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Harmony Tan Shi Le KED130002 1 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

Statics Assignment

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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