DESIGN OF SELF-ADJUSTING ORTHOSES FOR REHABILITATIONDung Cai, Philippe Bidaud, Vincent Hayward

Institut des Système Intelligents et de Robotique (ISIR)Université Pierre et Marie Curie

Pyramide - T55/65 CC 173 - 4 Place Jussieu75005 Paris, France

cai,bidaud,hayward@isir.upmc.fr

Florian GosselinCEA LIST, Sensory Interfaces Laboratory

18 route du Panorama, BP6, F-92265Fontenay Aux Roses, France

florian.gosselin@cea.fr

ABSTRACTSafety and comfort are primary concerns in rehabil-itation devices and exoskeletons. However, the re-sult of using simplified kinematic arrangements canbe discomfort, or even injury, as a result of overcon-straining the joint. In this paper, we describe a self-adjusting mechanism able to overcome misalignmentbetween the rotational axis of the mechanism that isattached to the user’s limbs and the rotational axisof the anatomical joint. Additional degrees of free-dom are added to the mechanism to eliminate inter-nal residual forces. Furthermore, a new technique forthe estimation of the Instantaneous Center of Rotationof the assisted joint based on velocity and positionsensors is demonstrated. We illustrate this techniquewith a mechanism which is able to self-adjust with orwithout resorting to motorized add-ons. Kinematicanalyses are presented and are validated by computersimulation on 2D examples.

KEY WORDSSelf-adjusting mechanism, Estimation of ICR

1 Introduction

An orthosis is a mechanical support designed to com-pensate or to correct a deficient function in a joint. Itcan be used, for example, to improve the physiolog-ical efficiency of a limb that has lost its function dueto trauma or disease, or that has been affected by acongenital anomaly. Many types of passive orthoseshave been developed over the years, especially forlower limb rehabilitation. Lower limb guidance or-thoses are devices attached externally to a lower bodysegment in order to control its motion, to provide me-chanical stabilization, to reduce discomfort by trans-ferring load to another area, to correct anomalies, andto prevent the progression of deformities. One of thefunctions that is specific to knee orthoses is the controlof the anterior translation of the tibia, as well as its ro-tation during knee flexion (bending) and knee exten-sion (straightening). As illustrated in Fig. 1, a typicalarticulated knee orthosis has inner and outer guideplates that are connected to the joints by adjustable

Figure 1. Example of knee orthosis with one polycen-tric joint - Image adapted from Herzberg and al. [1]

links. The plates are shaped to fit the anatomy of thethigh and of the leg. The plates are linked togetherby unicentric or polycentric hinges mounted on slid-ing elements to be adjusted to locate the joint axis toan optimum. Prefabricated orthoses with unicentrichinges can be used in simple applications such as toenhance lateral stabilization. A polycentric pivot jointis better able to track the anatomical knee throughoutits range of motion [2] [3] [4] [5] [6]. It allows naturalknee flexure and high lateral support thus ensuringgood control of the limb motion. These more com-plex designs are used in orthoses that are developedin the case of complex pathologies or for postopera-tive treatments. Because of the inter-individual vari-ability in joint kinematics [7] [8] [9], these orthosesmust be made-to-measure.

Muscular strengthening devices and power suitdevices must also provide a motion that tracks hu-man joint kinematics in order to avoid damage tothe joints. A typical approach is to allow some free-dom between the natural and the artificial kinemat-ics, for instance by connecting the natural and the ar-tificial limbs at the end-point [10], [11]. End-point-

664-030 215

based designs, however, are known to force naturaljoints in arbitrary directions, possibly causing hyper-extension [12]. For devices that are attached to thelimbs, the axis of rotation must be in coincidence withthe rotation axis of the anatomical joint as much aspossible [13], just as in the case of a passive orthosis.Then, the question of approximating the natural kine-matics with an artificial system arises similarly, sincemisalignments between the two systems generate un-desirable residual forces and torques to the limb. Theconsequences of an inadequate design can range fromreduced comfort to permanent injury.

A device that can be safe and comfortable mustbe able to reproduce the natural human joint kinemat-ics accurately. Such design must have two functions:It must be able to estimate the kinematics of a natu-ral joint which has an inter-individual variability andwhich can change in time, and then self-adjust its ge-ometry to match the kinematics of the natural joint asclosely as possible.

In the next section, a 2D kinematic model of thesystem is presented to demonstrate how the proposedmechanical solution makes it possible to estimate theinstantaneous center of rotation of a joint. In section3, the self-adjustment property of the mechanism inthe direction of the axis of the thigh is analyzed. Thisproperty facilitates the implementation of the mech-anism on the users’ limbs and has been leveraged bydesigners of knee orthosis devices. Finally, simulationmodels are used to demonstrate and validate theseproperties in section 4.

2 Kinematic model

2.1 System modeling

Fig. 2 shows a simple model of the proposed sys-tem. A slider-pin and a slider-joint are placed andattached to the limbs in their anterior plan. This con-figuration is selected in order to obtain a better sta-bility. It will also ease a three-dimensional design formore complex cases. Segments PM and PB repre-sent the limbs. A pin joint is placed at location B inorder to account for the flexibility of the attachmentdeformable tissues. We assume, however, that themechanism is rigidly attached to the first limb. Sincethe attachment location is arbitrary, point M is de-fined such that the segment MN is orthogonal to seg-ments PM and AN . Point K is on the segment BHsuch that segments PK and BH are orthogonal.

Let γ0 be the initial value of the angle PBH = θ4when the device is first attached. Misalignment canbe modeled as the energy stored in a torsional springcentered in B with stiffness k. The torsional torque,CB , caused by misalignment is

Figure 2. The first model of the problem. A pin jointP is used to represent the user’s joint. B is the at-tachment point. M is chosen such that the segmentPM which represents the higher limb and the seg-ment AN of the mechanism are parallel, and the seg-

ments MN and PM are orthogonal.

CB = k(PBH − γ0). (1)

As further shown below, self-adjustment isachieved by this arrangement, since during move-ments, the system will tend to minimize the elasticenergy stored in the torsional spring. The torque pro-duced by this spring will generate the self-adaptionmovement. For the design of a prototype, a pinjoint and a torsional spring can be inserted at pointB. The pin joint will reduce the residual torque ontissues layers and the spring will provide the auto-adjustment property. It is also possible to rely on theflexibility of the tissue of and the skin to act as a flex-ible energy storage. The second choice is simpler butthe residual torque could reduce the comfort of theuser. From now on we will consider point B to be apin joint with a torsional spring.

The complete model of the system is shown inthe Fig. 3 where r1 is the linear velocity of the part(1) relative to (0), θ2 is the angular velocity of the part(2) relative to (1), r3 is the linear velocity of the part(3) relative to (2), θ4 is the angular velocity of the part(4) relative to (3), and θ5 is the angular velocity of thepart (0) relative to (4).

The velocity of the user’s rotational joint can beexpressed at point P as:

V (P ) =

xP

˙yP

˙qP

= JP (q)

r1θ2r3θ4θ5

. (2)

xP and ˙yP are the components of the linear ve-locity of the point P relative to (0). ˙qP is the angular

216

velocity of the point P relative to (0). As P is a rota-tional joint, xP and ˙yP are equal to zero.

(0)

(0)

(1)

(2)

(3)

(4)

Figure 3. Model of the mechanism structure

The Jacobian matrix of the whole system can bewritten in the coordinate frame R1 = (A,

→x,→y ) at the

point P as:

JP (q) =

1 b cos θ2 −h cos(θ4 − θ2) 00 −a − sin θ2 −h sin(θ4 − θ2) 00 1 0 1 1

.

(3)

(a,b) are components of the vector→PA in the co-

ordinate frame R1 = (A,→x,→y ).

2.2 Estimation of the instantaneous center of rota-tion of the human joint

Given the Jacobian matrix (3), we apply the loop clo-sure constraint at P which provides the following sys-tem of equation,

r1 + bθ2 + r3 cos θ2 − θ4h cos(θ4 − θ2) = 0,−aθ2 − r3 sin θ2 − θ4h sin(θ4 − θ2) = 0,

θ2 + θ4 = −θ5.(4)

If we secure the attachment at the pointB so thatthe angle θ4 will remain constant during the move-ment (the other joints are supposed to be ideal andthe effects of friction are neglected), then the wholesystem can be considered to have only one degree offreedom. Therefore θ4 = 0, and we can write a and bas:

a = − r3 sin θ2θ2

. (5)

b = − r3 cos θ2 + r1

θ2. (6)

The location of the Instantaneous Center of Rota-tion (ICR) can be estimated by using the two expres-sions above, which require the measurement of the

angular rotation of the pin joint and the velocities ofthe mechanism’s joints.

3 Self-adjustment property

3.1 Mechanical constraint during the attachmentphase

It can be easily demonstrated that if during the move-ment of the limbs, the location of P and the value ofthe angle θ4 remain unchanged, then the distance b′

between P and the segment AH (b′ = HK) will bealso constant. So if b 6= b′ (where b = MN is thedistance between P and the segment AN , which isalso constant), the mechanism can not reach the po-sition where the segments AN and AH are collinearwithout any deformation at the attachment joint B.In order to avoid this phenomenon, the two distancesb and b′ must be equal, which means that the mech-anism must be placed at its singular position duringthe attachment to the limbs.

3.2 Analysis of the singularity model

When the mechanism is in its singular position,its particular geometry will lock the movement offlexion-extension of the limbs. As there is a flexibilityin the joint B, a deformation will take place in B thatwill modify the value of the angle θ4 and will then al-low the mechanism to move away from its singularposition. Then, the energy stored in B will act as a ro-tative actuator and will produce a movement of self-adjustment for the mechanism. The mechanism willthen move to the ideal position where θ4 = γ0. Wewill demonstrate that, if the location of the point Premains constant during the flexion motion, the seg-ment formed by the two centers of rotation will belocated in the symmetry plan of the mechanism.

(2) (3)

(4)

(0)

(0) (1)

Figure 4. The mechanism in its singular configuration

When the mechanism is in its singular configu-ration (Fig. 4), θ2 = 0, HK = b and BK = c − b =PB cos γ0. The system of equations becomes:

217

r1 + bθ2 + r3 − θ4h cos(γ0) = 0,−aθ2 − θ4h sin(γ0) = 0,

θ2 + θ4 = −θ5.(7)

The angle θ4 can now be calculated according toθ2 when π > γ0 > 0,

θ4 = − aθ2h sin(γ0)

. (8)

When a = 0, θ4 = 0. If the user moves her orhis limb, the angular velocity of the pin joint B willbe equal to zero. The mechanism escapes from its sin-gular position without any modification of the valueof the angle θ4. Afterward, the angle θ4 will remainconstant during the whole movement.

If a 6= 0 and if θ4 = 0, which means that the valueof the angle θ4 is constant, we shall obtain θ2 = 0and θ2 = θ5 6= 0 by (7) which leads to a contradic-tion. There is no possible movement, therefore θ4 isinevitably different from zero. As a result, the tor-sional spring placed at B will move away from itsequilibrium position. The source of energy stored bythis spring will then act as an actuator to generate theself-adaption movement of the mechanism.

3.3 Analysis of the self-adaption movement

The Fig. 5 shows a model for the study of the self-adaption motion. For the analysis of this property,the limbs of the user are supposed to be fixed (θ5 = 0)during the self-adaption motion.

(1)

(2)

(3)(0)

(0)

(0)

Figure 5. The mechanism’s model in a brief intervalof time when the user’s limbs are considered as fixed

The Jacobian matrix written in the coordinateframe R2 = (A,

→x2,

→y2) at the point B is:

JB(q) =

cos θ2 c 1 0sin θ2 L 0 0

0 1 0 1

. (9)

(−L,c) are components of the vector→BA in the

coordinate frame R2 = (A,→x2,

→y2).

The loop closure atB provides the following sys-tem of equations:

r1 cos θ2 + cθ2 + r3 = 0,r1 sin θ2 + Lθ2 = 0,

θ2 = −θ4.(10)

When θ2 = 0, if L 6= 0 then θ2 = θ4 = 0, r1 = −r3and θ4 = γ0 respectively. There is no possible angularmovement but there is an internal mobility which al-lows the two prismatic joints to slide and move awayfrom their rest position if there is an external load (forexample: the gravity force). We notice that this resultcan also be obtained by the precedent analysis of thesingularity model.

When θ2 6= 0, we obtain:

θ2 = −θ4,

r1 = − Lθ2sin θ2

,

r3 =(L cos θ2 − c sin θ2)

sin θ2θ2.

When L cos θ2 > c sin θ2 or tan θ2 < Lc , r1 and r3

will have opposite signs which means that they willslide in the same direction. The mechanism will moveto its equilibrium position where θ4 = 0 (or θ4 = γ0).We also notice that the value of c depends on the po-sition of the point A. The nearer the distance betweenthe points A and P is, the smaller the value of c willbe, thus it will be easier to obtain the self-adaptionmotion.

3.4 Kinematic analysis of the mechanism duringits motion after the self-adaption

Now let us consider the case where the mechanismis already readjusted, θ4 = γ0. And in its posteriormovement, this angle θ4 can be considered to be un-changed (because of the resistance of the torsionalspring at B). Thus we obtain HK = PH2 = b andBK = c − b whatever the value of the angle θ2 is. Inthis particular case, the joint B can be considered tobe a clamp to the limb so it can be neglected in themodel. The instantaneous center of rotation of thelimbs P is considered to be fixed. The whole system’mechanism-limbs’ can be remodeled as shown in theFig. 6.

The Jacobian matrix written at the point P , in theframe R2 = (A,

→x2,

→y2) is:

JP (q) =

cos θ2 l cos θ 1 0sin θ2 l sin θ 0 0

0 1 0 1

(11)

218

(0)(0)

(1)

(2)

(3)(3)

Figure 6. The model when θ4 is unchanging duringmotion

HK = b, thus PH1 = PH2 = b. The value of theangles (APH1) and (APH2) are:

(APH1) = (APH2) = arccos(b

l) = θ, (12)

with PA = l. The value of the angle θ2 is thus :

θ2 = (APH1) + (APH2) = 2θ. (13)

The expression (12) shows that the segment APis located at the symmetry axis (or symmetry plan in3D) of the mechanism. The loop closure at P providesthe following system of equations:

r1 cos θ2 + θ2l cos θ + r3 = 0,r1 sin θ2 + θ2l sin θ = 0,

θ2 = −θ4,(14)

r1 = − θ2l sin θsin θ2

, (15)

r3 =θ2l sin(θ − θ2)

sin θ2. (16)

Since θ2 = 2θ, according to (13), we obtain :

r3 = − θ2l sin θsin θ2

. (17)

Thus,r3 = r1. (18)

In this particular case, the point P remains atthe symmetry axis of the mechanism. The two pris-matic joints slide in the opposite directions with equalspeeds. We point out that when l tend towards zero,the velocities r3 and r1 will also tend towards zero,which means that the slider’s motions are insignifi-cant when the rotation axis of the mechanism is closeto the rotation axis of the limbs.

The conclusion of this study is that the Slider-Pin-Slider mechanism realizes auto-adjustment of the

pin joint regarding to the limbs. The mechanism mustbe attached to the limbs in its singular position. Whenthe mechanism escapes from its singular position, therestoring torque at the attachment will act as a passiveactuator and will move the mechanism to its new po-sition where the center of rotation of the limbs will belocated in the symmetry plan of the mechanism. Thenthe two prismatic joints slide in opposite directions atthe same speed (if the ICR of the limbs remains un-changed during motion). When the ICR moves, thetwo slider joints will slide with different velocities. Ifwe measure their velocities and also the angular ve-locity of the pin joint, it will be possible to track thisvariation of the ICR of the human joint.

4 Simulation

4.1 Simulation of the self-adaption property

A dynamic simulation (Cosmosmotion, SolidWorks)is used to verify the results. Two simulationswere carried out for two different mechanisms:The slider-pin-slider mechanism and the slider-multipleparallelogram-slider mechanism. The sec-ond mechanism is similar to the first one. The dif-ference is that its virtual axis of rotation is closer tothe center of rotation of the limbs [14].

In this simulation, the limbs are set to rotate ata constant angular velocity (5 degree/s). A torsionalspring (1 N.m/degree) is added to the pin joint of theattachment of the second limb. The friction coefficientof the two sliders is set at 0.005.

The Fig. 8 and 9 show different images of themechanisms during simulation. In the 1st image, wecan see that the rotation axes aren’t in their appro-priate positions. The 2nd image shows the adjust-ment motion. The mechanism moves the pin jointaxis (or multiple-parallelograms unit) to the new po-sition where the rotation axis of the limbs would belocated in the symmetry plans of the mechanisms.

The figures 10, 11, 12 and 13 show the sim-ulation’s results of the slider-pin-slider mechanismand the slider-multipleparallelogram-slider mecha-nism. We can point out that the auto-adjustmentmovements takes place respectively at 1.48 secondand 1.50 second in each case, the two sliders real-ize wide displacements in order to lead the mecha-nism to the equilibrium position. Afterward, theyslide slowly at the same linear speed. The angu-lar velocity of the pin joint fluctuates during theauto-adjustment motion and becomes equal to theangular velocity of the user’s limbs again once themechanism is readjusted. The simulation showsthat the self-adaption movement takes place soonerwith the slider-multipleparallelogram-slider mecha-nism because its instantaneous axis of rotation iscloser to the human joint. This result verifies the

219

Hinge joint 1Clamping bar Clamping bar

Subject’s limbsPin joint with torsional spring

Slider 1 Slider 2

Hinge joint 1

Slider 1 Slider 2

Clamping bar Clamping bar

Pin joint with torsional spring

Subject’s limbs

Virtual centreof rotation

(a)

(b)

Figure 7. The mechanisms used in simulation. (a)The mechanism slider-pin-slider. (b) The mechanism

slider-multipleparallelogram-slider

(a) (b)

(c) (d)

Figure 8. The configuration of the mechanism slider-pin-slider during simulation. (a) The mechanism atits initial position. (b) The mechanism before the self-adaption movement. (c) The mechanism at the self-adaption movement. (d) The mechanism after the

self-adaption movement

hypothesis that we made in Section 3.3. On theother hand, we also notice that the torsional springhas a larger deflection in the case of the multiple-

(a)

(c)

(b)

(d)

Figure 9. The configuration of the mechanism slider-multipleparallelogram-slider during simulation. (a)The mechanism at its initial position. (b) The mech-anism before the self-adaption movement. (c) Themechanism at the self-adaption movement. (d) The

mechanism after the self-adaption movement

-60

-40

-20

0

20

0 0.5 1 1.5 2 2.5 3Linear velocity - Slider 1 (mm/s)

Time (s)

slider-pin-slidermultiple-parallelogram

Figure 10. Simulation’s result: linear velocity of theslider 1

-20

0

20

40

60

80

0 0.5 1 1.5 2 2.5 3Linear velocity - Slider 2 (mm/s)

Time (s)

slider-pin-slidermultiple-parallelogram

Figure 11. Simulation’s result: linear velocity of theslider 2

parallelogram mechanism which creates more impor-tant speeds at the self-adaption moment.

220

-8

-6

-4

-2

0

2

4

6

0 0.5 1 1.5 2 2.5 3

Angular velocity (deg/s)

Time (s)

slider-pin-slidermultiple-parallelogram

Figure 12. Simulation’s result: the angular velocity ofthe hinge 1

0

200

400

600

800

1000

0 0.5 1 1.5 2 2.5 3Torque of the spring (newton.mm)

Time (s)

slider-pin-slidermultiple-parallelogram

Figure 13. Simulation’s result: the torque of the tor-sional spring

4.2 Simulation of the localization of the humanjoint’ICR

Hinge joint

Four-bar mechanism

ICR

Marker

Figure 14. Mechanism used in the simulation todemonstrate the possibility of localizing the ICR of

the limbs

In this simulation, a marker indicates the posi-tion of the ICR of the user’s joint. The marker coin-cides initially with the hinge joint of the mechanism.

We define two equations of movement for the extrem-ity of the marker following the directions

→x and

→y ,

according to the two expressions (5) and (6) obtainedpreviously in the section 2.2.

In order to better cope with the real kinematicsof the knee joint, we introduce a four bar mechanismwith two intersecting slots defining the real locationof the ICR of the knee joint. A torsional spring isadded at the attachment of the mechanism on the 2ndlimb.

(a) (b)

(c) (d)

(e) (f )

(g) (h)

Figure 15. The evolution of the mechanisms duringthe simulation. a) The mechanism at its initial posi-tion. The marker is placed at the position of the hingejoint. (b) At the beginning of the motion, the markermoves so that its extremity coincides with the posi-tion of the ICR. (c) The mechanism crosses its singularposition, a light oscillation takes place. (d) An abruptchange of rotational velocity takes place, the limbturns in the inverse direction, which generates an im-portant oscillation. (e) The mechanism crosses its sin-gular position again. (f) A new change of rotationalvelocity, but without changing the rotation direction,a short oscillation produces. (g) Another change ofrotation speed in the opposite direction produces an-other short oscillation. (h) The marker pursues thetrajectory of the ICR until the end of the simulation

The mechanism is initially placed in the posi-tion where the rotation angle of the hinge joint is -10 degree. A constant angular velocity (7 degree/s) isfirst set to the first hinge joint of the four-bar mecha-nism. At 1 second, the angular velocity is changed to-10 degree/s, then it will be changed to -20 degree/sat 2 second and to 5 degree/s at 2.8 second. A tor-sional spring (10 N.m/degree) is added to the attach-

221

ment’s pin joint of the second limb. The two slider’sfriction coefficient is set at 0.001. The simulation endsat 3 second.

The figure 15 shows the evolution of the simula-tion. The results of the simulation confirm the resultsof the analysis made in section 2.2. Except the oscil-lations, the extremity of the marker indicates exactlythe position of the ICR during its motion.

-51

-50

-49

-48

-47

-46

-45

-44

6.8 7 7.2 7.4 7.6 7.8 8 8.2

y axis (mm)

x axis (mm)

position of the markerposition of the ICR of the limbs

Figure 16. The trajectory of the ICR and the marker

6.8

7

7.2

7.4

7.6

7.8

8

8.2

8.4

0 0.5 1 1.5 2 2.5 3

Displacement at x axis (mm)

Time (s)

displacement of the markerdisplacement of the ICR

Figure 17. Displacement along the x-axis

As shown in the figures 16, 17 and 18, the resultsof the simulation verify the validity of the formula(5) and (6) established in Section 2.2. The extremityof the marker and the ICR are in coincidence duringthe motion. Light oscillations occur when the mech-anism crosses its singular position (which happens ataround 0.8 second and 1.2 second in this simulation).This is caused by the deflection of the torsional springas the mechanism enters its singular configuration.

Oscillations may occur in case of abrupt changesof rotation speed of the user’s joint. The duration ofthese oscillations is shorter than those caused by themoving of the mechanism through its singular posi-tion. However, we notice that if a non-smooth opera-tion of the mechanism takes place at the same instant

-54

-52

-50

-48

-46

-44

0 0.5 1 1.5 2 2.5 3

Displacement at y axis (mm)

Time (s)

displacement of the markerdisplacement of the ICR

Figure 18. Displacement along the y-axis

-60

-50

-40

-30

-20

-10

0

10

0 0.5 1 1.5 2 2.5 3

Rotation angle (deg)

Time (s)

Rotation angle

Figure 19. Rotation angle of the hinge joint

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 0.5 1 1.5 2 2.5 3

Spring torque (newton.mm)

Time (s)

Spring torque

Figure 20. The spring torque

of the kinematic singularity crossing, an large oscilla-tion may occur. We can observe this phenomenon atthe moment of the first change of the angular velocity(when the simulation is at 1 second).

To reduce the amplitude of the oscillation, it isnecessary to place the mechanism initially in its sin-gular configuration and, at the same time, to increase

222

the stiffness of the torsional spring placed towards theattachment, which means that the attachments of themechanism on the members must be tightened well.Abrupt movements must be avoided when the mech-anism is near its singular position.

5 Conclusion

In this paper, we have demonstrated that it is pos-sible to design orthosis devices which can self-adaptto a human joint’s kinematics. As a by-product, theseself-adjusting mechanisms can be used to estimate theeffective axis of rotation during movement. These re-sults show the possibility to build an intelligent ortho-sis which is able to track human joint and is adaptableto large human joints.

In future work, 3D mechanical designs will bestudied in order to build orthoses which can trackcomplex kinematics of human joints. Solutions forthe self-adaption in both horizontal and vertical di-rections will also be examined. We will also take aninterest in the control of these mechanisms.

Acknowledgements

The authors would like to thank Han Xu, trainee atISIR - University Pierre et Marie Curie, for his con-tribution in the work of simulation, Guillaume Moreland Nathanaël Jarrasse for the discussions about theconception of active orthoses used in rehabilitation,Dr. Philippe Decq and his colleagues of the hospitalHenri Mondor for their comments on this work.

References

[1] T. Herzberg, A. Albrod, Knee-Joint Orthosis,United States Patent, Pub. Num. 6,309,368 B1, Oct.30, 2001.

[2] J. O’Connor, J. Goodfellow, The mechanics of theknee and prothesis design, The Journal of Bone andJoint Surgery, 1978.

[3] P.N. Smith, K.M. Refshauge and J.M. Scarvell,Development of the concepts of knee kinemat-ics, Archives of Physical Medicine and Rehabilitation,2003, Volume 84, Issue 12, 1895-1902.

[4] G. Lambert, Knee Orthosis, United States Patent,Pub. Num. US2006/0089581 A1, Apr. 27, 2006.

[5] S.R. Lamb, R. Moore, Anatomic Fracture BraceFor The Knee, United States Patent, Pub. Num.4,523,585, Jun. 18, 1985.

[6] G.V. Aaserude, R.H. Rubin, Polycentric Vari-able Axis Hinge, United States Patent, Pub. Num.4,699,129, Oct. 13, 1987.

[7] V. Patel, K. Hall, M. Ries, J. Lotz, E. Ozhin-sky, C. Lindsey, Y. Lu, S. Majumdar, A three-dimensional MRI analysis of knee kinematics,Journal of Orthopaedic Research, 2004, 283-292.

[8] K.L. Markolf, J.S. Mensch, and H.C. Amstutz,Stiffness and laxity of the knee–the contribution ofthe supporting structures. A quantitative in vitrostudy, The Journal of Bone and Joint Surgery, 1976,58:583-594.

[9] K.L. Markolf, A. Graff-Radford, and H.C. Am-stutz, In vivo knee stability. A quantitative assess-ment using an instrumented clinical testing appa-ratus, The Journal of Bone and Joint Surgery, 1978,60:664-674.

[10] A. Gupta, M.K. O’Malley, V. Patoglu andC. Burgar, Design, Control and Performance ofRiceWrist: A Force Feedback Wrist Exoskeletonfor Rehabilitation and Training, The InternationalJournal of Robotics Research, 2008.

[11] M. Casadio, P. Morasso, V. Sanguineti, P. Gian-noni, Impedance-controlled, minimally-assistiverobotic training of severely impaired hemipareticpatients, Biomedical Robotics and Biomechatronics,2006. BioRob 2006. The First IEEE/RAS-EMBS In-ternational Conference on , 2006, 507-512.

[12] A. Forner-Cordero, J.L. Pons, E.A. Turowska andA. Schiele, Kinematics and dynamics of wearablerobots, in José L. Pons (Ed.), Wearable Robots -Biomechatronic Exoskeletons, (Chichester, John Wi-ley and Sons, 2008) 70-74.

[13] A. Schiele and F.C.T. Van der Helm, KinematicDesign to Improve Ergonomics in Human Ma-chine Interaction, IEEE Transactions On NeuralSystems And Rehabilitation Engineering, 14(4), 2006.

[14] B.L. Shields, J.A. Main, S.W. Peterson, andA.M. Strauss, An Anthropomorphic Hand Ex-oskeleton to Prevent Astronaut Hand FatigueDuring Extravehicular Activities, IEEE Transac-tions On Systems, Man, And Cybernetic PART A:Systems And Humans, 27(5), 1997.

223