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Harmony Tan Shi Le KED130002!!
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ABSTRACT
The principle of equilibrium can be used to describe and analyze various problems, and is pivotal in
operations of all engineering disciplines. In this report, we will explore the application of
equilibrium in a branch of prosthetics: knee implants. With the increasing frequency of and demand
for knee implants, future innovations depend on fulfilling the characteristics of an equilibrium
system in order to provide appropriate functionality. Newer knee implants are now being designed
to closely mimic knee joints in the human body more accurately, by studying the anatomy of the
individual components of a knee joint, i.e. the ligaments, cartilages, and how they are able to
support the body and maintain stability while allowing its unique range of movement.
1.0 INTRODUCTION
1.1 Principle of Equilibrium
The two main conditions of a system in equilibrium are:
∎ the sum of forces acting on the system is equal to zero ! = 0
i.e. the system has zero net resultant force !! = 0
∎ the sum of the moments of all forces and couples in the system about an arbitrary point 0 is
equal to zero !! = 0 i.e. the system has zero net resultant torque (!!)! = 0 .
1.2 Knee Joint
The knee is the largest, most complex joint in the body, and is responsible, in conjunction with the
hip and ankle joints, for supporting the body’s weight during a variety of activities, such as
standing, walking, and running. However, the anatomy of the knee must provide this support while
having the largest range of motion (up to 160 degrees) of any joint of the lower limb, lacking the
large muscle mass that supports and strengthens the hip, and lacking the strong ligaments that
support the ankle joint.
The knee is made up of the inferior extremity of the femur, the superior extremity of the tibia, and
the patella (kneecap). Structurally, the knee is composed of two joints within a single synovial
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capsule: the tibiofemoral joint (between femur and tibia) and
the patellofemoral joint (between patella and femur). The
contact surfaces of these bones are covered with articular
cartilage, a smooth substance that protects the bones and
enables them to move easily. Semilunar cartilages called
menisci, located between the femur and tibia, absorb shock
transmitted to the knee joint and help prevent side-to-side
rocking of the femur on the tibia. Ligaments hold the three
bones together and provide stability, while the long thigh
muscles give the knee strength.
Normally, all of these components work in harmony, but disease such as arthritis or injury can
disrupt this harmony, resulting in pain, muscle weakness, and reduced function. When nonsurgical
treatments like medications and walking supports are no longer suitable, knee replacement surgery
is recommended to relieve pain, correct leg deformity, and resume normal activities.
1.3 Knee Replacement Surgery (Knee Arthoplasty)
According to the Agency for Healthcare Research and Quality, more than 600,000 knee
replacements are performed each year in the United States. Knee replacement surgery, one of the
most common joint replacement surgeries performed worldwide, involves the resection of the
articulating surfaces of the tibia and femur and replacing them with metal and plastic bearing
surfaces. Depending on circumstances, up to three bones surfaces may be replaced. In total knee
replacements, all three bone surfaces, i.e. the
inferior extremity of the femur, superior
surface of the tibia, and posterior surface of
the patella are resurfaced and are replaced
with artificial components. Figure 2: Total (right) knee replacement
Figure 1: Normal (right) knee anatomy
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2.0 KNEE IMPLANTS
Knee implants are surgical prosthetic replacements used to replace damaged knee joints. In order to
effectively replace the structure and function of the knee joint, the various designs for knee implants
must fulfill the criteria of an equilibrium system in three dimensions. Poorly designed knee
implants may cause discomfort, pain, disability, and irreparable damage to the muscles, ligaments,
and bones involved in the knee. To avoid creating designs that result in these complications, we can
apply the principle of equilibrium to develop knee implants with improved mobility and durability.
The components of the knee implant must be properly aligned, properly constrained, and statically
determinate. Improper alignment of the members with their connections and supports will disturb
the equilibrium of the knee joint. Improper constraints will cause instability due to inadequate
reactive forces to balance the external forces acting on the joint. Statical indeterminacy resulting
from redundant constraints, on the other hand, is equally undesirable because it may hinder
movement and require additional but unnecessary invasive surgery, not to mention increase bulk
and weight of the implant.
Each knee implant in total knee replacement consists of three components: a femoral component, a
tibial component, and a patellar component. The components are designed so that metal articulates
against plastic, providing smooth movement and minimal wear. The femoral component replaces
the lower ends of the femur (femoral condyles) and the groove where the patella (kneecap) sits, by
curving around the end of the femur and having an interior groove so the patella can move up and
down smoothly against the bone as the knee bends and straightens. The tibial component is
typically a flat metal platform with a cushion of strong, durable plastic called polyethylene, which
provides the bearing surface. For additional stability, the metal portion of the femoral and tibial
components may have a stem that inserts into the center of the bone.! The patellar component
replaces the inner surface of the kneecap;!usually, the patellar button is a dome-shaped piece of
polyethylene, duplicating the shape of the patella, cemented into the posterior surface of the
kneecap.
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The connections of the implant
components to the femur, tibia and patella
must be secure enough to withstand the
forces and torques acting upon the knee
region from the thigh and leg. Component
fixation varies according to the implant
model and patient’s situation. In Figure 5,
femoral and tibial fixation are achieved by
way of long single stems inserted into the
bones – typical in joint revision
components (replacing knee prostheses) or
in cases of severe arthritis – each is a rigid
support with three reactive forces !! ,!! ,!! and couple-moment
!! ,!! ,!! components.
The RBKTM Knee System by FlexiTech Instruments, shown in
Figure 6, features a short cone-shaped stem and four pegs on the
underside of the tibial component, designed to resist torsional
forces and provide additional fixation.
Figure 3: 2-D left lateral view of left knee prosthesis
Figure 4: 3-D view of general knee prosthesis
Figure 5: Support reactions at components' fixations
Figure 6: Mobile-bearing knee prosthesis – RBKTM Knee System
!!
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Biomechanical studies reveal that designs with long cylindrical stems are more stable than devices
with short tapered ones. This is because there are reactive forces acting perpendicular to the stem
along its length at the points of contact between the bone and stem. The resultant force of these
numerous reactions passes through the centroid of the stem. The longer the stem, the further the
centroid is from the knee joint, thus the more secure the fixation. Longer stems transmit force more
efficiently along the thigh and leg, and with less strain on the bone.
In cases where the knee is very unstable and a large
amount of bone is missing, it may be necessary to join
the femur and tibia with a metal "hinge" in the center.
The smooth pin connection between the femoral and
tibial components restricts lateral and superior-inferior
translation, preventing dislocation or malpositioning
and reducing wear.
Traditional knee implants, as has been discussed above,
do not feature a ball-in-socket mechanism, probably
because early knee implants were developed on the
hinge concept. However, despite innovative efforts,
traditional knees continue to be ‘noisy’ due to anterior sliding of the femur on the tibia during
bending, as demonstrated by the knee-‘pops’ and -‘clicks’ experienced when descending stairs. To
overcome this, Wright’s EVOLUTION® Medial-Pivot Total Knees feature ball-in-socket
articulation, which has been shown to enhance stability and produce a greater range of motion than
traditional knee implants, allowing the prosthesis to move and feel more like a normal, healthy
knee. This makes sense in terms of engineering mechanics because ball-in-socket connections allow
three dimensional rotation while preventing three dimensional translation. The attached ligaments
and curved-shape of the femoral component on the tibial component impede unwanted rotation
about the other 3-D axes.
Figure 7: Rotational-hinge knee prosthesis
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!Figure 8: Unstable rotation with anterior-posterior sliding in traditional knee implants
!Figure 9: Stable rotation with no anterior-posterior sliding in ball-and-socket knee implants
Knee implants are designed by observing the forces and torques acting on the knee joint in various
positions e.g. standing, sitting, squatting, kneeling, jumping, stretching. There should be zero
resultant force and torque at the joint in each scenario – otherwise, the implant will not mimic the
behavior of a healthy knee joint and it will be hard to control movements involving motion of the
knee – almost all daily activities. The main focus is to ensure
that the implant is properly constrained, i.e. the lines of action
of the reactive forces
are neither concurrent,
nor parallel, nor
intersect a common
axis.
!!
Figure 10: Knee implant system in various angles of flexion
!
!!
!!
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3.0 CONCLUSION
There is still much room for improvement in the development of knee implants. By applying the
principle of equilibrium with a little ingenuity, knee prostheses have evolved to behave more and
more like normal knee joints, and in future, advances in knee implant technology with better
performance and increased longevity may reduce the need for revision surgery.
REFERENCES
1. Hibbeler, R. C., Yap, K. B. (2012). Mechanics for Engineers: Dynamics (13th ed.).
Equilibrium of a Rigid Body (pp. 199-259). Singapore: Pearson, Prentice Hall. ISBN
9780132911276.
2. Martini, F. H., Timmons, M. J., Tallitsch, R. B. (2012). Human Anatomy (7th ed.). The
Knee Joint, (pp. 231-235), Chapter 8 The Skeletal System Articulations. USA: Pearson.
ISBN 9780321688156
3. American Academy of Orthopaedic Surgeons. (2013). Knee Replacement Implants.
Retrieved 20th December, 2013 from website:
http://orthoinfo.aaos.org/topic.cfm?topic=A00221
4. Aesculap Implant Systems. (2013). Types of Knee Implants. Retrieved 20th December,
2013 from website: http://www.soactivesofast.com/default.aspx?pageid=2127
5. Arthritis Research UK. Complex or Revision Knee Replacement. Retrieved 20th
December, 2013 from website: http://www.arthritisresearchuk.org/arthritis-
information/surgery/knee-replacement/different-types/complex-knee-replacement.aspx
6. Sahara Medical Tourism. (2010). Knee Replacement Surgery. Retrieved 20th December,
2013 from website: http://www.saharamedicaltourism.com/knee-replacement-surgery-
india.html
7. Global Orthopaedic Technology. Knee Products. Retrieved 21st December, 2013 from
website: http://www.globalortho.com.au/product-list.php?cat=Knee
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8. Wright Medical Technology. (2013). Why A Ball-In-Socket? Retrieved 21st December,
2013 from http://www.wmt.com/evolution/physicians/why-a-ball-in-socket.asp
9. Agarwal, S. Knee Replacement Surgery. Retrieved 21st December, 2013 from website:
http://cardiffhipandknee.com/id2.html
10. Matthys Orthopaedics. (2011). Revision Knee Replacement. Retrieved 21st December,
2013 from website: http://www.jointpain.md/Procedures/KneeRevision.aspx
APPENDIX
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