The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30, 2015 DOI Number: 10.6567/IFToMM.14TH.WC.OS1.006

Design and Analysis of an Exoskeleton for People with Motor Disabilities

I. Geonea1 M. Ceccarelli2 G. Carbone3 University of Craiova University of Cassino University of Cassino

Craiova, Romania Cassino, Italy Cassino, Italy

Abstract: In this paper, a new mechanism for human leg motion assistance has been proposed for rehabilitation purposes. The structure of human leg and its motions have been used as inspiration for design purposes. A 3D model of the proposed system has been elaborated in Solid Works®, both for design and simulation purposes. It is developed a kinematic model of the mechanisms, useful for further design optimization. There has been build an experimental model of the mechanism and they are conducted experimental researches, the results show that the proposed mechanism performs movements similar to those of a human leg. Keywords: Leg mechanism, rehabilitation, kinematic analysis, design and simulation

I. Introduction There are many devices and robotic systems used for walking rehabilitation. In the recent literature many works deal with robotic lower-extremity rehabilitation [1, 2, 3, 4]. Passive robotic rehabilitation devices, although less complex and cheaper, cannot supply energy to the affected limbs, hence are limited compared to active devices [10].

The rehabilitation process consists in regain a proper mobility of legs and can be divided into three phases [10]: (1) the patient is mobilized into the chair as soon as possible, (2) restoration of gait, and (3) improvement of gait.

Traditional rehabilitation therapies are very labor intensive especially for gait rehabilitation, often requiring more than three therapists together to assist manually the legs and torso of the patient to perform training. This stimulates innovation in the domain of rehabilitation [17, 18, 19, 20] in such way it becomes more affordable and available for more patients and for a longer period of time. Robotics for rehabilitation treatment is an emerging field which is expected to grow as a solution to automate training. Robotic rehabilitation can replace the physical training effort of a therapist.

Over the last decade, several lower-limb rehabilitation robots have been developed to restore mobility of the affected limbs [2, 3, 7, 11, 12, 13]. These systems can be grouped according to the rehabilitation principle, as in Fig. 1[10]:

(a) treadmill gait trainers,

(b) foot-plate-based gait trainers,

(c) overground gait trainers,

(d) stationary gait trainers,

(e) ankle rehabilitation systems: stationary systems and active foot orthoses.

1igeonea@yahoo.com 2ceccarelli@unicas.it 3carbone@unicas.it

Fig. 1. Robotic system types for lower-limb rehabilitation [10]

Traditional therapies usually focus on treadmill training to improve functional mobility [2, 10]. This rehabilitation technique is known as partial bodyweight support treadmill training. From ten system of treadmill type, only three of them are on the market: the Lokomat, the LokoHelp, and the ReoAmbulator [10].

The Active Leg Exoskeleton (ALEX) [16] is a powered leg orthosis with linear actuators at the hip and knee joints, and with a force-field controller developed to provide assistance to the patient by using the assist-as-needed approach. The gait rehabilitation robot LOPES (LOwer-extremity Powered ExoSkeleton) can move in parallel with the legs of a person walking on a treadmill.

Some rehabilitation machines are based on programmable foot plates. That is, the feet of the patient are positioned on separate foot plates, whose movements are controlled by the robotic system to simulate different gait patterns. [7]

The Gangtrainer GT I, commercialized by Reha-Stim, can assist the patient in the recovery of his freedom of movement by relieving the body of its own weight and adapting speed from the individual ability of the patient [7]. TheHapticWalker is a haptic locomotion interface able to simulate not only slow and smooth trajectories (like walking on an even floor and up/down staircases), but also

a) b)

c)

d)

e)

foot motions like walking on rough ground or even stumbling or sliding.

The GaitMaster5 (GM5) is a recently developed gait rehabilitation system at the University of Tsukuba [7, 10]. ReWalk is a wearable, motorized quasi-robotic suit from ARGO Medical Technologies Ltd., that can be used for therapeutic activities.

Hybrid Assistive Limb (HAL) is a wearable robot designed for a wide range of applications, from rehabilitation to heavy works support, and built in several versions (full body version and two-leg version) [7, 10]. Current version 5 has been used to conduct clinical tests [10]. A single-leg version of HAL has also been developed to support the walking of persons with hemiplegia.

The objective of stationary gait trainers is to obtain efficient strengthening of the muscles and the development of endurance, as well as joint mobility and movement coordination. The MotionMaker (Swortec SA) is a stationary training system which allows to carry out fitness exercises with active participation of the paralyzed limbs [10].

Systems for ankle and knee rehabilitation are grouped into stationary or active foot orthoses. The Rutgers Ankle was the first of this kind. It is a Stewart platform-type haptic interface that supplies 6 DOF resistive forces on the patient’s foot, in response to virtual reality-based exercises. The Istituto Italiano di Tecnologia (IIT) has developed a High Performance Ankle Rehabilitation Robot [6, 10].

On the contrary to stationary systems, active foot orthoses are actuated exoskeletons that the user wears while walking over ground or in a treadmill, see Fig. 1, e. [7].

Exoskeletons are electromechanical devices that are worn by a human operator and designed to increase the physical performance of the wearer. These devices are designed to guide the motion of the lower limbs to follow normal gait patterns. It is widely accepted that walking and running activities are characterized by motion of the legs, and the largest joint powers are observed in the sagittal plane [9, 11, 12]. Most exoskeleton prototypes provide assistance primarily to the flexion/extension DOFs, and therefore in the sagittal plane [10].

The purpose of this research is to build an exoskeleton with one degree of mobility on each leg. Mechanical reproduction of the human locomotion system is useful in various applications such as rehabilitation, prosthetic limbs, military purposes [1, 2, 4, 8, 9].

The achievements presented in this research field consist of several open or closed kinematics chains [1, 4, 5, 14, 15]. Open kinematics chains are more easily to achieve, but due to the large number of degrees of freedom are expensive and difficult to control. On the other hand, many of the configurations with closed kinematics chain do not provide the appropriate movement for the elements of the human legs [14]. Currently there are mechanical systems to assist human limb movement, used for walking, up and down stairs, running and even jumping [14].

Existing solutions are currently used on walking biped robots with an anthropomorphic structure (human-like). They use three or more actuators at least for the hip, knee and ankle. This type of structure is used to obtain

anthropomorphic legs type, and has the same degrees of freedom as human limb [15]. However, there are some weaknesses: the construction is very complex and expensive, given the number of engines and their proper location and in addition requires a complex control system. This solution is not effective from energy point of view due to the effect of back-driven and the weight of electric motors [15].

Pantograph mechanisms are frequently applied to robot arms and legs with 1 or 2 DOF’s. They have suitable static and dynamic characteristics because they are closed-loop mechanisms and driven by actuators fixed on a frame [15]. In conclusion, for a simple control algorithm, the leg mechanism should be able to generate an ovoid-foot-point-path, with a continuously rotating crank.

Also, the mechanism must capable to generate an approximately straight path in the propelling portion of the foot path [1].

II. Human gait experimental analysisIn order to design a mechanism for human leg motion rehabilitation, we have to establish hip, knee and ankle joints mobility. The mechanism must be designed and optimized in order to assure human leg suitable mobility.

The hip joint has three DOFs that are all rotations and therefore is considered to be a ball-and-socket joint [6]. The allowed motions at this joint are flexion/extension, adduction/abduction, and internal/external rotations.

The knee joint has two rotational DOF and is considered a condyloid joint [6]. The motions at this joint are flexion/extension and internal/external rotations. The knee joint is, however, often reduced to one DOF due to the very limited internal/external rotations.

The ankle joint is considered to act as a hinge joint with one DOF that allows rotations in the sagittal plane (flexion/extension). Any actuation applied to the ankle of an exoskeleton is applied to this DOF. However, because the ankle joint is connected to the ground via the foot, the complex structure and internal DOFs of the foot must be considered [3]. We have evaluated five human subjects by using Contemplas motion analysis equipment, with two high speed video cameras for capturing and recording sequences and a DELL notebook for sequences analysis in real time with Templo Standard module software [21].

The reflective markers, where attached on a human leg (Fig.2) and the captured motion was processed, as it shown in Fig. 3, to establish human joints angular variations during walking, Fig. 4.

Fig. 2. Human leg reflective markers positioning

hip

knee

ankle

Human subjects analyzed were clothed in black, reflective markers attached being visible when interacting with any light source, so their position is easily identifiable by Templo Motion Analysis software in automatic mode.

Anthropometric parameters of human subjects are presented in Table I.

Subject Paramaters

S1 S2 S3 S4 S5

Weight 58 53 58 53 56

Height 1,80 1,75 1,85 1,72 1,78

Age 19 16 20 18 21Shoe size 40 36 39 36 37

TABLE I. Anthropometric parameters of human subjects

Fig. 3. Human leg attached markers trajectory tracking

Fig. 4. Establish of human joints angular variations

They are obtained laws of variation of the angles of the joints from the human leg, while walking.

140

150

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200

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220

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

An

gu

lar v

ari

ati

on

s [d

eg

res

]

Time [sec]

Hip joint angular variations

S1 S2 S3 S4 S5

Fig. 5. Human hip joint angular variations

100

110

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130

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150

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190

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

An

gu

lar v

ari

ati

on

s [d

eg

ree

s]

Time [sec]

Knee joint angular variations

S1 S2 S3 S4 S5

Fig. 6. Human knee angular variations

80

90

100

110

120

130

140

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

An

gu

lar v

ari

ati

on

s [d

eg

ree

s]

Time [sec]

Ankle joint angular variations

S1 S2 S3 S4 S5

Fig. 7. Human ankle joint angular variations

In Fig. 5, 6 and 7 they are presented the obtained results for angular variations of human hip, knee and ankle joints, for five human subjects.

The purpose of human gait analysis is to obtain the medium variations laws of the leg joints, in order to compare them with the variation laws achieved by the exoskeleton. The medium variation laws of the angles from human leg joints are calculated in Excel, and they will be used for comparison with the angular variations achieved by the exoskeleton leg joints.

III. Proposed mechanism descriptionFor human walking, the motion of a leg can be divided into two phases, swing and propelling [1]. A scheme of the proposed mechanism is presented in Fig. 8. There is shown, in Fig. 9 the swing leg in non-propelling phase and the leg mechanism position in the propelling phase. The ankle motion trajectory is depicted with solid line and is an ovoid curve (linear portion corresponds to the propelling phase of the leg, and the curved portion to the swing phase of the leg). The step length L and step height H represented in Fig. 9, are indicated in Table II.

In order to design a leg mechanism with back-forth and up-down motion capability in sagittal plane, the foot point M of a reduced DOF leg mechanism should be able to generate an ovoid curve [1], which is composed of a straight-line segment and a curved one. The straight-line segment is related to the propelling phase when the corresponding leg touches the ground and guarantee stable propelling of the body. The curved segment is related to the non-propelling phase, which is produced by the leg when it swings from back to forth. In this paper, the proposed one DOF leg mechanism consist of a Chebyshev four-bar linkage ABCDE and a linkage with three closed contours, DCEFG, GHJBA, HJKLI, as shown with design parameters in Fig. 8.

B

CD

EF

G A

K

L

JH

I

M

x

y

9

8

7

6

5

43

2

1

Fig. 8. Kinematic scheme of leg mechanism

Fig. 9. Virtual model of the leg mechanism in different walking phases

The mechanism can generate an ovoid curve for the point M, see Fig. 9. Designed mechanism structure is similar with human leg: link 5 is equivalent with the human femur, link 9 with tibia and joint G and I represent the hip and knee. To connect with other links, femur and

tibia are drawn with an original design shape with welded ends sides, to 90 and 65°. Link 5 has to rotate around point G, for that is connected by means of link 4 to point E, of Cebyshev linkage. Structure is completed with quadrilateral linkage HKIL, side IL is welded under angle β with portion IM, to achieve tibia link. Link 6, connect the crank AB to HK side of quadrilateral linkage, and achieves the knee joint proper rotation.

With Grubler-Cebyshev formula, the mechanism degree of freedom is:

5 43 2 3 9 2 13 1M n C C (1)

where: n - number of kinematic elements; C5 - number of joints with one degree of mobility;

C4 - number of joints with two degree of mobility. The mobility of the mechanism is calculated without

considerind the contact with ground of point M. The main ideeas in obtaining this structure was the solution to conect tibia and femur by means of an quadrilateral linkage, the design shape of tibia and femur, and completion of structure with proper linkages to achieve suitable movements of femur and tibia. The further optimization tasks concern optimal point M guidance and angular variations for knee and hip joints similar to humans.

IV. Kinematic analysisIn order to analyse and evaluate the prototype leg

mechanisms performance, a kinematics analysis has been carried out. A coordination system XY is fixed at the point A in its original reference position. Design parameters of the leg mechanism are depicted in Fig. 8. As input data for the kinematics analysis we know the elements length as it’s shown in Table I. The loop closure equations of the mechanism are written as (Eq. 2 and Eq. 3), where the

unknowns are the angles , 2,9i i . These loop closure

equations are solved using a package program for solving equations, developed on Maple environment.

l1=lAB=12 l4=lEF=76 lGH=300

lBC=45 l6=lBJ=348 lGI=350

l3=lCD=35 l8=lKL=48 lHJ=40

lCE=45 lFG=55 lJK=60

lIL=90 xA=0, yA=0 L=188

lIM=315 xD=-33.64, yD=-45.5 H=90

lIH=50 xG=-90.7, yG=32 β=65°

TABLE II. Design parameters of a model leg mechanism

1

1

2 3 3

2 3 3

2

2

4 4 5

4 4 5

cos ;

sin .

cos cos ;

sin sin .

cos ;

sin .

cos cos ;

sin sin

B A AB

B A AB

C B BC D

C B BC D

E C CE

E C CE

F E G GF

F E G GF

H G GH

x x l

y y l

x x l x l

y y l y l

x x l

y y l

x x l x l

y y l y l

x x l

5

5

cos 90 ;

sin 90 .H G GHy y l

(2)

1

2 3

4

56

7

8

9

5

5

6 7

6 7

7

7

8 8 9

8 8 9

cos 90 ;

sin 90 .

cos cos ;

sin sin

cos ;

sin .

cos cos

sin sin .

I G GI

I G GI

J B BJ H HJ

J B BJ H HJ

K J JK

K J JK

L K I IL

L K I IL

x x l

y y l

x x l x l

y y l y l

x x l

y y l

x x l x l

y y l y l

9

9

cos 2 ;

sin 2 .

M I IM

M I IM

x x l

y y l

(3)

The coordinates of the leg mechanism joints, see Fig. 8, are computed with Eq. 2 and 3. Coordinates of fixed joints A, D, G are presented in Table II.

This nonlinear system of equations can be written as Eq. (4), which is a trigonometrically equation with variable coefficients, with solution under the form:

2 2 2

sin cos 0; 2,9.

2

i i i i i

i i i ii

i i

A B C i

A A B Carctg

B C

(4)

Where the variable coefficients, have the expressions, as Eq. (5):

2 2 2 22 1 2 1 2 3 1 1

2 2 2 23 1 3 3 1 3 3 1 1 3

2 2 2 24 2 4 4 2 4 4 4 2 2

2 2 2 25 2 5 2 5 4 2 2

2 2 2 26 2 6 1 6 1 2

7

2 ; 2 ;

2 ; 2 ;

2 ; 2 ;

2 ; 2 ;

2 ; 2 ;

BC BC BC

BC

GF

GF GF GF

BJ BJ JH BJ

A b l B a l C l a b l

A b l B a l C l a b l

A b l B a l C l l a b

A b l B a l C l l a b

A c l B c l C l c c l

A

2 2 2 22 7 1 7 1 2

2 2 2 28 2 8 8 1 8 8 1 2 8

2 2 2 29 2 9 1 9 1 2 8

1 1

2 2

1 2

1 2

2 ; 2 ;

2 ; 2 ;

2 ; 2 ;

where

,

,

,

,

JH JH BJ JH

IL

IL IL IL

D B D B

G E G E

H B H B

I K I K

c l B c l C l c c l

A d l B d l C l d d l

A d l B d l C l d d l

a x x b y y

a x x b y y

c x x c y y

d x x d y y

(5)

Fig. 10. Computed angular variations of link 5 (femur)

Fig. 11. Computed angular variations of link 9 (tibia)

The position of point M can be evaluated as an input crank angle function:

1 1 2 4 4

5 5 9

1 1 2 4 4 5

5 9

cos cos cos

cos cos / 2 cos 2

sin sin sin sin

sin / 2 sin 2

M BE

FG GI IM

M BE FG

GI IM

x l l l

l l l

y l l l l

l l

(6)

1 1 1 2 2 4 4 4

5 5 5 5

9 9

1 1 1 2 2 4 4 4

5 5 5 5

9 9

sin sin sin

sin sin / 2

sin 2

cos cos cos

cos cos / 2

cos 2

M BE

FG GI

IM

M BE

FG GI

IM

x l l l

l l

l

y l l l

l l

l

(7)

2 21 1 1 1 1 1 2 2

22 2 4 4 4 4 4 4

2 25 5 5 5 5 5

25 5 9 9

9 9

cos sin cos

sin cos sin

cos sin cos / 2

sin / 2 cos 2

sin 2

M BE

BE

FG FG GI

GI IM

IM

x l l l

l l l

l l l

l l

l

2 21 1 1 1 1 1 2 2

22 2 4 4 4 4 4 4

2 25 5 5 5 5 5

25 5 9 9

9 9

sin cos sin

cos sin cos

sin cos sin / 2

cos / 2 sin 2

cos 2

M BE

BE

FG FG GI

GI IM

IM

y l l l

l l l

l l l

l l

l

(8)

Fig. 12. Computed translational displacement

of point M

Computed results for the angular variations and position of the ankle joint M, are presented in Fig. 10-12. Adams computed trajectory of the ankle joint, in situation when leg operates on a supporting stand and walking on ground are presented in Fig. 13. Ankle joint in Adams program is modeled with a torsion spring.

Fig. 13. Computed trajectory of point M with no ground contact and on ground

V. Exoskeleton experimental testing

To investigate the efficiency, of the proposed leg mechanism, a prototype has been built in the Laboratory of Mechanisms, Faculty of Mechanics, Craiova. Design parameters of the prototype leg mechanisms are those indicated in Table II.

Fig. 14 shows the prototype of the rehabilitation exoskeleton, composed of two legs. For actuation it is used a single motor, mounted on the upper frame. By means of a chain transmission the motion is transmitted to the shaft mounted on ball bearings on the upper frame. The cranks of legs are connected to the shaft extremities with 180 degrees angular offset, in order to achieve the human walking phases.

Tests were performed in case when the rehabilitation exoskeleton walks on the ground without the human. In order to keep balance, during experiments, the upper frame

is mounted on two vertical supports, equipped with wheels.

Fig. 14. A prototype of human leg rehabilitation exoskeleton

With the motion analysis software Contemplas, based on ultra-speed video cameras and marker tracking, they are determined the angular variations from the hip, knee and ankle joints of the exoskeleton.

Fig. 15. Reflective markers for motion tracking

hip

knee

ankle

Fig. 16. Video tracking for knee joint angle calculation

Fig. 17. Video tracking for markers trajectory calculation

Corresponding to Fig. 8 the hip joint of the human is identified with joint G, the human knee correspond with the joint I and the human ankle joint is identified with the joint M. The exoskeleton motion analysis was achieved simultaneously with two cameras.

Fig. 18. Hip joint angles from right and left leg

Fig. 19. Knee joint angles from right and left leg

Fig. 20. Ankle joint angles from right and left leg

Results obtained for the angular variation of right leg (red line) and left leg (blue dashed line) are presented in Fig. 18-20.

The diagrams of exoskeleton left leg joints angular variations are compared with diagrams obtained in the case of human walking, see Fig. 5, 6 and 7. The human gait analysis is performed on five human subjects, retaining for comparison the medium variations laws, see Fig. 21, 22 and 23.

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Compared hip joint motion laws

Human Exo

Fig. 21. Compared hip joint motion laws

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Compared knee joint motion laws

Exo Human

Fig. 22. Compared knee joint motion laws

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Compared ankle joint motion laws

Human Exo

Fig. 23. Compared ankle joint motion laws

VI Conclusions In this paper a kinematics and experimental analysis of a one DOF human leg mechanism is carried out, in order to characterize the mechanism performance. Kinematics equations of the proposed leg mechanism are formulated for a situation when the leg operates on a supporting stand and solved in Maple computational algorithm, some obtained results are presented in Fig. 10- 12. They will be used for further kinematic optimization of the mechanism. Has been developed an experimental model of the proposed mechanism, and they are conducted tests in situation of walking on ground, with Contemplas motion analysis platform equipped with ultraspeed video cameras. It is obtained the graphics of variation for the angles of the knee, hip and ankle joints. Results from the mechanism, in Fig. 21, 22 and 23, are compared with average results obtained on five human subjects, and they are quite similar, the conclusion being that the mechanism is suitable for human rehabilitation purposes. In Adams software is simulated the walking activity taking into account the ground contact with the foot. There are obtained the paths for trajectories when leg operates on a supporting stand and walking on ground, in Fig. 13. Simulation and experimental results show suitable performance of the proposed leg mechanism structure. The novelty of the design structure is that for each mechanism is used only one motor, so is no needed a complex command and control algorithm.

Acknowledgments This work was supported by the strategic grant POSDRU/159/1.5/S/133255, Project ID 133255 (2014), co-financed by the European Social Fund within the Sectorial Operational Program Human Resources Development 2007-2013.

VII References [1] Araidah, O. Conceptual Design of a Single DOF Human-Like Eight

Bar Leg Mechanism, In Jordan Journal Of Mechanical and Industrial Engineering, Vol. 5, No. 4, pp. 285-289, 2011.

[2] Ariel A. Design of a mechanical system in gait rehabilitation with progressive addition of weight, In Journal of Physics: Conference Series 332, 2011.

[3] Banala Sai K. Gravity-Balancing Leg Orthosis and its Performance Evaluation. In IEEE Transactions on Robotics, Vol. 22, No. 6, pp. 1228-1239, December 2006.

[4] Carbone G. and Ceccarelli M. Legged Robotic Systems. In Cutting Edge Robotics ARS Scientific Book, Wien, pp. 553-576, 2005.

[5] Ceccarelli M., Carbone G.. and Ottaviano E. Leg Designs for Walking Machines at LARM in Cassino. In ASI workshop on Robotics for moon exploration, Rome, July, 2009.

[6] Cenciarini M. Biomechanical Considerations in the Design of Lower Limb Exoskeletons. In 2011 IEEE International Conference on Rehabilitation Robotics, Switzerland, 2011.

[7] Ferris Daniel P. Powered lower limb orthoses for gait rehabilitation. In Top Spinal Cord Inj Rehabil, 11(2): pp. 34–49, 2005.

[8] Hirai K., Hirose M., Haikawa Y. and Takenaka T. The development of Honda humanoid robot. In Proceedings of IEEE International Conference Robotics and Automation, Leuven-Belgium. pp. 1321-1326, 1998.

[9] Inagaki K. Reduced DOF Type Walking Robot Based on Closed Link Mechanism, In I-Tech, Vienna, Austria, ISBN 978-3-902613-15-8, pp. 544, 2007.

[10] Inaki Diaz. Lower-Limb Robotic Rehabilitation: Literature Review and Challenges. In Journal of Robotics, 2011.

[11] Kawamoto H. and Sankai Y. Power assist system HAL-3 for gait disorder person. In Lecture Notes on Computer Science (LNCS). Vol. 2398. Berlin, Germany, 2002.

[12] Kazerooni H. and Steger R. The Berkeley lower extremity exoskeleton. In Transactions of the ASME, Journal of Dynamic Systems, Measurements, and Control. Vol. 128. pp. 14-25, 2006.

[13] Kazuya Kubo. Gait Rehabilitation Device in Central Nervous System Disease: a Review. In Journal of Robotics, 2011.

[14] Li T. and M.Ceccarelli. An Experimental Characterization of a Rickshaw Prototype. In Mechanisms, Transmissions and Applications, Springer, ISBN978-94-007-2727-4, pp.203-214, 2011.

[15] Liang C., M. Ceccarelli and Y. Takeda. Operation analysis of a Chebyshev-Pantograph leg mechanism for a single DOF biped robot. In Front. Mech. Eng. 7(4) pp. 357–370, 2012.

[16] Mohd Azuwan. Recent Trends in Lower-Limb Robotic Rehabilitation Orthosis:Control Scheme and Strategy for Pneumatic Muscle Actuated Gait Trainers. In Robotics Journal, pp. 120-148; doi:10.3390/robotics3020120, 2014.

[17] Sargsyan Suren. Robotic Rehabilitation Devices Of Human Extremities: Design Concepts And Functional Particularities. In Proceedings of the 11th Biennial Conference on Engineering Systems Design and Analysis ESDA 2012 July 2-4, Nantes, France, 2012.

[18] Shieh, W.B., Tsai, L.W., and Azarm, S. Design and Optimization of a One-Degree-of-Freedom Six-Bar Leg Mechanism for a Walking Machine. In Journal of Robotic Systems. Vol. 14(12). pp. 871-880, 1997.

[19] Walsh C., Endo K., and Herr H. A quasi-passive leg exoskeleton for load-carrying augmentation. In Int. Journal H.R. Vol. 4(3). pp. 487-506, 2007.

[20] Zoss A.B., Kazerooni H. and Chu A. Biomechanical design of the Berkeley lower extremity exoskeleton (BLEEX). In IEEE ASME Trans Mechatron. Vol. 11(2). pp.128-138, 2006.

[21] CONTEMPLAS Motion Analysis Equipment User manual, 2010.