Design and optimization of exoskeleton
structure of lower limb knee joint based on
cross four-bar linkage
Cite as: AIP Advances 11, 065124 (2021); https://doi.org/10.1063/5.0053899
Submitted: 12 April 2021 . Accepted: 26 May 2021 . Published Online: 11 June 2021
Moyao Gao,
Zhanli Wang,
Shuang Li, Jing Li,
Zaixiang Pang, Shuai Liu, and
Zhifeng Duan
COLLECTIONS
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AIP Advances 11, 065124 (2021); https://doi.org/10.1063/5.0053899
© 2021 Author(s).
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scitation.org/journal/adv
Design and optimization of exoskeleton structure
of lower limb knee joint based on cross four-bar
linkage
Cite as: AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
Submitted: 12 April 2021 • Accepted: 26 May 2021 •
Published Online: 11 June 2021
Moyao Gao,a)
Zhanli Wang,b)
Shuang Li,c)
Jing Li,d) Zaixiang Pang,e)
Shuai Liu,f) and Zhifeng Duang)
AFFILIATIONS
School of Mechatronic Engineering, Changchun University of Technology, Changchun 130012, China
a)
gaomoyao@163.com
Author to whom correspondence should be addressed: wangzl@ccut.edu.cn
c)
shuang_0313@163.com
d)
Lj5286@126.com
e)
pangzaixiang@ccut.edu.cn
f)
m15526835521@163.com
g)
18243159982@163.com
b)
ABSTRACT
This research introduces the knee exoskeleton system that assists in knee joint rehabilitation, which is centered on human wearing comfort.
According to the bionic principle, this paper proposes a bionic knee exoskeleton structure based on a cross four-bar linkage mechanism.
The cross four-bar linkage mechanism is used to simulate the internal cruciate ligament of the human knee joint to realize the instantaneous
rotation center movement of the knee joint. The motor drives the telescopic rod to simulate the movement of the exoskeleton of the knee
joint by the thigh muscle of the human body. The auxiliary limit locking structure simulates the knee joint patella to prevent hyperextension
of the exoskeleton of the knee joint. The particle swarm-based algorithm is used to optimize the size and position of the connecting rod of
the cross four-bar linkage to follow the motion of the human knee joint better. The results show that the optimized and synthesized cross
four-bar linkage mechanism has a small average error value, which can better reproduce the anthropomorphic motion characteristics of the
human knee joint, achieve an ideal match between the motion form of the human knee joint and the exoskeleton, and improve coordination
and adaptability with human joint movement. Through the wearer test, it is found that the structure has a variable instantaneous center of
rotation trajectory. Under the condition of satisfying the flexion angle and torque of the human body, the knee joint movement could be
simulated with the optimal trajectory to achieve the consistency with the human knee joint movement, so as to alleviate the discomfort of
the wear movement of the patients in the auxiliary rehabilitation process, and it provides an advantage for the wear comfort of the human
rehabilitation movement.
© 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0053899
I. INTRODUCTION
Walking is an important part of human daily life. The phenomenon of walking inconvenience, lower limb muscle weakness,
lower limb dyskinesia, and limb function decline is caused by senile
diseases due to certain neuromuscular diseases, sports injuries,
aging, etc. The number of these groups is increasing year by year.1 In
order to improve their quality of life and make them better integrate
into society, they need not only their psychological confidence but
AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
© Author(s) 2021
also physical support. Appropriate physical support can promote the
daily lives of people with functional disorders, such as neuromuscular diseases and lower limb movement disorders. Nowadays, with the
rapid development of technology, exoskeleton robots have become
wearable rehabilitation aid devices, which are used to assist the
human body or enhance the muscle strength of the wearer. In particular, the lower extremity exoskeleton rehabilitation robot could
help patients have continuous, effective, and multi-modal rehabilitation treatment, strengthen patients’ awareness of active training,
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accelerate the recovery process of the motor function of the affected
limb, achieve normal walking, and improve walking ability. The
market share of lower limb exoskeleton robots in the rehabilitation
industry is rapidly expanding. Compared with previous rehabilitation assistance methods, such as wheelchairs that cannot move on
uneven surfaces such as stairs, lower limb exoskeleton robots enable
patients to move on any surface. The main goal of the lower limb
rehabilitation robot is to help patients regain better gait, reduce the
workload of the therapist, provide patients with more comfortable
and complete services, and improve the quality of life.2
In recent years, the lower limb exoskeleton rehabilitation robot
has been heralded as a promising medical aid device for the medical rehabilitation of healthy individuals and disabled patients.3 The
rapid development of robotic bionic technology has also provided
new ideas for lower limb exoskeleton rehabilitation robots. Many
well-known studies on walking rehabilitation-assisted exoskeleton
robots have been reported. For example, the HAL series of lower
limb exoskeletons from the University of Tsukuba in Japan can help
patients adjust appropriate walking gait;4 eLEGS is a lower limb
assisted exoskeleton robot developed by the Berkeley Bionic Laboratory of the University of California;5 and ReWalk assisted lower limb
exoskeleton was developed by Israel through crutches.6 These lower
extremity exoskeleton robots all have motors or hydraulic actuators
on the hip/knee joints to assist in power, and they have gyroscopes
and electrical sensors, such as force position or EMG, which can
quickly determine the patient’s movement intention and realize the
human–machine interaction.
In this article, we focus on the knee exoskeleton. Numerous scientific research institutions and medical institutions at home and
abroad have successively carried out research on the structure of the
knee joint exoskeleton. Previous studies on the knee joint exoskeleton include the SEA elastic-driven knee exoskeleton from the Delft
University of Technology7 and MIT adaptive knee exoskeleton.8,9 .
In terms of knee exoskeleton robots, currently, many existing knee
exoskeletons are constructed from single-axis knee joints. For knee
orthoses, they have a simple hinge structure, which can be easily constructed and has good durability. However, they can only control
the flexion phase but cannot fully control the walking gait phase.
The actual human knee joint has an instantaneous center of rotation
[Instantaneous Center of Rotation (ICR)] motion mode. In addition,
the knee joint, as one of the three major joints of the lower limbs of
the human body, not only needs to stabilize and protect the body
but also has a certain degree to which compliance helps the lower
limbs achieve normal movement.10 Due to this feature, a single-joint
exoskeleton cannot fully track the motion of the human knee joint.
Due to the misalignment of the center, part of the energy is lost.
For multi-center joints, its structure is complex and its durability
is lower than that of single-axis joints. However, the instantaneous
center of rotation (ICR) changes during the rotation, which generates torque that helps to reduce the energy required by the wearer
during walking.11,12 At the same time, in the walking gait phase, the
change of ICR will change the distance between the foot and the
ground, thereby providing the patient with a more stable movement
posture.13
In recent years, due to the continuous optimization of the
mechanical design of the lower extremity exoskeleton robot and the
more perfect human–computer interaction system, the structure of
the lower extremity exoskeleton robot has become more complex
AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
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and contains more parts. However, due to the space and weight limitations of the exoskeleton robot, the anthropomorphic mechanical
design must be adopted to meet the degree of freedom and movement required by the human body. The design of the lower extremity
exoskeleton is similar to the design of the uniaxial knee joint.14,15
However, the human knee joint exhibits multi-axis rotation behavior,16 and these uniaxial knee joint structures cannot reproduce this
behavior. In addition, because the transfer of force to the lower
extremity in the non-moving direction will cause power loss, the
inaccuracy of movement between the exoskeleton and the human
leg may be a more critical problem for fast and dynamic gait, which
will affect the normal wearer. Gait imposes kinematic restrictions
or increases the mass of mechanical devices to the wearer’s body.17
The limitation of kinematics and the extra mass will bring unexpected external force to the human body, change the normal gait,
and increase the metabolic cost; the efficiency of the equipment is
low, and it is difficult to cooperate with the human joints to complete
the coordinated rehabilitation training.
However, better motion alignment, higher ground clearance,
and appearance are the advantages of multi-axis knee exoskeleton
robots. Many research institutions in South Korea have studied
multi-axis knee exoskeleton robots. Instantaneous rotation center
movement is realized by the linkage mechanism, and the fixed and
mobile knee exoskeleton rehabilitation robots are applied.18–20 In
recent years, other national research institutions have also applied
mechanical design of various multi-axis mechanisms to modular
lower limb knee exoskeleton robots.21–23 The literature uses an adaptive knee exoskeleton, which can effectively eliminate the negative impact on the human knee joint.24 In order to better adapt
to the structure of the human knee joint, Technische Universität
Darmstadt improved the linkage mechanism to the form of flexible
joints.25 In addition to the use of linkage mechanisms for adaptive knee exoskeleton structures, there are also mechanisms such as
pneumatic mechanisms, crank mechanisms, and hydraulic mechanisms that have been optimized and improved to be used in adaptive
knee exoskeleton robots.26–28
We found that the multi-axis knee joint mechanism is usually used in orthotics for amputees and patients with knee injuries.
It is well known that the multi-center knee joint mechanism can
expand the area of voluntary knee joint stability so that the patient
has a more natural gait in the knee flexion gait.29 However, as far
as we know, it is still rare to find an actively driven lower extremity
exoskeleton that uses a multi-center knee joint mechanism.
In order to solve this problem, according to the theory of bionics, this paper designs a bionic knee exoskeleton structure based
on a cross four-bar linkage mechanism that is used to simulate
the cruciate ligament of the human knee joint. An auxiliary limit
locking structure of the knee joint patella is simulated, and the
lower limb thigh muscle is simulated with a tie rod. The instantaneous center of rotation (ICR) movement of the knee joint is
realized by a motor drive, so as to reduce the discomfort of the rehabilitation patient during the exercise process and help the patient
achieve a more accurate walking gait. At the same time, a method
for designing and optimizing the knee joint exoskeleton structure
of a lower limb rehabilitation robot is proposed to better reproduce and optimize the microstructure movement of the knee joint.
This method can easily design and verify the knee joint by simply changing specific variables. The rationality of the exoskeleton
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structure helps patients achieve comfortable rehabilitation training.
Experimental results show that the optimized and synthesized cross
four-bar linkage mechanism can better reproduce the anthropomorphic characteristics of the knee joint and improve the coordination and adaptability with the motion of the human knee joint.
The study of the exoskeleton structure of the bionic knee joint has
a good role in promoting the lower limb exoskeleton rehabilitation robot to help patients achieve more comfortable rehabilitation
training.
II. BIOMECHANICS MODEL OF THE KNEE JOINT
Based on the principles of ergonomics and the biomechanical
structure of the human body, the analysis shows that the motion of
the human knee joint is essentially multiaxial. The human knee joint
includes the femur, tibia, anterior cruciate ligament, posterior cruciate ligament (Fig. 1), and knee joint. When bent, the femur will have
a tendency to slide and roll on the tibia, with a variable instantaneous
center of rotation (ICR) (Fig. 2). Therefore, before designing a bionic
exoskeleton knee joint structure, it is very important to understand
and quantify the motion form of the human knee joint. Since the
human knee joint is not a single-axis joint, although many research
institutions, domestic and foreign,30–32 have tried to find the instantaneous rotation center of the knee joint in the mathematical model
of the human knee joint motion, still the motion trajectory of the
instantaneous center of rotation of the knee joint cannot be accurately described, and there are many errors; therefore, it is necessary
to quantify the instantaneous rotation center of the human knee
joint and convert it into a mathematical model so that the designed
bionic exoskeleton knee joint is more suitable for the human knee
joint movement.
In the study of the instantaneous center of rotation of the
knee joint, it is found that the femoral posterior ankle bone of
the human knee joint can be simulated as a spherical surface, and the
three-dimensional movement of the femur on the tibia is defined.33
The expression of the average motion of knee joint flexion and
extension was determined, and the center of the sphere was taken
as the reference point. Figure 3 shows the radius and position of
the condyle ball and the direction of the axis considered in the
model.
FIG. 1. Anatomical diagram of the knee joint.
AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
© Author(s) 2021
FIG. 2. Knee joint flexion process.
In order to analyze the influence of varus and internal rotation on the movement of the tibia and femoral joints in the sagittal
plane, the planar knee centrode is obtained by projecting threedimensional femoral axis motion on the sagittal plane. The bestfit equations (1)–(4) for the motion parameters of varus rotation
(Varus), varus (IntRot), anterior-posterior translation (Zdist), and
near-distal translation (Ydist) were calculated using the knee flexion
angle (F) as an independent variable as follows:
Varus = (0.0791 × F) − (5.733 × 10−4 × F 2 )
− (7.682 × 10−6 × F 3 ) + (5.759 × 10−8 × F 4 ),
(1)
Introt = (0.3695 × F) − (2.958 × 10−3 × F 2 )
+ (7.666 × 10−6 × F 3 ),
(2)
Ydist = (−0.0683 × F) + (8.804 × 10−4 × F 2 )
− (3.3750 × 10−6 × F 3 ),
(3)
Zdist = (−0.1283 × F) + (4.796 × 10−4 × F 2 ).
(4)
FIG. 3. Human knee joint anatomy model and ICR model generation.
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Here, the knee flexion angle is measured in degrees and the displacement is measured in millimeters. These equations are used to
determine the coordinates of an instantaneous knee center of rotation in the sagittal plane at a lateral distance equal to the value of
the X 1 coordinate. This article assumes that the exoskeleton knee
joint structure is placed at 60 mm from the origin of the inner and
outer coordinate system of the knee joint (consider the distance
between the skin and the exoskeleton), and at any given angle F,
by using the Euler angle transformation matrix [Eq. (5)],34 the new
Y and Z coordinates of the center point on the femoral axis are
obtained.
At the knee flexion angle of 0○ –120○ , the transformation coordinate Y 2 –Z2 of the midpoint of the Y 1 –Z1 system on the femoral
axis is obtained by using the above equation. The ICR coordinates
of the knee joint flexion angle are calculated. Using formula (6), the
motion curve at any distance can be
⎡X2⎤ ⎡CV ⋅ CR (SF ⋅ SR + CR ⋅ SV ⋅ CF) (−CF ⋅ SR + SF ⋅ SV ⋅ CR)⎤
⎥
⎢ ⎥ ⎢
⎥
⎢ ⎥ ⎢
⎢Y2⎥ = ⎢ −SV
⎥
CF ⋅ CV
SF ⋅ CV
⎥
⎢ ⎥ ⎢
⎢Z2⎥ ⎢CV ⋅ SR (−SF ⋅ CR + CF ⋅ SV ⋅ SR) (CF ⋅ SR + SF ⋅ SV ⋅ SR) ⎥
⎦
⎣ ⎦ ⎣
⎡X1 ⎤
⎢ ⎥
⎢ ⎥
(5)
⋅ ⎢Y1 ⎥,
⎢ ⎥
⎢Z1 ⎥
⎣ ⎦
obtained by calculating the cross section between the ICR and the
vertical plane in the entire buckling range of the grid,
X2 = 60,
Y2 = −SV ⋅ X2 + YDIS,
Z2 = CV ⋅ SR ⋅ X2 + ZDIS.
(6)
The coordinate of instantaneous center of rotation of the knee
joint is given by the above formula. The instantaneous center of rotation is an effective tool to compare and analyze the relative motion
of rigid bodies, especially the motion of the human knee joint. If a
mathematical model of knee motion based on the instantaneous center of rotation (ICR) is obtained, the knee exoskeleton can more realistically simulate physiological motion through this mathematical
model.
scitation.org/journal/adv
FIG. 4. Single-axis knee exoskeleton structure diagram.
Based on the biomechanical analysis of the human knee joint,
the knee exoskeleton structure similar to the human knee joint musculoskeletal system is designed according to the principle of bionics. Figure 6 shows a simple exoskeleton system that simulates the
motion of the human knee joint. The two ends of the mechanism
are fixed on the femur and tibia, respectively. As a simple rotational
joint, the general lower extremity knee exoskeleton robot structure rotates on the sagittal plane. However, the rotation center of
the human body and the knee joint used for the lower extremity
exoskeleton robot is inconsistent with the bending of the human
knee joint, and during the movement, the joint axis dislocation will
occur. Therefore, in order to make the movement of the human
knee joint and the exoskeleton knee joint consistent, the knee joint
exoskeleton structure similar to the human knee joint is designed,
and the four-bar linkage mechanism is used to realize the characteristics of the multi-axis knee joint. At present, the four-bar linkage mechanism is also used in a variety of rehabilitation aids. Like
the lower extremity robot, this linkage mechanism has produced
numerous research results.35,36 However, the cross four-bar linkage
used in the rehabilitation aid equipment has better multi-degreeof-freedom controllability and structural bionics than the four-bar
III. ANALYSIS OF THE BIONIC KNEE JOINT MOTION
MECHANISM
At present, in order to simplify the design of the knee joint,
most research institutions design their knee joint exoskeleton structure as a single-axis center rotation with a single degree of freedom
(as shown in Fig. 4). From the description in Sec. II, we can see that
the human knee joint can be regarded as a simple hinge joint, but
its function is similar to a multi-axis joint—an instantaneous center of rotation joint (shown in Fig. 5). When a single-axis knee joint
exoskeleton structure is supported on a multi-axis knee joint, relative sliding will occur between the exoskeleton and the limbs. This
movement can easily cause slippage and exert an unnecessary external force on the limbs. Patients wearing the exoskeleton will feel
discomfort due to sliding movement and pain due to the restraining
force exerted by the bandage on sliding.
AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
© Author(s) 2021
FIG. 5. Knee movement trajectory.
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FIG. 6. Summary view of the knee exoskeleton structure.
linkage mechanism. In addition, the cross four-bar linkage mechanism can provide multi-axis motion similar to the human knee joint,
which can reduce the relative motion between the wearer and the
auxiliary equipment. If relative movement is not reduced, the generated friction will scratch the user’s skin and become a major source
of the additional external force of relaxation. Because the movement
of the cross four-bar linkage is similar to that of a human knee joint,
the cross four-bar linkage can minimize these problems and improve
the comfort when wearing an exoskeleton.
In view of the above-mentioned problems, this paper proposes
a bionic knee exoskeleton structure based on a cross four-bar linkage
mechanism. The cross four-bar linkage mechanism is used to simulate the internal cruciate ligament of the human knee joint to realize
the instantaneous rotation center movement of the knee joint. The
motor was used to drive the telescopic rod to simulate the movement of the human thigh muscle to drive the exoskeleton of the
knee joint, and the auxiliary limit locking structure simulates the
knee joint patella to prevent hyperextension of the exoskeleton of
the knee joint. Figure 7(a) shows a schematic diagram of the knee
joint exoskeleton robot structure. The structure has the advantages
of simple structure, strong robustness, and easy processing. It could
be accurately defined by mathematical models, and the overall size
was changed by changing the length of the femur stem to meet the
needs of people with different body lengths [Fig. 7(b)]. In this study,
the cross four-bar linkage mechanism is applied to the knee joint
brake module, and the length of the linkage mechanism is determined by the parameter optimization scheme described in Sec. IV
(Fig. 8). In addition, the knee joint exoskeleton robot is analyzed to
estimate the torque and the bending angle, which change according to the rotation of the cross four-bar linkage. The drive part
of the executive module is composed of an integrated servo motor
reducer. The motor selected is MYACTUATOR RMD-X10 48 V.
Although the diameter of the motor is large, the integrated design
of the motor reducer makes the overall weight and design of the
exoskeleton lighter, and the instantaneous torque and rated power
are 50 N m and 700 W, respectively.
When walking on the level ground, the average maximum knee
extension torque is 40.5 N m, and the maximum output power of
the knee joint is 154.4 W.37 In the normal walking process, since
the flexion and extension states of the knee joint are completely
within the maximum range, the parameters of the four-bar linkage drive module we selected meet the conditions required by the
torque and speed. The cross four-bar linkage mechanism can perform knee exoskeleton rehabilitation assisted walking exercise. Their
relationship will be introduced in Sec. IV.
AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
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FIG. 7. Knee joint exoskeleton structure.
IV. LOCATING THE ICR OF A FOUR-BAR LINKAGE
In order to drive the knee joint exoskeleton cross four-bar linkage, the drive motor is connected to the tibial base frame (L1) (Fig. 9)
through a telescopic rod. By using the cosine law based on the given
special angle fixed point, we derive the mapping function of the angle
from the knee actuator θac to the knee joint θKnee from the cosine law
as follows:
θKnee = f (θac ).
(7)
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FIG. 9. Analytical model of the knee joint exoskeleton linkage mechanism.
four links cross is the instantaneous center of rotation of the knee
joint.
Figure 11 shows the position of the reference four-bar linkage.
Using the Freudenstein equation link mechanism analysis method,
a closed-loop structure is created around the link for the position
analysis of the four-bar mechanism. The size of the position vector
is the link length of the four-bar mechanism to be synthesized.39 α is
the input angle because the exoskeleton linkage mechanism will be
braked by the thigh during walking. Similarly, the inclination of link
1 (β) can be known from the initial configuration. The relationship
between the angle θ3 and other four-bar linkage parameters to define
the complete configuration of the four-bar linkage at any moment is
found as follows:
AB + BC = AD + DC,
(8)
FIG. 8. Cross four-bar linkage model of the exoskeleton mechanism.
When the knee joint flexes, it drives the tibial base frame (L1)
and the connecting rod (L2) rotate. The ICR of the cross four-bar
linkage mechanism (the same as the intersection of L2 and L3 in this
figure) moves along a predetermined path, which is most similar to
the ICR of the human knee joint. Since the system assists the wearer’s
legs through multi-axis motion, it helps to maintain the comfort and
restraint between the wearer and the system by reducing friction.
Using the cross four-bar linkage mechanism, the torque and
speed of the system are controlled by the operation of the motor
connected to the truss frame. In the initial state, the system generates high speed and low torque. When the rotation angle increases
(the wearer’s knee joint is bent), the speed decreases and the torque
increases. The motor drive module in this study uses a coupler to
drive the telescopic rod to move. From the literature,38 the force of
the cross four-bar linkage is calculated with the change in the knee
joint bending angle (Fig. 10).
The displacement analysis of the cross four-bar linkage can be
expressed in a mathematically closed form according to the length
and position of the four rods of the actuator. The point where the
AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
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FIG. 10. Bending angle and force diagram of the connecting rod.
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cos θ3 =
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1 − tan2 ( θ23 )
1 + tan2 ( θ23 )
,
θ3
θ3
) + B tan + C = 0
2
2
a simplification is obtained as follows:
√
−B ± B2 − 4AC
θ3 = 2 ⋅ arctan(
).
2A
A tan2 (
B(−l3 cos θ3 , l3 cos θ3 ),
(9)
Using the coordinates of the two points
l42 = [l1 − l2 cos α + l3 cos θ3 , l2 sin α − l3 cos θ3 ]
⋅ [l1 − l2 cos α + l3 cos θ3 , I2 sin α − l3 cos θ3 ],
(10)
the following formula is obtained:
l42 − l12 − l22 − l32 + 2l1 l2 cos α − 2l1 l3 cos θ3 + 2l2 l3 cos(α − θ3 ) = 0,
(11)
R1 =
l1
,
l2
(12)
R2 =
l1
,
l3
(13)
l2 − l2 − l2 − l2
R3 = 4 1 2 3 ,
2l2 l3
(14)
A = R2 ⋅ cos α + cos α + R3 − R1,
(15)
B = 2 sin α,
(16)
C = R2 ⋅ cos α − cos α + R3 − R1.
(17)
Using the trigonometric formulas
sin θ3 =
2 tan θ23
,
1 + tan2 ( θ23 )
(19)
(20)
During knee flexion, the tibia rotates around the femur around
the knee joint, that is, connecting rod 1 (L1) rotates with respect
to connecting rod 4 (L4) centered on ICR, and ICR connects rod 2
(L2) and Link 3 (L3) passes through the intersection of two straight
lines. The first line passes through pivot points A and C, and the
second line passes through pivot points B and D of the four-bar linkage, as shown in Fig. 11. The equations of the two straight lines are
calculated in the form of slopes [see Eq. (20)].
FIG. 11. Mathematical model of the cross four link mechanism.
C(l1 − l2 cos α, l2 sin α).
(18)
V. KNEE JOINT OPTIMIZATION BASED ON PARTICLE
SWARM OPTIMIZATION
As the four-bar mechanism moves, the actual output trajectory has deviated from the expected movement trajectory. For this
reason, many scholars have studied the parameter optimization of
the four-bar mechanism and produced different design and optimization methods. Using genetic algorithm (GA) optimization or
Gauss–Newton iterative algorithm optimization and other optimization methods to improve it, the optimization objective function
is established, and the optimal simulation parameters are obtained
through MATLAB software, which can effectively reduce the lateral
and initial trajectory errors.40–42 However, for high-precision driving devices, the lateral and initial errors of the four-bar mechanism
are difficult to meet the design requirements, and the GA coding is
more complicated and less efficient. However, based on the swarm
intelligence proposed by Kennedy and Eberhart in 1995, Particle
Swarm Optimization (PSO) is an evolutionary computing technology. It originated from the study of bird predation and is considered
an iterative-based optimization tool.43 Obviously, the pace of evolution slowed down later because random particles are often at the
same level in the optimization process and tend to fall into the local
optimum solutions. The particle swarm optimization algorithm is
also a multidisciplinary field, which can be abstracted as a numerical
function optimization problem, and it can effectively solve the phenomenon that the PSO algorithm is easy to be premature and the
algorithm is easy to oscillate near the global optimal solution.44
In this regard, if the particle swarm optimization algorithm is
used to optimize the parameter variables of the four-bar mechanism,
the error variation curve of the optimized four-bar mechanism can
be obtained, so that the error of the four-bar mechanism can be
reduced, which provides a theoretical basis for further study of the
motion error of the spatial four-bar mechanism,
−l1 sin β ⋅ l2 cos α − l1 sin β ⋅ l4 cos θ3 + l1 cos β ⋅ l2 sin α − l1 cos β ⋅ l4 sin θ3
,
tan α ⋅ l1 cos β − tan α ⋅ l4 cos θ3 − l1 sin β − l4 sin θ3
−l1 sin β ⋅ l2 cos α − l1 sin β ⋅ l4 cos θ3 + l1 cos β ⋅ l2 sin α − l1 cos β ⋅ l4 sin θ3
Y = tan α ⋅
.
tan α ⋅ l1 cos β − tan α ⋅ l4 cos θ3 − l1 sin β − l4 sin θ3
X=
AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
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(21)
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In this paper, the geometric parameters of the cross four-bar
linkage mechanism are optimized by introducing particle swarm
optimization. A schematic diagram of the connecting rod size and
motion angle model of the plane cross four-bar mechanism is created, and the horizontal and vertical equations of the motion track
points through the vector relationship are solved. The parameter
variables of the four-bar mechanism are analyzed, the lateral and
initial error functions of the motion trajectory are calculated, and
the motion conditions of the four-bar mechanism are restricted. The
particle swarm optimization algorithm is used to search for the optimal value of the geometric parameters of the four-bar mechanism.
A. Objective function
When the bionic exoskeleton knee joint cross-four-bar mechanism is more similar to the ICR of the human knee joint, the cross
four-bar linkage mechanism and the human knee joint movement
coordination will be better. Therefore, the optimization objective of
this paper is to find a four-bar linkage mechanism that can simulate the instantaneous rotation center movement of the anatomical
knee joint under the condition of satisfying the constraints. This can
be achieved by minimizing the distance between the instant center
of the composite four-bar linkage and the knee joint motion center.
Therefore, the objective function is to minimize the Euclidean norm
square variance of the vector from the i-th point of the reference center of the knee joint xI to the i-th point of the cross four-bar linkage
instantaneous center point xF ,
(22)
i−1
B. Constraint condition
Before constraint optimization, it is necessary to limit the
length of the four-bar mechanism to an appropriate scale to limit
the size of the four-bar mechanism so that its entire range of motion
matches the size of the human knee joint. According to the published research on the size and range of motion of the femur and
tibia of the human knee joint structure,45 the connecting rod size in
the literature20 is taken as the basic size before the optimization of
the cross four-bar linkage. The knee joint exoskeleton cross four-bar
linkage mechanism designed in this paper can be defined according
to the parameters of the dual rocker mechanism. Therefore, the constraint conditions of the four-bar mechanism should be satisfied as
follows: (1) the femoral connecting rod is the longest and the tibia
connecting rod is the shortest; (2) the sum of the length of the shortest rod and the longest rod is less than the sum of the lengths of the
other two rods. Therefore, the motion constraint conditions of the
four-bar mechanism are
20 ≤ l1 , l2 , l3 , l4 ≤ 60,
(23)
l1 + l4 < l2 + l3 .
(24)
VI. RESULT
A. Optimized analysis
Compared with other optimization methods, the optimization process of the particle swarm algorithm makes the
AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
© Author(s) 2021
solution of the cross four-bar linkage more convenient and accurate. Finally, the optimal solution of the cross four-bar mechanism is obtained, and at the same time, it can give the wearer a
comfortable walking posture under the condition that the mechanism is fully rotated. In addition, the restrictions on the mechanism and the range of motion have been made in advance, and
the optimal solution of the cross four-bar mechanism was finally
determined.
Figure 12(a) shows a schematic diagram of the optimized front
knee joint ICR motion trajectory (blue line) and four-link motion
trajectory (red line). Through the optimization analysis of the position, length, and angle of the link, combined with the determination of the parameter size of the connecting rod in the literature,35
Fig. 12(b) shows the results of the optimization of the motion curve
of the cross four-bar linkage by the genetic algorithm in the range
of 0○ –120○ of the human knee joint movement. Figure 12(c) shows
the results of the optimization of the motion curve of the cross fourbar linkage by particle swarm optimization in the range of 120○ of
the human knee joint movement. Through comparative analysis, we
found that the trajectory of the cross-bar linkage mechanism following the human knee joint by particle swarm optimization is more
accurate, and the average error range of the knee joint axis point
and the value of the instantaneous center point of the cross four-link
are less than 1 mm. The optimized parameters of the cross four-bar
linkage mechanism are shown in Table I.
B. Tests
n
F(x)min = ∑ [(xI − xF )2 − (yI − yF )2 ].
scitation.org/journal/adv
To test the feasibility and applicability of the knee exoskeleton
robot flexion and extension, first, we tested the flexion and extension
exercises of healthy volunteers (male; height, 177 cm; weight, 65 kg)
in the closed loop position of the exoskeleton robot and applied rotational flexion and extension exercises to the subjects (as shown in
Fig. 13), and the volunteers were fixed on the exoskeleton of the knee
joint at the same time. For testing the utility of the knee exoskeleton,
the only two basic measurements are the knee bending angle and the
torque between the legs on the sagittal plane. Taking into account the
geometric shape of the four-bar linkage mechanism and the movement of the center of rotation, it is necessary to determine the value
by measuring the geometric relationship and the angle between any
two linkages (Fig. 14). Through the geometric relationship of the
two linkages shown in Fig. 9 in Sec. IV, we obtain the bending angle
changes of the knee joint.
The torque tracking performance of the knee exoskeleton was
tested at a clear flexion angle. Figure 15 shows the simulation and
experimental results of torque tracking. During this period, volunteers voluntarily wore the device, and it can be observed that the
torque tracking performance of the knee exoskeleton is very satisfactory for rehabilitation exercises. In the whole knee flexion range,
it can be observed in the process of torque trajectory change. Due to
the small range of motion at the knee joint, the deviation of some
large torques appears in the simulation process. In the actual detection process, it is in line with the knee exoskeleton walking gait
torque range value.
Finally, in order to further prove the effectiveness of the assistance provided by the knee exoskeleton robot, the changes in the
flexion angle torque of the knee exoskeleton were detected when
walking and without assistance. The solid line in Fig. 16 indicates
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TABLE I. Connecting rod size optimization parameters.
L1
44.8 mm
L2
L3
L4
β
52.2 mm
47.7 mm
40.4 mm
27.8○
the changes in the flexion torque of the knee when the knee flexion is 0○ –120○ . Specifically, the wearer was in a standing state, and
the wearer performed unilateral leg flexion tests and full gait cycle
walking tests by wearing a knee exoskeleton.
FIG. 13. Structure of the exoskeleton knee joint.
FIG. 12. (a) Trajectory diagram before optimization, (b) GA optimized trajectory
diagram, and (c) PSO optimized trajectory diagram.
AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
© Author(s) 2021
FIG. 14. Connecting rod motion model diagram.
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FIG. 15. Simulation experiment verification.
caused by joint dislocation. The design of the bionic knee exoskeleton robot in this study provides a good promotion for the comfort of
wearers’ movement. At the same time, the optimization design of the
exoskeleton structure will help to play an important reference role
in the structural design of the lower limb exoskeleton rehabilitation
robot and help patients to achieve more comfortable rehabilitation
training.
ACKNOWLEDGMENTS
FIG. 16. Knee joint exoskeleton flexion torque test.
This research was supported by the National Natural Science
Foundation of China (Grant No. 5187052524).
This work was supported, in part, by the National Natural Science Foundation of China under Grant No. 61873304,
the China Postdoctoral Science Foundation Funded Project under
Grant Nos. 2018M641784 and 2019T120240, and the Key Science
and Technology Projects of Jilin Province, China, under Grant No.
20200404208YY.
The authors declare no conflict of interest.
DATA AVAILABILITY
This study measured that the knee exoskeleton structure has
good compliance and comfort in standing, walking, and flexion at
different flexion angles, and it will not cause discomfort in wearing the legs due to large-angle bending. In the stage of standing and
walking, the limit baffle and the locking mechanism can keep the
joint in a comfortable position to prevent the secondary injury of
the knee joint caused by the overload of the exoskeleton structure.
Therefore, this research proposes that the exoskeleton structure of
the knee joint is feasible in actual sports.
VII. CONCLUSIONS
In this research, a bionic knee exoskeleton robot centered on
human wearing comfort is introduced. The exoskeleton structure
simulates the design of the cruciform ligament of the human knee
joint skeletal muscle system. By introducing its principle and functional characteristics, a knee exoskeleton structure based on the cross
four-bar mechanism is proposed to optimize and realize the instantaneous rotation center motion of the knee exoskeleton. Through the
wearer test, the knee exoskeleton robot can reproduce the anthropomorphic characteristics of the knee joint well and improve the
coordination and adaptability with human joint motion. Under the
condition of standing and walking flexion of the knee exoskeleton
structure, the knee exoskeleton robot can follow well the human
knee joint movement and will not produce the wear discomfort
AIP Advances 11, 065124 (2021); doi: 10.1063/5.0053899
© Author(s) 2021
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
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