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Acta Universitatis Sapientiae
Electrical and Mechanical Engineering, 11 (2019) 42-53
DOI: 10.2478/auseme-2019-0004
42
Design of a Human Knee Reeducation Mechanism
Allaoua BRAHMIA1, Ridha KELAIAIA2
1 Faculté de Technologie, Université 20 Aout 1955, Skikda, Algerie,
e-mail: a.brahmia@univ-skikda.dz
2 Faculté de Technologie, Université 20 Aout 1955, Skikda, Algerie,
e-mail: r.kelaiaia@univ-skikda.dz
Manuscript received January 21, 2019; revised July 7, 2019
Abstract: To establish an exercise in open muscular chain rehabilitation (OMC), it is
necessary to choose the type of kinematic chain of the mechanical / biomechanical system
that constitutes the lower limbs in interaction with the robotic device. Indeed, it’s accepted
in biomechanics that a rehabilitation exercise in OMC of the lower limb is performed
with a fixed hip and a free foot. Based on these findings, a kinematic structure of a new
machine, named Reeduc-Knee, is proposed, and a mechanical design is carried out. The
contribution of this work is not limited to the mechanical design of the Reeduc-Knee
system. Indeed, to define the minimum parameterizing defining the configuration of the
device relative to an absolute reference, a geometric and kinematic study is presented.
Keywords: Rehabilitation robots, lower limbs, open muscle chain, kinematic chain,
model geometric and kinematic.
1. Introduction
During the last decades, scientific research in the field of medical engineering
and rehabilitation has led to important advances. Thus, rehabilitation robots have
been created in order to help therapists during complex and repetitive tasks [1-3].
The robot then allows the realization of predetermined movements constituting
the heart of the physical exercise to be performed. Furthermore, the use of a
rehabilitation device following the appearance of the deficit allows rapid recovery
of motor function. In addition, locum robotics makes it possible to facilitate
notably the realization of daily tasks (demotic, chair lifts, object lifts, etc.) [4].
Moreover, the use of robotic devices has become widespread in the field of sports
training. Indeed, the addition of controlled actuators makes it possible to extend
the range of movements proposed in order to achieve specific objectives that
cannot be achieved by conventional drive machines whose principle is limited to
the displacement of a heavy load [5]. Thus, the realization of such devices
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Design of a Human Knee Reeducation Mechanism 43
requires, in addition to the medical expertise necessary for the formalization of
needs, varied knowledge from many disciplines such as: robotics, biomechanics,
mechatronics, automation, and electronics. Robotics Rehabilitation and training
has grown considerably in recent years. Motorized devices have been designed
and are generally based on architectures similar to those of the weight machines
found in the weight rooms. The definition of reference trajectories, the achievable
domain or the consideration of articular biomechanics requires collaborative
work between experts in the medical field and the designers of the robotic system.
From the point of view of the automatic controller, the objective is to guarantee
a safe operation for the user while ensuring the realization of the movements
according to the performances desired by the medical profession. The automatic
controller then allows the definition of control structures ensuring the stability of
the controlled system during movements performed, but also allows to take into
account the user's interactions with the rehabilitation device to generate
physiologically consistent trajectories.
The objective of this work is therefore the design of a new device for knee
rehabilitation. The adopted approach follows a process of several stages: study
and definition of the objectives in terms of rehabilitation, design of the
mechanical architecture, dimensioning of the actuators, and study of the control
part, experimental validation and finally clinical study. Note that this entire
process cannot be performed in a single job and, therefore, the last three points
will be subject to further study.
2. Kinematic description of the movements of the knee joint
A. Segments and joints of the lower limb
The human body is considered as a set of rigid poly-articulated segments.
Thus, the joints each have one or more degrees of freedom and each segment may
be associated with a reference frame to position it in space. The analysis of the
human movement can, by convention, be realized with respect to three planes of
references, also called anatomical planes, which are the sagittal plane, the
frontal/coronal plane and the transverse plane, as well as three anatomical axes,
which are the sagittal axis, the transverse axis and the longitudinal axis (Fig. 1).
The lower limb consists of three body segments: the thigh, the leg and the foot.
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44 A. Brahmia, and R. Kelaiaia
Figure 1: Anatomical planes.
B. The knee joint
The knee is a synovial joint that joins the leg to the thigh, it is located at the
lower end of the femur and the upper end of the tibia, it is a joint that supports
the weight of the body. It involves three bones, the femur, the tibia and patella
(Fig. 2), through three joints, the patellofemoral joint the double femoro-tibial
joint.
C. Amplitudes of the movements of the knee
The knee is the distal articulation of the thigh. It arouses the interest of the
biomechanical community because of its complexity and the multiplicity of its
pathologies.
Figure 2: The knee joint [6]. Figure 3: Kinematic description of knee joint
movements.
Recent studies have shown that, from an anatomical point of view, the
kinematic description of the movements of the knee joint has six axes and six
degrees of freedom [7]. These are presented in Fig. 3, and consist of three
rotations and three translations arranged in a simple kinematic chain [8]. Note
that it is commonly accepted that the amplitudes of the translational movements
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Design of a Human Knee Reeducation Mechanism 45
are negligible vis-à-vis the amplitudes of the movements for ordinary tasks
(walking, lifting chair). The amplitudes of the flexion-extension movement of the
knee vary between 0 ° in hyperextension and 150 ° in hyper-flexion Fig. 4.a
shows that knee flexion can reach 160 ° when the patient is in a squat position
[9]. In addition, the internal and external rotations respectively admit maximum
amplitudes of 30 ° and 40 ° (Fig. 4.b). Thus, in this work, a single axis of rotation
will be considered [10], that is to say: the mediolateral axis around which the
flexion-extension takes place.
Figure 4: Amplitudes of knee movements.
3. Open Muscular Chain exercises (OMC)
Usually, clinicians commonly accept a definition of OMC exercise: it is an
exercise of the lower limbs during which the foot is free during the movement
[11]. A knee flexion-extension exercise is performed in an open muscular chain
if the dynamic resultant of the force Fd opposing the movement is perpendicular
to the longitudinal axis of the leg. Fig. 5 [12] presents, in a simplified way, the
knee flexion and extension movements in OMC.
Figure 5: OMC exercises.
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46 A. Brahmia, and R. Kelaiaia
4. Concept of the reeducation mechanism “Knee-Reeduc”
The goal of our work is to develop a machine for lower limb rehabilitation to
perform open muscle chain exercises. For a device to perform this type of
exercise, its kinematic structure must meet certain constraints. By analogy with
robotic systems, the mechanical assembly consisting of the lower limbs and the
rehabilitation device is a set of polyarticulated rigid segments. Indeed, man is
often considered in biomechanics of movement as a poly-articulated and self-
controlled mechanical system [13,14].
A. Kinematic concept
For a knee rehabilitation movement to be considered as an exercise in OMC
[11], it is possible to consider that the foot must rest on a support. In order to
achieve this constraint, the considered choice of the Knee-Reeduc mechanism
assumes that the hip is not fixed relative to the frame and that the movement is
generated by a mobile support on which the foot rests. In addition, in order to be
able to develop a kinematic chain allowing OMC movement to be achieved, the
mechanical assembly consisting of the lower limb must form an open kinematic
chain, and the rehabilitation device chosen is formed of a closed kinematic chain
(Fig. 6.a and Fig. 6.b). The kinematic design of the new device therefore amounts
to defining the nature of Li links (Fig. 7).
L1 corresponds to the connection between the frame and the segment-thigh.
The patient is seated on a seat, which is not fixed to the frame of the machine.
The resulting kinematic linkage is a pivot connection corresponding to the coxo-
femoral hip joint (connecting the lower limb to the hip). L2 corresponds to the
knee. Let us note that only the movements of the knee along the main axis of
flexion extension are sufficient for the kinematic definition of the concept
Reeduc-Knee. L3 represents the connection between the mobile support and the
linear module of the machine. This is done by a pivot connection. L4 corresponds
to the connection between the linear module and the frame of the machine. It is
characterized by a helical connection along the longitudinal axis defined by the
lower limb in full extension. L5 corresponds to the connection between the
moving part of the linear module with the frame. It is characterized by a slider
joint.
Fig. 7 shows the kinematic concept used for the knee rehabilitation machine
in the sagittal plane. Note that here; the kinematic structure is presented for only
one of the two lower limbs. Indeed, the functions of each of the lower limbs are
symmetrical.
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Design of a Human Knee Reeducation Mechanism 47
Figure 6: (a) Kinematic chain of the rehabilitation device;
(b) Kinematic chain of lower member in OMC.
Figure 7: Kinematic concept of Knee-Reeduc in the sagittal plane.
B. Mechanical structure
The design of the mechanical structure of Knee-Reeduc is performed in
accordance with the kinematic structure proposed above. Thus, Knee-Reeduc
comprises a motorized linear transfer performing the translation L3. The latter
then sets in motion a mobile support (leg-segment and thigh-segment) realizing
the rotation L2 and thus allowing the flexion/extension of the foot. The thigh-
segment provides the connection between the leg-segment (pivot link) and the
frame through a pivot link L1. Fig. 8 shows the type of linear transfers retained to
carry out the translation L5. The moving part of this module is set in motion by
the rotation of a transmission screw L4, the latter being actuated by a reducing
motor. The design of this module is carried out for a useful run of 0.8 m to reach
a wide panel of users taking into account the maximum length of the lower limb
in full extension of a large patient. Finally, the linear module is mounted on a
fixed platform (frame). Fig. 9 shows the mobile support (segment-leg and
segment-thigh) made to support the lower limbs. The design of this support is
made for a width of 0.25 m. The maximum length of this support including the
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48 A. Brahmia, and R. Kelaiaia
two segments is equal to 0.95 m (this length is adjustable). Fig. 10 shows the
mechanical part of the Knee-Reeduc machine as a whole.
Figure 8: Linear module. Figure 9: Mobile support.
Figure 10: Mechanical part of the machine Knee-Reeduc.
5. Geometric and kinematic modeling of the “Knee-Reeduc” machine
The device is driven by a DC motor, which delivers a constant rotation speed
ω (control variable). A nut forming a support is driven by the transmission screw
by the speed ω, which makes it possible to move the nut by a translation speed
VB (configuration variable or operational variable). The therapist needs to know
the value of the flexion of the knee α (the output) at each position λ (the entrance),
for that, we have to find a relation between these quantities according to the
constants of the system.
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Design of a Human Knee Reeducation Mechanism 49
A. Geometric model
For a geometric closure, we have:
(1)
(2)
Figure 11: Mechanism of the Knee-Reeduc Device.
In (2), λ is the race (λ0 ≤ λ ≤ D1);
We have:
(3)
(4)
(5)
Replace (3), (4) and (5) in (2) we find:
(6)
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50 A. Brahmia, and R. Kelaiaia
Therefore, we can find this system
(7)
The system (7) can be written in the form
(8)
Putting and , the system (8) becomes:
(9)
The resolution of the system (9) can give:
(10)
We finally find:
(11)
The angular closure allows us to write:
(12)
: flexion angle of the knee
Interpretation of the geometric model:
- If the value of λ is minimal (λ = λ0), we will have a maximum value of α:
equivalent to a maximum knee flexion (α - α0 = 150 °).
- If the value of λ is maximal (λ = D1), we will have a minimum value of α:
equivalent to a minimum knee flexion (α - α0 = 0).
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Design of a Human Knee Reeducation Mechanism 51
B. Kinematic model
The kinematic model consists of calculating the configuration variable (or
operational variable) VB according to the control variable ω.
We consider that:
, (13)
where φ represents the angle of rotation of the screw (constant uniform rotation),
and t represents the time.
We will have a uniform translation of point B.
If:
, (14)
the pitch “S” of the screw corresponds to the unit advance “La”
By advancing one turn of the screw, this gives φ = 2π and La = S.
Therefore, we get:
. (15)
For the establishment of the inverse kinematic model, we use the relation between
ω and VB, which is given by:
. (16)
To get uniform translation movement, we use the following expression:
. (17)
This equation allows us to calculate the value of the race at any moment t. This
value is introduced into the system (10) to find the value of knee flexion α at any
moment t.
Interpretation of the kinematic model:
The velocity vector of the knee joint is none other than the derivative with
respect to the time of the position vector
.
So:
(18)
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52 A. Brahmia, and R. Kelaiaia
Therefore:
(19)
To validate the equations of the geometric and kinematic model, a simulation
in Matlab is carried out. Fig. 12. shows the different configurations of the Knee-
Reeduc for a race of 0.7 m. Table 1 shows the values of the flexion / extension
angles for each position of the Knee-Reeduc, i.e. as a function of the λ stroke, for
values of: D2 = 0.45 m; D3 = 0.4 m; α0≈39.5°.
Figure 12: Knee-Reeduc Configuration for 0,1m ≤ λ ≤ 0,8m.
Table 1: Values of the flexion / extension angles as a function of the race λ
The race λ [m]
flexion / extension angle [°]
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
168.284
153.615
139.195
124.228
108.200
90.397
69.257
39.571
Thus:
- the maximum flexion of the knee is: α - α0 = 168.284-39.5 = 128.78 °
- the minimum flexion of the knee is: α - α0 = 39.57-39.5 = 0.07 °.
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Design of a Human Knee Reeducation Mechanism 53
6. Conclusion
In this paper, we have presented a mechanical design of a new human knee
reeducation mechanism, named Knee-Reeduc, which is consistent with a fixed
hip and a free foot. First we have studied the movements of the knee joint (type,
amplitudes, etc.), then we have studied the open muscular chain exercises
(OMC), which allowed us to design the mechanical structure of the reeducation
mechanism “Knee-Reeduc”. Finally, a geometric and kinematic modeling of the
developed mechanism was presented. Taking into account the generic approach
followed in this design problem and based on the obtained results, future work
concerns the realisation of this machine.
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