1. 1
ABSTRACT
The few microcontroller based active/semi-active prosthetic knee joints available
commercially are extremely expensive The life style of lots of amputees are miserable without a
proper prosthetic device. The purpose of the proposed Active Prosthetic Knee (APK) design is to
investigate a new schema that allows the device to provide the full necessary torque at the knee
joint which is actual replica of the actual leg. This study involves the design features of the
mechanical aspects, sensing system, communication and fuzzy logic. The proposed prosthesis
utilizes a passive pneumatic system accompanied by a stepper motor to provide movement of
the prosthesis leg. This knowledge is based on study of human gait cycle. The design dimensions
where taken from real test subject. The kinematic model of the proposed design is analysed and
respective force equations are penned. After study various instrumentations, apt sensing and
control system is chosen.
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INTRODUCTION
In the past, the only resources available for the people who lost their lower limb were
walkers, wheelchairs, wooden pegleg and crutches. Leg and knee play crucial roles in the
body. Leg contributes to keep the body balanced and supported while standing up. Knee joins
the upper and lower legs together and provides the bending motion that allows us to walk.
The few microcontroller based active/semi-active prosthetic knee joints available
commercially, such as Otto Bock's prosthetic C-Leg, are extremely expensive. Therefore,
they are only affordable by a few, and despite their high cost, they suffer from sensitivity to
input uncertainty which could impact their performance. The drive mechanism of the APK
should be simple to enable easy maintenance and high robustness.
Lower Limb Anatomy
Between the hip and ankle joints, four main bones exist: femur, patella, tibia, and
fibula. The longest and strongest bone of the human skeleton, femur, extends from the pelvis
to the knee. Tibia and fibula are two long bones in the human leg between the knee and ankle.
Tibia is the interior and thicker whereas, the fibula is the exterior and thinner one. The upper
end of tibia joins femur to form the knee joint which is the most complex joint in the human
body. The femur has two lower rounded ends (condyles). The one toward the center of the
body called the medial condyle, and the one to the outside called the lateral condyle. Above
the condyles on both sides are epicondyles which work as sites for muscle and ligament
attachment. The cruciate ligaments attach to the space between the two condyles called
intracondylar fossa. Cruciate ligaments are the most important ligaments in the knee joint and
they serve to stabilize it and guide its motion. The patella (kneecap) protects the knee joint
and increases the quadriceps lever arm thus allowing the quadriceps to apply force to the tibia
more effectively during extension. This triangular-shaped bone is not connected to femur or
tibia directly. The patella is connected to the femur by being contained within the patellar
tendon that connects the quadriceps muscles to the tibia. Fibula has no contact with the knee
and attaches to the tibia by ligaments below the tibial bearing surfaces of the knee.
Gait Cycle
Human waling cycle is a repetitive pattern of events. The repetitive pattern can be
divided into two distinct events: 1) foot strike and 2) toe-off. When in a walking cycle, both
legs contribute to four different events: 1) foot strike, 2) opposite toe-off, 3) opposite foot-
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strike, and 4) toe-off. Since the events occur in a similar sequence and are independent of
time, the gait cycle can be described in terms of percentage, rather than time, thus allowing
normalization of the data for multiple subjects. The initial foot strike occurs at 0% and occurs
again at 100% . The opposite leg undergoes the same events, only out of phase by 180
degrees, with the opposite foot strike occurs at the 50% mark and the second opposite foot
strike occurs at 150%.
Each stride represents one gait cycle and is divided into two periods (main phases): stance
and swing . Stance is the period when the foot is in contact with the support surface and
constitutes 62% of the gate cycle. The remaining 38% of the gait cycle constitutes the swing
period that is initiated as the toe leaves the ground. The stance phase is divided into four
phases: initial double support, mid-stance, terminal stance, and second double support.
The initial double support extends from foot strike to opposite toe-off (0-12%). The initial
limb support is characterized by a very rapid weight acceptance onto the forward limb with
shock absorption and slowing of the body’s forward momentum. Mid-stance (phase #2) and
terminal stance (phase #3) are involved in the task of single limb support when the weight of
the body is fully supported by the reference limb. The mid-stance phase (10-30%) initiates
with lifting of the opposite foot and continues until body weight is aligned over the
supporting foot. The terminal stance (30-50%) commences when the heel rises and continues
until the opposite foot strikes the ground. Body weight progresses beyond the reference foot
during this phase. The second double support (phase #4), which is also called pre-swing,
prepares the limb to swing; it begins after the opposite limb has reached the floor and begins
to accept weight. Transfer of body weight from the reference limb to the opposite 10
limb takes place in this stage; the length of this phase is exactly the same as that for phase #1
(50-62%). The swing period can be subdivided into three phases: Initial swing, mid-swing,
and terminal swing. Initial swing (phase #5) starts with toe-off and ends with foot clearance
when the swinging foot is opposite the stance foot (62-75%). Mid-swing (phase #6) continues
from the end point of the initial swing and continues until the swinging limb is in front of the
body and the tibia is vertical (75-85%). In the terminal swing (phase #7), the limb is
decelerated and finally strikes the ground for the second time. Limb advancement is occurs
during the pre-swing phase and throughout the entire swing period.Figure 1-1 shows the
pattern of human walking cycle.
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Anthropometric study
Any design can provide better comfort unless they are designed with proper
dimensions. After study of human anthropometry, the height of the human body has direct
correleeation with each and every part of the human body. Every part of human body is
percentage of the total human height. In order to design a perfect fit, we got figure out the
dimensions of each and every part of the human limb. After study of human body of height
157 cm and weight totalling 62 kg, it was found out the total length of leg segment is 40 cm.
The leg segment is defined as the length from the lateral epicondyle of the thigh (the knee
joint) down to the lateral malleolus (ankle joint). It is calculated that tibial portion is 0.246H
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is calculated as 45 cm.
Foot 240 mm
Thigh 300 mm
Leg 447mm
Total length from hip to toe 832 mm
Mechanical Design
The design is consists of three phases. The first phase involve studying the human
movement from one step to another step. The second step involves making design criteria.
The third step involves study of actuator and finding the best actuator for fitting the purpose.
The design criteria ithis applied are any prosthetic leg will be efficient if they are able to
function if climbing stairs. The average stair height is considered to be a 3 cm. From studying
the human leg, we can see that the knee portion is the one which decides the amount leg
movement in forward direction. From analysis the knee joint provides angular movement, the
leg muscles contracts and expands in accordance to it. The leg muscles contracts as soon as
toe is off the ground and expands when toe strike the ground. In order to provide a angular
movement for the knee we chose a motor. There is wide range of motors available namely
brushless, servo and stepper motor. Torque is most important parameter when motor is
selected. The maximum and minimum torque required for knee is 35 nm to 120 nm. We
selected a stepper motor for this case. The mechanism of chosen in this design is piston and
crank mechanism. The knee is made up of stepper motor. When motor rotates in the
anticlockwise direction, the knee pulls up connecting rod. The connecting rod is welded with
foot. The connecting rod forces the femur bone up. The angle of rotation is directly
proportional to the distance travelled. A safe limit washer is used in this design to limit the
angle of rotation of the motor. As per basic analysis, the amount of rotation required for knee
flexion is -45 degree to +45 degree. Any rotation in this axis is chosen as operating region.
Safe limit washer is placed at an angle -60 degree and + 60 degree. This angle is chosen as
safe limit region. Any rotation apart from this angle disintegrates the design. When the motor
rotates anticlockwise, prosthesis foot strikes off the ground. The motor rotates in positive
direction; the connecting rod pulls down foot down.
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Mechanical system
The mechanical system shown above has stepper motor attached perpendicular to
knee joint. In this design r is the length of the arm that connects piston and the stepper motor.
Where α is the angle between the socket and tibidal section or leg section. The angular
velocity is denoted as ω.
The angular velocity of the knee and the stepper motor is same. So the angular velocity of
the knee or the stepper motor is given by the equation
ω= V/ r sinα
The torque on the knee is calculated with the expression
ζ= F.r.sinα
Distance travelled by the prosthetic limb is calculated using the expression
D= L1 sinα
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L1 is length of the calf or femur region.
The longitudinal distance travelled by the prosthetic limb is given by the expression
Q= L2 cosα
L2 is the length between the knee joint and the foot.
Materials
Prosthesis leg consists of different components. The types of components are given
below
Socket
The comfort and effectiveness of a prosthesis is largely governed by how well it fits
onto the remaining part of the patient's own limb, which is called their residual limb. The
connecting part of a prosthesis is called the socket and it's carefully molded around a plaster
cast taken from the residual limb. The fit of a socket has to be precise or the new limb may
damage the residual one, causing discomfort or tissue damage and perhaps even making it
impossible to wear the prosthesis for a time. A patient's residual limb is likely to change
shape and size over months and years so new sockets will be needed from time to time. More
precisely fitting sockets can now be made by scanning a patient's residual limb with lasers
and cutting-edge techniques such as 3D printing are also now being used. In this design we
are using a carbon fibre cloth. As per the test subject, the dimensions procured are outer
dimension 150 mm and inner diameter 100 mm. The total length of the femur bone is 300
mm. The thickness of the socket depends upon the weight of the person .It is given by the
expression
Socket thickness = weight of the person/ 20 kg
=60/20=3mm
L2
L1
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Liner
The liner is a protective cover made of a flexible, cushioning material. Worn over
your residual limb, it reduces movement and chafing between the skin and the socket. Liners
are designed with specific characteristics to work with different suspension systems.
Selecting the right liner helps ensure that your prosthesis fits well and is comfortable to wear.
To meet a range of needs, standard models are available in three primary materials:
Polyurethane has a unique ability to flow away from high pressure. That means the pressure
in your socket is well distributed. A polyurethane (sometimes abbreviated as PUR) liner
offers a precise, intimate and comfortable fit for all types of residual limbs. These “flow
characteristics” and damping of pressure on your limb make it a good choice for sensitive,
bony or scarred residual limbs. Polyurethane performs best with vacuum suspension or
suction suspension.
Knee Joint
Knee joint is made up of Aluminium 6060. Knee section looks in the shape of c type
of model. In this design, there are three safe limit washer placed a two side and one at the
core. The safe limit washer will help to limit the movement of the connecting rod away from
the recommended position. On the side of the knee joint, the stepper motor is attached. Knee
joint is provided with a shaft that connects the stepper motor and the connecting rod. The One
end of the shaft is connected to stepper motor and other end is bolted to connecting rod. A
shown in figure
Stepper Motor
Stepper motor is used to drive the knee section. The stepper motor has 1.8 degree
movement for each and every step. In this design the operating parameters are +45 to -45
degree. The total number of step required for movement in the anti clockwise direction is
N= angle /1.8 = 45/1.8 =25
Thus the motor has to rotate 25 steps backward and 90 steps forward to complete full gait
cycle. The rotary speed for the apk is assumed to be 0.5 rev/ sec. That it is 30 rpm. In this
design, stepper motors leadshine 42SH03 are used. The nominal torque for the motor is 30 to
150Nm. The service life of the motor is 20,000 hrs. The reason behind the fitting the motor
outside is to remove the motor easily and fit again as they have a short life.
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Connecting rod and piston
The connecting rod in this design is actuated using stepper motor. When the motor
rotates the shaft that connects both moves the connecting rod in the upward direction and
when rotates clockwise direction it pushes in the downward direction. The connecting rod
used in this case made of aluminium, which drastically reduces the weight of the entire
system. When connecting rod moves up, air is sucked into the cylinder through the hole
present at the bottom of the cylinder. When the rod moves down, the air is expelled out.
Shank
The shank corresponds to the anatomical lower leg, and is used to connect the socket to the
ankle-foot assembly. A shank, a central pylon, which is a narrow vertical support, rests inside
a foam cosmetic cover. Shank allow for adjustment and realignment of prosthetic
components. The strength of the shank is provided by a hard outer shell that is either hollow
or filled with lightweight material. In this design the shank is made up two systems of
components one connected to the piston and connecting rod and other connected to the foot
assembly. When the foot touches the ground the shank moves down to decreases the shock
acting on the system and the shank expands when the feet moves up.
Foot
Dynamic Response foot/ankle mechanisms emerged in the 1980s with the objective of
providing improved response over existing designs by simulating passive subtalar joint
motion within the prosthetic foot. The SAFE foot was introduced followed by the Seattle
Foot, The Carbon Copy II and the Flex-Foot. In this design ottobacks foot made up of carbon
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fibre is used. The main reason for using carbon fibre is reduces the impact of the shock acting
on the device. The shock is produced when the foot strikes the ground. The length chose in
this 240 mm.
Socket Carbon fibre cloth
Motor Graphite stepper motor
Suspension Aluminium 6060
Body cover Pp copolymer
Pneumatic cylinder Aluminium
Foot Carbon fibre cloth
Kinematic analysis of designmodel
From the above figure A) is the free body diagram and B) simplified model
The assumptions made in kinematic analysis is
i) the location of center of mass is constant for pneumatic cylinder and rotating shaft.
However, in reality, due to motion of piston and motor the center of mass for these
components are not fixed in place.
ii) the mass of the cylinder and shaft are negligible.
Fax is the constrain force apply from the hip unit since this part acts as a sliding
mechanism. Fay is the force acting to move the amputee in the upward direction. P1 is the
force acting on the femur and the knee. α2 is the angle between the femur and the knee. L1 is
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the distance between the hip joint and the knee. L2 is the distance between the knee joint and
the shank. α1 is the angle between the hip and the femur.α3 is the angle between the tibia and
the knee joint.P2 is force applied on the tibia and femur by the shaft. The applied torque on
the hip joint and knee joints are ζ1 and ζ2 respectively
Torque T1= L3 P1 Sin α1 +L4 Sin α2
Torque T2 = L2 P2 Sin α3
[ p1 = [ L3 Sinα1 L4 Sin α2 [ ζ1
P2] 0 L2 Sin α3 ] ζ2]
Sensing system
Sensing system is important when a person has one amputee knee and other normal human
knee. The sensing system is used to measure the amount movement done by the actual knee.
This data is important as the amputee motion should be vice versa of the actual knee motio.
The potentiometer was used to measure the knee flexion/extension angle. The
potentiometer sensor is attached to the human knee. The accelerometer was mounted on the
femur to read its inclination angle. Comparing to the tibia, the femur has lower acceleration,
momentum, and range of motion. As a result, there is less disturbance effect on the femur
than the tibia.
Communication
The communication between sensory part and actuator is accomplished via wireless
communication by employing two boards, the transmitter and receiver. The transmitter board
collects data from accelerometer and rotary potentiometer, converting it from analog to
digital and sending it through the Bluetooth communication.
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When the data is sent to motor, the motor rotates depending on angular movement in the
active human knee.
Fuzzy logic
The fuzzy logic-based controller consists of a feed forward architecture designed from
nominal empirical data. Consequently, a feed forward architecture is only sufficient under
nominal conditions and will fail if excessive disturbance is introduced into the system.
Therefore, the initial controller architecture is modified to include a feedback loop containing
a proportional-integral (PID) controller which tracks the actual position of the APK. The
error signal is calculated by comparing the actual APK position to the desired APK position
and is fed into the PID controller which outputs a control signal (torque command) that
supplements the output of the fuzzy logic controller. Hence the feed forward fuzzy control
predicates which phase of the gait cycle the APK is in and outputs a nominal output torque
corresponding to the determined phase. Meanwhile the PID control compensates for
excessive ground reaction forces (disturbances) by supplying additional torque to drive the
APK to its desired position.
Fuzzy Logic Design:
Angular data from the healthy leg is fed into the fuzzy logic controller which
determines the current phase of the APK and outputs an associated torque command to the
motor. The fuzzy inferencing system (FIS) consists of two components: a set of input
membership functions that map angular data to a set of phases within the gait cycle and a set
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of if-then rules which describe the human-like reasoning mechanism of the FIS. Each of the
seven phases in the gait cycle has an associating membership function corresponding to the
angle of the healthy femur and tibia.
Conclusion
A simple mechanical system might lead very accurate control sytem. The
prosthesis is driven by rotary motor couple with pneumatic system. On paper the design looks
satisfactory unless fabrication is done the model can be verified. Different types of sensing
systems are investigated to extract signals from the user’s intact leg and send the captured data to
the APK. Thigh and shank are portions were the battery and the controller will located. The
potentiometer together with the accelerometer is chosen as the sensing unit. Battery used in this
design is lithium ion battery of 10,000 mah. The battery will last for day of intense walking. The
communication between the sensory part and actuator was established by employing two boards,
the transmitter and reciever, which talk to each other through bluetooth communication. The
knowledge-based system proposed herein to generate knee torques considers the uncertainty of
inputs
Limitations
The prosthetic design might lack stability when walking in steep terrain. The motor can
work effectively for only 20000 hrs. That is only 2 years. The socket design might not have a
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perfect fit only the base values are considered not changing dimensions of the thigh muscles.
Battery doesn’t last long as stepper motor consumed lot of energy for operation.
Appendix
bore diameter cylinder
d =√4𝑚𝑎𝑟/√𝜋𝑝
=0.020 m
W = v/r sinα
=0.5/15*sin 45
=0.047
ζ = 1*9.8 *15 mm*sin 45
=0.1nm/sec
D=300 *sin 45
=21.2 cm
Q= 45*cos 45
=31 cm
