 21 and by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0094016).

5. CONCLUSION The humans gait is separated to the swing phase and stance phase in which the necessity of forces vary significantly in relation with the angular velocity of the knee motion. With the proposed exoskeleton system design, the high velocity requirement during swing phase and the high power requirement during stance phase has been distributed to the two different kinematic chains (namely quadriceps and hamstring) inspired from

the biomechanics to efficiently operate the gait cycle. The system has been analyzed for the kinematic relations and the operation of the mechanism has been illustrated. According to our initial efficiency and feasibility investigations, the proposed system with separated actuation chains will provide about 41% reduction in total power requirement. In addition, the systems overall weight can also be decreased. Even though the weight reduction may not be very considerable, the proposed system with significantly less power requirement will provide the product durability in terms of battery requirements and lifetime of the exoskeleton. For the future work, the optimization and realization of the proposed system will be initiated on a laboratory prototype to verify the applicability and helpfulness in gait rehabilitation of patients.

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[8] D. Zhaoa, S. A. Banksa, K. H. Mitchelld, D. D. DLimae, C. W. Colwell Jr,, and B. J. Fregly, Correlation between the Knee Adduction Torque and Medial Contact Force for a Variety of Gait Patterns, Journal of Orthopaedic Research, pp.1-18, 2006.

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