Design and Analysis of Affordable Artificial Knee Joint Model. Motion and Stress Analysis will be done on a digital model using SolidWorks

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Design and Analysis of Affordable Artificial Knee Joint Model. Motion and Stress

Analysis will be done on a digital model using SolidWorks

A Graduate Project Report

Submitted to

San José State University

In Partial Fulfillment

Of the Requirements for the Degree

Masters of Science in Engineering

GENERAL ENGINEERING

by

GAUTAM SINGH

FALL 2016

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ABSTRACT

Knee joint consists of different components, i.e. femur, tibia, patella and menisci which make

it a complex structure, undergoing different critical loads in human body performing motions

and physical activities. Amputation or limb loss has been a problem faced by humans for long.

Looking at a decade back, the major available resort to the amputees were walkers, crutches,

peg-leg or wheelchairs. Due to the major advancements in medical science and biomedical

design, a mechanical replacement of any such limb loss are present and it can be custom

designed based on any patient’s needs. The loss of limb can result due to the medical conditions

such as diabetes, peripheral arterial diseases which causes poor blood flow to the extremities,

or due to injuries such a burn, accidents or perhaps due to cancer. In any of such cases, the

affected arm or limb needs to be removed. One way to do that is through amputation. In order

to cope with after effects of amputation, many prosthetics have been designed. A prosthetic is

an artificial extension that replaces missing body part (upper or lower body extremity). It is

part of the field of biomechatronic (mechanical devices with human muscle, skeleton, and

nervous systems) to assist or enhance motor. However, one of the key difference or gap in the

design of knee prosthetic is the lack mechanics around knee movement. Some designs which

did consider knee movements cost higher amount.

In order to fil this gap, I have looked into many literature reviews and tried to design and create

my own knee joint using SolidWorks software. It includes understanding of SolidWorks,

designing and studying each part involved in knee motion and assembling the created part into

one to build a low-cost human knee joint. Later motion analysis has been performed in order

to check the weight bearing, movement and angles the knee joint can take into account.

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ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my supervisor, Lecturer/Consultant Dr. Ken Youssefi for

his positive attitude and constant support and also to my co-supervisor Dr. Raj E. Venkatesh for giving

me the opportunity and for his valuable guidance and unfailing support.

I would like to express my gratitude to San Jose State University Student Center, for giving me the

opportunity to use their Engineering Laboratory for using SolidWorks.

Finally, I express my gratitude to the God, my parents, family, friends and my roommate who have

always been a constant source of encouragement. To all the others who assisted me in one way or

another, I express my sincere gratitude.

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TABLE OF CONTENTS

ABSTRACT....................................................................................................................................I

ACKNOWLEDGMENTS................................................................................................................III

TABLE OF CONTENTS..................................................................................................................IV

LIST OF FIGURES........................................................................................................................VII

LIST OF TABLES...........................................................................................................................IX

LIST OF GRAPHS...........................................................................................................................X

CHAPTER 1: INTRODUCTION.......................................................................................................11

1.1 INTRODUCTION......................................................................................................................11

1.2 Background.......................................................................................................13

1.2.1 What is Knee and its Anatomy? ....................................................................13

1.2.2 Knee Joint and its Structure ..........................................................................15

1.2.3 Knee Joint Movement …………………................................................................16

CHAPTER 2: LITERATURE REVIEW ……………...................................................................................19

2.1 Prosthesis and its Types …………………..................................................................19

2.2 Knee Prosthesis History and its Development ….…………….………………………………22

2.2.1 Structure of Knee Joint .................................................................................22

2.2.2 Motion of Knee ………………………………………………………………………..………………23

2.2.3 Knee Joints Loads …………………………………………………………………………………….24

2.3 Total Knee Replacement …………………………………………………………………………………24

2.4 Prosthetic Knee ………………………………………………………………………………………………25

CHAPTER 3: MECHANICAL DESIGN ………………………………………..………………………………………………..30

3.1 Design Features …………………….………………………………………………………………………30

3.2 Mechanical System……………………………………………………………………….…………......31

3.3 Degrees of Freedom ……………………..………………………………………………………………34

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3.4 SolidWorks…………………………………………….………………………………………………...35

3.4.1 Proposed Design …………………………………………………………….………….………...36

3.4.2 SolidWorks Design – Parts …………………………………….……………………………...39

3.4.3 SolidWorks Design – Assembly ……………………………………………………………...41

CHAPTER 4: Results and Analysis ………………………………..…………………………………………………………43

4.1 Anthropometric Analysis ………………………………………………………………………...43

4.2 Stress Analysis ………………………..……………………………………………………………….45

4.3 Motion Analysis ……………………………….………………………………………………………57

4.3.1 Description of our Problem Statement ………………………………………………….57

CHAPTER 5: Conclusion and Future Works …………………………………………………………………………...62

REFERENCES………………………………………………………………………………………………………………………….69

APPENDICES...……………………………….…………………….………………………………………………………………....69

Appendix 1 Part Report…………….…………………………………………..…………………….73

Appendix 2 Assembly ………………………………………………………………………………...79

Appendix 3 Stress Analysis …………………………………….…………………………………..84

Appendix 4 Motion Analysis ………..……………………………………………………………89

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LIST OF FIGURES

Fig. 1: Patient with Below Knee Amputation …………………………………………………………………………….12

Fig. 2: Amputation in below knee joint..........................................................................................12

Fig. 3: Human Knee Joint (a) Anterior View (b) Posterior View (c) Cross sectional View ……………13

Fig. 4: The axes and planes of biological knee joint …………………………………………………………………..17

Fig. 5: Biological Knee planes …………………………………………………………………………………………………….17

Fig. 6: Trans-radial Prosthesis ……………………………………………………………………………………………………20

Fig. 7: Trans-humeral Prosthesis ……………………………………………………………………………………………….20

Fig. 8: Trans-tibia Prosthesis …………………………………………………………………………….……………………….21

Fig. 9: Trans-humeral Prosthesis …………………………………………………………………………………………..…..22

Fig. 10: Total knee Implant………………………………………………………………………………………………………..23

Fig. 11: Prosthetic Knee……………………………………………………………………………………………………………..24

Fig. 12: Force platform to calculate Ground Reaction Force……………………………………………………...26

Fig. 13: Load assessment on one Knee ……………………………………………………………………………...........31

Fig. 14: Four Bar Knees ……………………………………………………………………………………………………………...32

Fig. 15: Nabtesco 6-bar knee (P-MRS)……….……………………………………………………………………………..…33

Fig. 16: Single Axis Knee …………………………………………………………………………………………………………..…34

Fig. 17: Knee Joint Motion ………………………………………………………………………………………………………....34

Fig. 18: Top view of the Knee Joint Design ………………………………………………………………………………....36

Fig. 19: Final Version of Knee model …………………………………………………………..………………………….…..38

Fig. 20: (A) Dimensions of Part …………………………………………………………………………………….……………..39

(B) Mass properties of Part 1………………………….……………………………………………………………....39

(C) Part 3………………………………………………………………………………………………………………………….40

(D) Part 4………………………………………………………………………………………………………………….……..40

(E) Part 5…………………………………………………………………………………………………………………….…...40

(F) Part 6……………………………………………………………………………………………………………………..…..40

(G) Part 7……………………………………………………………………………………………………………………..….41

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Fig. 21: (A) Assembly of Part 1………………………….………………………………………………………………………..41

(C) Assembly of Part 3…………………………………………………………………………………………………….41

(D) Assembly of Part 4……………………………………………………………………………………………………41

(E) Assembly of Part 5………………………………………………………………………………………………......42

(F) Assembly of Part 6……………………………………………………………………………………………………42

(G) Assembly of Part 7……………………………………………………………………………………………………42

Fig. 22: Final Knee Model …………………………………………………………………………………………..……….….…..42

Fig. 23: (A) Original Model………………………………………………….....………………………45

(B) Analyzed Model …………………………………………………………………………………………………………45

Fig. 24: Knee Model Information………………………………………………………………………………………………….48

Fig. 25: Material Properties ………………………………………………………………………………………………………….50

Fig. 26: Load and Fixtures …………………………………………………………………………………………………............50

Fig. 27: Connector ………………………………………………………………………………………………………………………...51

Fig. 28: Mesh Information ………………………………………………..…………………………………………………………..53

Fig. 29: Solid Mesh (Knee Model)…………………………………………………………………………………………………..53

Fig. 30: Stress Analysis …………………………………………………………………………….…………………....................55

Fig. 31: Strain Analysis…………………………………………………………………………………………………………………..55

Fig. 32: Factor of Safety………………………………………………………………………………………………………………...56

Fig. 33: Human (knee) Position while sitting………………………………………………………………………………….57

Fig. 34: Face 1 and Face 2 are perpendicular to each other……………………………………………………………58

Fig. 35: Virtual position of motor…………………………………………………………………………………………………..58

Fig. 36: Moment analysis around knee…………………………………………………………………………………………..59

Fig. 37: (A) Leg (Tibia and Femur)…………………………………………………………………………………………………..59

(B) Knee Joint…………………………………………………………………………………………………………………….59

(C) Knee bonded with thigh acting as Human Femur………………………………………………………….59

Fig. 38: Units of the measurement…………………………………………………………………………………………………60

Fig. 39: Distribution of Stress on Knee Model…………………………………………………………………………………63

Fig. 40: Applied and Distributed Load on Knee Model……………………………………………………………………63

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LIST OF TABLES

Table 1: Functional Range of Motion of Human Knee ………………………………………………………15

Table 2: Study Properties ………………………………………………………………………..………………………..49

Table 3: Resultant Force……………………………………………………………..…………………………….………49

Table 4: Stress Analysis comparison with Knee model and Biological Knee Implant ….………53

Table 5: Motion Analysis Data for Knee model ………………………………………………………………….62

Table 6: Motion Analysis Data for Knee model…………………………………………………………………..64

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LIST OF GRAPHS

Graph 1: Torque vs Time …………………………………………..………………………………………………………..60

Graph 2: Torque and Angular Displacement vs Time ……………………..………………………………………61

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Chapter 1: INTRODUCTION

1.1 Introduction

Amputation or limb loss has been a problem faced by humans for long. Looking at a decade

back, the major available resort to the amputees were walkers, crutches, peg-leg or wheelchairs.

Due to the major advancements in medical science and biomedical design, a mechanical

replacement of any such limb loss are present and it can be custom designed based on any

patient’s needs. The loss of limb can result due to the medical conditions such as diabetes,

peripheral arterial diseases which causes poor blood flow to the extremities, or due to injuries

such a burn, accidents or perhaps due to cancer. In any of such cases, the affected arm or limb

needs to be removed. One way to do that is through amputation. Using surgery, the doctors

removes the affected extremity in order to treat the disease or injury. In some cases, where due

to infection, antibiotics fail to react, amputation surgery needs to be performed. As a result of

amputation surgery, the patients need artificial arms and limbs to do daily activities. There are

many devices that are used to recover from amputation surgery. The most commonly used is

prosthetic devices. An artificial extension that replaces missing body part (upper or lower body

extremity). It is part of the field of biomechatronic (mechanical devices with human muscle,

skeleton, and nervous systems) to assist or enhance motor. The type of artificial limb used is

determined largely by the extent of an amputation or loss and location of the missing extremity.

The knee amputation can be of two part – below knee amputation which is amputation

performed for ankle and foot related problems. [15] The below knee amputation usually leads

to artificial leg that can allow a patient to walk. [16]

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Figure 1: Patient with Below Knee Amputation

This is performed near the area between foot and ankle. This amputation provides good results

for a wide range of patients with many different diseases and injuries. [17]

Figure 2: Amputation in below knee joint

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For the above-knee amputee, the prosthetic knee joint is one of the most critical components

of the prosthesis. Any type of surgical operation that severs thigh section between the knee and

joint is known as above knee amputation. It generally happens when the amputee has gone

through some disease or accident leading to complete loss of foot and shaft sections. However,

the thigh section is partially lost. The purpose of my project is to study the review of previous

knee models and designs a knee joint which could benefit the patients such that the design

could replicate the human knee joint as much as possible. [1] Also, the knee model has to be

frugal so that patient and the amputees all around the world could benefit from it.

Modern prosthetics now provide wide selections of prosthetic knee joint. Each selection is

honed to wide selection of amputees covering specifications such as hydraulic, friction, lock,

safety. These single axis knees thus provide many advantages due to such specifications

mentioned before. [3] We will now study the background of knee, knee joints and its anatomy

to better under the biology of it before designing the human knee using SolidWorks.

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1.2 Background

1.2.1 What is Knee and it anatomy?

The knee is the largest joint in the human body and plays very important roles in

our daily lives. The knee is involved in virtually every daily function that we do, ranging from

walking to climbing to driving and to sitting. [1]

The knee joint is one of the most complex joint, but it might look like a simple joint to many

of us. Moreover, the knee is more likely to be injured than any other joint in the body. The knee

joint consists of a curved lower end of the thighbone (femur), which rotates on a curved upper

end of the shinbone (tibia), and the kneecap (patella), which slides in a groove at the end of the

thighbone. [1] The knee muscles which go across the joint are the quadriceps (front of the knee)

and the hamstrings (back of the knee). The ligaments are equally important in the knee joint

because these ligaments hold the bones together. Basically, the muscles move the joint while

the ligaments stabilize it. [1]

Figure 3: Human Knee Joint (a) Anterior View (b) Posterior View (c) Cross sectional View [1]

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Four main bones exist between the hip and ankle joints namely femur, patella, tibia, and fibula.

The longest and strongest bone of the human skeleton is femur. It extends from the pelvis

region to the knee region. Tibia and fibula are two long bones in the human leg between the

knee and ankle. Tibia is the interior and thicker region. 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 called 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 intercondylar fossa. These Cruciate ligaments are the most important ligaments in the

knee joint. Their main function is serve to stabilize it and guide its motion. The patella, also

known as 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. Patella is the

triangular-shaped bone. It is not connected to femur or tibia directly. They are in turn 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 tibia bearing surfaces of the knee.

1.2.2 Knee Joint and its structure

Human knee joint is synovial joint. It is defined by a joint cavity, articular cartilage and an

articular capsule consisting of a fibrous capsule lined with synovial membrane. The synovial

fluid provides lubrication of the human knee joint. The synovial fluid is secreted from the

synovial membrane, giving nearly frictionless motion. [2] The main surfaces of the joint, which

are covered in articular cartilage, are the convex medial and lateral condyles of the femur, the

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medial and lateral condyles of the tibia, also known as the tibial plateau, and the posterior

surface of the patella. [2]

Human knee joint is stabilized by four separate ligaments. Medial collateral ligament (MCL)

and lateral collateral ligament (LCL) lie on the sides of the joint. These two ligaments mainly

stabilize the joint in a lateral – medial direction. In the front part of the knee joint center, there

is the anterior cruciate ligament (ACL), which is very important femur stabilizer. Another most

important function is to prevent rotating and sliding forward tibia during jumping and

deceleration activities. Directly behind the ACL is its opposite, the posterior cruciate ligament

(PCL). Main function of the PCL is to prevent the tibia from sliding to the rear part of a knee.

[1]

1.2.3 Knee Joint Movement

The biological knee joint is having three axes and planes of rotation. The anatomical planes

allow for position/orientation representation of the knee in any of its three original planes. The

line connecting medial and lateral femoral condyles outlines flexion-extension motion (phi

angle). [3] The line along the tibia governs the axis of rotation for the internal-external angle

(psi angle). The perpendicular axis to the other two axes states as the abduction-adduction angle

(theta angle). [3]

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Figure 4: The axes and planes of biological knee joint [3]

The median plane (sagittal) is an upright plane passing from front to back. The median plane

separates the body into right and left halves. [3]

The front plane (coronal) is the perpendicular plane running from side to side. This coronal

plane splits the body into anterior and posterior parts.

The horizontal plane (transverse) is a flat plane, which divides the body into upper and lower

regions. [3]

Figure 5: Biological Knee planes [3]

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The human knee has various sets of motion along with the movement involved. Some of the

important motions and knee analysis terms are defined below.

(a) Translational or Translation motion is the movement of element along a straight line.

(b) Rotation or Rotational motion is a movement about a pivot point.

(c) Centre of Rotation is the point about which rotation movement occurs.

(d) Single Axis Knee is any knee in which the shin moves in pure rotation about center of

rotation.

(e) Polycentric knee is any knee whose designs allow the shin to move in a combination of

rotational and translational motion.

(f) Instantaneous center of rotation of Instant center is the point about which shin tends to move

in pure rotation at any given instant of motion.

(g) Four bar linkage knee is a polycentric knee design. It has four elements each joined at four

different points. These four elements are thigh, shin and two links.

(h) Six bar linkage is designed to have more instant inactive joints than a four-bar linkage,

hence making the prosthetic knee more stable in the standing phase.

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Chapter 2: Literature Reviews

2.1 Prosthesis and its Types

When a person becomes a limb amputee, he or she is faced with confounding emotional and

financial lifestyle changes. The amputee requires a prosthetic device(s) and services which

become a life-long event. A prosthesis is an artificial extension that replaces a missing body

part such as an upper or lower body extremity. It is part of the field of biomechatronics, the

science of fusing mechanical devices with human muscle, skeleton, and nervous systems to

assist or enhance motor control lost by trauma, disease, or defect. An artificial limb is a type

of prosthesis that replaces a missing extremity, such as arms or legs. The type of artificial limb

used is determined largely by the extent of an amputation or loss and location of the missing

extremity. Artificial limbs may be needed for a variety of reasons, including disease, accidents,

and congenital defects. [5]

There are four main types of artificial limbs. These include the trans-tibia, trans-femoral, trans-

radial, and trans-humeral prostheses:

A trans-radial prosthesis is an artificial limb that replaces an arm missing below the elbow.

Two main types of prosthetics are available. Cable operated limbs work by attaching a harness

and cable around the opposite shoulder of the damaged arm. The other form of prosthetics

available are myoelectric arms. These works by sensing, via electrodes, when the muscles in

the upper arm moves, causing an artificial hand to open or close. [5]

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Figure 6: Trans-radial Prosthesis [16]

A trans-humeral prosthesis is an artificial limb that replaces an arm missing above the elbow.

Trans-humeral amputees experience some of the same problems as trans-femoral amputees,

due to the similar complexities associated with the movement of the elbow. This makes

mimicking the correct motion with an artificial limb very difficult. [5]

Figure 7: Trans-humeral Prosthesis [16]

A trans-tibia prosthesis is an artificial limb that replaces a leg missing below the knee. Trans-

tibia amputees are usually able to regain normal movement more readily than someone with a

trans-femoral amputation, due in large part to retaining the knee, which allows for easier

movement. [5]

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Figure 8: Trans-tibia Prosthesis [16]

A trans-femoral prosthesis is an artificial limb that replaces a leg missing above the knee.

Trans-femoral amputees can have a very difficult time regaining normal movement. In general,

a trans-femoral amputee must use approximately 80% more energy to walk than a person with

two whole legs. [5] This is due to the complexities in movement associated with the knee. In

newer and more improved designs, after employing hydraulics, carbon fiber, mechanical

linkages, motors, computer microprocessors, and innovative combinations of these

technologies to give more control to the user. Usually, the type of prosthesis depends on what

part of the limb is missing. [5]

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Figure 9: Trans-femoral Prosthesis [16]

An important thing is to consider that the prosthetic must be able to withstand rigorous physical

demands while also being light enough and durable for prolonged use. This leads to increase

in material cost which causes cost to go quite up. One way to do is to minimize on the material

leading to comptonization in building materials.

2.2 Knee Prosthetic History and Development

Apart from emotional and physical penalties, management of amputation is a high-priced

treatment. Straight cost of lower extremity amputation ranges from $20,000 to $60,000

depending on the degree of the amputation (e.g. toe amputation vs. trans-femoral amputation).

[8] Along with the amputation surgery and associated hospitalization costs, amputees need

prosthetic devices to achieve a certain degree of mobility. Accouterment costs range from a

few thousand dollars for the passive models (Mauch Knee: $5,200, (Össur, Iceland)), [17]

about $25,000 for micro-processored models (Plie MPC: $18,475 (Freedom Innovations, CA,

USA), C-leg: $20,000, (Otto Bock, Germany), Rheo Knee: $30,000, (Össur, Iceland)) and

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$100,000 for the powered models (Power Knee: $100,000, (Össur, Iceland)). [8] [17]

Currently, prosthetics technology has come a long way compared to Paré’s mechanical device

by using hydraulic, pneumatic and electrical/computer controlled elements in order to

minimize the consequences of passive mechanisms (Zissimopoulos, 2007; Struyf, 2009; Kuo,

2007). Nevertheless, with the exception of Össur’s Power Knee (Össur, Iceland), [17] [8]

despite the increasing sophistication of prosthetic knee technology, the majority of the

prostheses are controlled damping systems, which replicate the negative work functions of a

biological knee, but cannot contribute positive work to gait (Martinez- Villalpando, 2009). The

emerging prosthetic knee designs [6] elaborate the importance of efficient energy flow at the

knee joint by harvesting/returning energy in a spring. A spring not only permits significant

power demand reduction by providing energy storage capacity but also allows high power-to-

weight ratio [7] [8] [54]

Therefore, instead of using heavy motors, gearboxes and bulky batteries, a spring can

help the peak power demand of the prosthesis, by producing the needed positive energy during

the stance phase with less weight. In this work, the significance of energy flow in trans-femoral

amputee gait was explored along with recent developments, which emphasize harvesting/

returning energy in a spring by compressing/releasing it controllably during gait. However,

constant spring stiffness is suboptimal to varying gait requirements for different types of daily

activity as suggested by Pfeifer in 201. This is due to the variability of the impedance functional

stiffness and the power requirements of the knee caused by the passive characteristics, viscous

and elastic attributes and the activation dependent properties of the muscles in the joint. [8]

[54] As it is not realistic to replace the energy storage element of the prosthesis for each

performed activity, the efficiency of the spring should be supplemented by smart systems such

as microprocessors, valves, pumps, motors etc. through adjusting the amount and timing of the

spring compression/release depending on the biomechanical demands of the performed

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activity. Nonetheless, for more efficient prosthetic knee design process, mimicking of the

healthy human knee functional stiffness is necessary for providing the desirable quantitative

values for loading and unloading intervals, which match the biomechanical demands of the

performed activity to the best extent possible. [8] [54]

2.3 Knee Replacement Implant

When there occurs any damage in any bone or any joint parts of human body, to overcome

those defective organs people generally prefer replacement of those with an specific artificial

organ or as we can say implant as prescribed by the surgeon and going through an operative

method. Knee replacement can be done by total knee replacement or some people get benefited

with partial knee replacement. Implants are generally made up of metals, metal alloys, strong

plastic materials, ceramic material which can be implanted in our body, to make the joint

strengthened strong polymeric material like acrylic paste [9] [54].

Implant Design:

There are several kinds of implant designs for knee replacement implants. As we know knee

joint is a type of hinge joint because with the help of knee joint different motion as be performed

by the leg like straightening and bending of legs [9] [54]. There lots of flexion and extension

motions are being carried out in the knee joint, which makes it a complex structure, were

surfaces if bone generally glides and roll over each other. Accounting on this function of knee

first implant designed was the hinge i.e. a connecting hinge was placed in between the parts of

the knee joint. Newer implants were designed according to the complexity, durability,

biocompatibility, its tensile strength etc. and to design it in such a manner so that it can mimic

the actual functioning of the normal knee functions. Some of the implant models were designed

modeled to preserve the actual ligament of the patient where as other parts were replaced by

an artificial organ. Now days in the market area there are about 150 models of knee replacement

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implants design. Recent designed knee implant mostly focused on the gender specificity.

According to different studies and research it was found that the portions and shape of women’s

knee is different from man’s knee structure. So, may manufacturers design knee implant with

a attach thighbone component at the end so that it can easily match the knee structure of women

knee joint. It provides better functioning than any standard implant [10] [54]. Right choice of

implant design can be used after the specification given by the doctor or surgeon according to

the brand and model design as referred to one’s weight, age, and health and activity level. [54]

2.4 Prosthetic Knee

2.4.1 Different types of Prosthetic Knee

Passive Knees

The knee joint is the most crucial part of lower limb. Muscle action provides power for a

biological knee in two ways; the active force is applied by muscles contraction; also, variable

stiffness is provided by muscles. Only the latter action is used in “passive” prosthetic knee.

Passive prosthetic knees can be categorized into two groups: simple-passive and semi-passive.

There is no automated control over prosthesis stiffness in simple passive knees. However, the

level of stiffness can be adjusted manually. During the weight bearing, the leg can be kept from

buckling and stumbling by means of i) manual lock, ii) weight activated stance mechanisms,

iii) fluid resistance, or iv) polycentric mechanism. One manual locking knee is presented in

Figure 12 (a). A remote release cable is utilized in this device to provide stability in knee

extension. This device leads to high energy cost during ambulation. In weight-activated knee,

a constant-friction is used to provide high stability during the stance phase. Transferring the

body weight to the knee activates an embedded brake that prevents buckling. This brake will

release when the knee becomes unloaded. However, a constant friction still presents during the

swing phase which results in inefficient gait. An energy storing element such as spring can also

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accompany the knee during the swing phase. It is loaded in weight bearing and is released

during swing phase. An example of this type of prosthesis is depicted in Figure 12 (b). Fluid

resistive knees consist of hydraulic or pneumatic cylinders to provide variable resistance.

Therefore, amputee would be able to have different walking speed. Piston of the cylinder is

attached to a hinge joint in the thigh section behind the knee joint. From the other end, cylinder

is connected to a pivot in shank. Hydraulic knees are more efficient than pneumatic ones.

However, the pneumatic knees are lighter, cheaper, and cleaner than hydraulic ones.

Polycentric knees have multiple axes of rotation. These prosthetic devices are kinetically

locked during mid-stance and provide stability. An example of polycentric knees is depicted in

Figure 12(c). To provide variable walking speed for amputees, pneumatic or hydraulic cylinder

can be embedded in polycentric knees. The aforementioned “simple-passive” knees are low-

cost compare to the other types of prosthetic knees. Therefore, most consumers of these devices

are children since they need to change their prostheses as they grow up.

Figure 12: (a) manual locking knee (3R39, Otto Bock Healthcare GmbH) (b) weight-activated

knee (3R38, Otto Bock Healthcare GmbH) (c) Polycentric knee (3R66, Otto Bock Healthcare

GmbH) [9]

In a microcontroller based passive knee joint, the controller changes the knee impedance

(damping and/or stiffness) based on sensory information. This resistive torque for the knee

joint can be provided by electric brakes, or by hydraulic, pneumatic, Magneto-Rheological

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(MR) dampers. These types of knee joints are called “semi-passive” prostheses since their

stiffness can be altered by the controller.

Aeyels et al [21] developed the first micro-controller based knee joint which comprised of an

electromagnetic brake. A gear box accompanies the brake to increase the applied resistive

torque to 50 Nm. The resistive moment is varied continuously based on the sensory information

from the remnant stump and prosthesis state.

The hydraulic damper with variable impedance comprises a double acting cylinder where two

sides of the piston are connected through a valve. The commands determine the position of a

valve that controls the flow of oil from one chamber to the other [22]. The drawback of

hydraulic based knees is the presence of a minimum level of damping during all phases of the

gait cycle, even when it is not needed. Carlson et al [23] and Kim et al [24] replaced the

hydraulic damper with an MR damper to achieve a faster response for different speeds of the

gait cycle. The problems with MR dampers are their susceptibility to: degradation of the MR

fluids, sealant failure, leakage, and performance problems as well as high cost for commercial

applications.

1.4.2 Active Knees

Although lower limb prostheses have traditionally been passive, there have been attempts at

providing active versions.

Most of the developed hydraulic and pneumatic powered knees are tethered to an external

power supply because associated prostheses suffer from high energy consumption. Flowers

and Mann [23] and Stein and Flowers [25] suggested a powered electro-hydraulic knee joint

tethered to a power source. They used a hydraulic cylinder controlled by a 4/3 servo valve to

actuate the knee. Recently, Sup [26] developed a pneumatically actuated powered-tethered

lower limb which is controlled by a computer to alter the impedance of the actuators.

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One of the commercialized pneumatic knee joints is Intelligent Prosthesis, IP, (Chas A.

Blatchford and Sons, Ltd.). A pneumatic cylinder is employed to provide the rotary motion of

the knee joint during the swing phase. One stepper motor is used to adjust the position of a

needle valve (orifice) which controls the flow rate between two sides of the piston. The stepper

motor is controlled by a microcontroller based on the sensory information according to the

swing speed of the prosthetic leg. Buckley et al [26] revealed rationale for the commercialized

IP when they compared the energy cost of the IP and conventional artificial knee joint.

Although IP is not tethered like the other aforementioned hydraulically/pneumatically actuated

knee joints, its utilized system mobilized the knee joint only during the swing phase.

Wang et al [27] proposed a hydraulic system, which compresses the fluid in an accumulator

during stance, and then energizes and controls the knee during swing by using a needle valve.

The hydraulic circuit consisted of an accumulator, two cylinders (one for the ankle joint and

one for the knee joint), and two flow control valves. Also, the motion of the ankle joint causes

the motion of a piston in an ankle cylinder. This piston is connected to a control rod that

switches the shut valve to control fluid flow from the knee cylinder to the accumulator. A

stepper motor actuates a needle valve which controls the flow rate between accumulator and

knee cylinder. The problems of low efficiency and large size are the main flaws of the

aforementioned system.

It is worth noting that Saito [28] developed a tethered lower limb active orthosis equipped with

a bilateral-servo actuator to mimic the function of a bi-articular muscle. Orthosis is an added

support mechanism, usually a brace, to help a disabled person function. Saito accomplished

such task by using master and slave hydraulic cylinders. A ball screw mechanism accompanied

with a stepper motor controlled the master hydraulic cylinder. The slave side system comprised

of a cylinder and two piston rods acts as a bi-articular muscle. Both master and slave cylinders

can be controlled by open-shut solenoid valves.

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Sawicki et al [20] proposed a wearable bilateral lower limb orthosis. They used pneumatic

artificial muscles attached to the orthoses to provide flexion and extension torque at individual

joints. Although these pneumatic artificial muscles are light-weight and suitable for lower limb

exoskeleton and orthosis, they cannot generate enough power for fully active lower limb

prosthesis.

Recently, Kapti and Yucenur [21] proposed a tethered fully active knee powered by an electro

motor and a gear reduction system. They tried to decrease the user‟s energy cost by providing

a fully powered trans-femoral joint. Popovic et al [22] presented a methodology to determine

the optimal motor size for a motorized prosthetic knee.

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Chapter 3: Mechanical Design

Individuals with lower limb amputation have shown to expend more metabolic energy than an

individual with a healthy leg during normal walking. Walters in 1976 reported that trans-

femoral amputees expend up to sixty percent or more and Colborne in 1992 reported that trans-

tibial amputees tend to expend twenty to thirty percent more metabolic energy in normal

walking. Currently, most of the commercial prostheses available are passive prostheses. These

are not able to bring positive work at phase stance, causing risk to joint and back pain. Some

researchers have shown that powered prostheses for lower limb are able to mimic human gait.

They can provide negative and positive work in the stance phase as well as to improve amputees

performance in a more natural gait and normal walking.

Ideally a good prosthetic design need to have some important characteristics: They include

(a) Show be able to produce sufficient power to gait i.e. human motion

(b) Energy consumption should be very low to lowest

(c) It should fit properly i.e. should not exceed amputees’ limb or arm

Many prosthetic devices are now equipped with elastic elements. They help in increase

tolerance to load impact, proper storage and release of energy, as well as reducing energy

requirements with an increase power output.

3.1 Design Features

One of the important functional requirement of any knee design is its ability to replicate joint

motion as closely as possible. Compromise on any motion or degree of freedom will a sub-

optimal design. The following are major functional requirements for the design of knee

prosthesis: (a) able to bear load of human upper body weight, (b) can provide knee motion

similar to biological knee (c) should be able to hold under stress and strain. The thickness needs

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to be as uniform as possible to avoid any concentrated stress failure. Also, the maximum force

acting on the knee joint shall be the impact load while running. Considering the normal load

on the one side of knee joint to be half of total load of body weight such that load is equally

distributed. Then the maximum stress can be calculated as:

𝜎 =𝐵𝑒𝑛𝑑𝑖𝑛𝑔 𝑀𝑜𝑚𝑒𝑛𝑡 (𝑀)𝑥 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 (𝑦)

𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝐼𝑛𝑒𝑟𝑡𝑖𝑎 (𝐼)

Figure 13: Load assessment on one Knee

Bending Moment (M) = (patient weight/2) * moment arm (shaft size)

σ = maximum stress

deflection (y) = thickness/2 where thickness is based on the weight of patient

moment of inertia (I) = bh3/12

Therefore, by substituting the value of each parameter, we can calculate the maximum stress it

can hold. This shall be done on the final model using SolidWorks.

3.2 Mechanical System



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mentioned before.

(a) Mechanical Four Bar Knee:

The knee prosthesis has a four-bar linkage arrangement at the knee, by which the motion can

be transmitted from the thigh to foot during squatting action and during swing phase of

walking. These are specific class of polycentric knees. The knee is characterized by four

elements joined at thigh, shin and two links. Knee flexion angle achieved is 150 deg.

Figure 14: Four Bar Knees [18]

Benefits of four bar linkage knee includes natural and smooth swing phase, stable stance phase,

low weight and compact design.

(b) Mechanical Six Bar knee: Fundamental types of six bar mechanism are Watt type and

Stephenson type. Ortho-europe developed Nabtesco 6-bar knee (P-MRS) provides

natural stance flexion from heel contact to mid stance. This feature results in absorbing

shock a heel strike. They also have added hydraulic cylinder in P-MRS system which

enhances walking during stance and swing phase by working as a shock absorber.

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Figure 15: Nabtesco 6-bar knee (P-MRS) [18]

(c) Single Axis knee: The swing block is connected to the upper joint section through the

swing axis and with the lower joint section through the knee axis and acts as a load-

dependent brake. This together with proper knee alignment secures the stance phase.

To control the swing phase, the axis friction and the spring force of the extension assist

are adjustable.

Figure 16: Single Axis Knee [18]

Our Knee model design includes the single axis knee. The reason being it is simple and cost

effective solution for low activity to requiring maximum stance security.

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3.3 Degrees of Freedom

The biological knee has six degrees of freedom. These are three rotational and three

translational.

(a) Rotation:

- The flexion and extension has up to 160 degree of flexion. Negative 5 degree (185

degree) in terms of hyperextension.

- Varus and Valgus has 6-8 degree in extension

- Internal-external rotation has 25-30 degree in flexion

(b) Translation:

- Anterior-posterior has 5-10 mm

- Compression has 2-5 mm

- Medio-lateral has 1-2 mm

Figure 17: Knee Joint Motion [12]

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The overall number of degree of freedom of the system can be calculated using the following

equation: [3]

𝑀 = 3(𝑛 − 1) − 2𝑓1 − 𝑓2

where M represents the degrees of freedom for the overall system, n, the total number of fixed

link segments, f1, the joints with one degree of freedom (DOF) and f2, the joints with two

degrees of freedom. The overall knee system is found to have 5-DOF, where the main knee

joint has 1-DOF. The human knee in comparison has 6-DOF, a much more complex system.

However, to maintain mechanical durability and remain within the bounds of a low-cost device,

the knee joint is simplified to a hinge-type 1-DOF mechanism. It contains three anatomically

equivalent parts – the upper tibia, knee joint and the moment arm that represents the active

knee joint [3]

Table 1: Functional Range of Motion of Human Knee

Activities Knee Flexion

Normal gait/Level Surfaces 60 deg

Stair Climbing 80 deg

Sitting/Rising from chair 90 degree

Sitting/Rising from toilet seat 115 deg

Advanced function > 115 deg

3.4 SolidWorks

SolidWorks 2016 was used to design the various components of the knee model. The San Jose

State University student laboratory was used to develop the design. CAD stands for Computer-

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Aided Design. It is very power tool in designing 2-D or 3-D images of physical object. CAD

are divided into two types – AutoCAD and SolidWorks.

AutoCAD are mainly used in civil engineering for designing bridges and buildings.

SolidWorks are mainly focused into electrical engineering and Biomedical engineering.

SolidWorks is what we call a "parametric" solid modeller used for 3-D design. Parametric

means that the dimensions can have relationships between one another and can be changed at

any point during the design process to automatically alter the solid part and any related

documentation (blueprint).

3.4.1 Proposed Design

The design proposed includes the knee joint and it extension which joins to shaft below the

knee to ankles and thigh above the knee.

Figure 18: Top view of the Knee Joint Design

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mentioned before.

Apart from that, literature research showed that by using hydraulic cylinder (as in P-MRS

system) enhances walking during stance and swing phase by working as a shock absorber. But

the application of hydraulics will result in higher cost. The alternative to hydraulic cylinder

was to apply spring system. A spring not only permits significant power demand reduction by

providing energy storage capacity but also allows high power-to-weight ratio [7] [8]

Therefore, instead of using heavy motors, gearboxes and bulky batteries, a spring can

help the peak power demand of the prosthesis, by producing the needed positive energy during

the stance phase with less weight. In this work, the significance of energy flow in trans-femoral

amputee gait was explored along with recent developments, which emphasize harvesting/

returning energy in a spring by compressing/releasing it controllably during gait. Applying

such knowledge to our design shown above in figure (19), we can redesign it to a new version

as shown below.

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Figure 19: Final Version of Knee model

The size of the spring was kept small to avoid any sideways movement which could cause

stress-strain leading to its breakage.

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3.4.2 SolidWorks Designs – Parts

Figure 20 (a): Dimensions of Part 1

Figure 20 (b): Mass properties of Part 1

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Figure 20(c): Part 2 Figure 20(d): Part 3

Figure 20 (e): Part 4 Figure 20 (f): Part 5

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Figure 20 (g): Part 6 Figure 20 (h): Part 7

3.4.3 SolidWorks Designs – Assembly

Figure 21(a): Assembly of parts 1,2,3,6 Figure 21(b): Assembly of parts 1,2,3,7

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Figure 21(c): Assembly of parts 1,2,3,7,5 Figure 21(d): Assembly of parts 1,2,3,7,5,6,4

Figure 22: Final Knee Model

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Chapter 4: Result Analysis and Discussions

4.1 Anthropometric Analysis

In order to perform motion analysis, proper gathering of data needs to be done. The data

measurement was obtained using human subject’s biological knee design. In my case of study,

I used the measurements similar to my knee model. The mass of the subject was 85kgs. The

maximum mass which was accessed was 112 kg and minimum mass assessed was 71 kg. The

height of the subject was 6 feet 3 inches which is 190 cm. The force exercised on human leg

was approximately equal to F= (m*g)/2= (84kg*9.8)/2= 412N. Based on this, maximum force

exerted was taken to be 550 N and 350 N. The length for both leg was assumed to be equal and

was equal to 0.863 m. The torque exerted was equal to Torque, T=F*L*Sin(theta) with

F=412N,

Leg length, L = 0.8636metre,

Knee angle, theta = 180 deg, so SIN(theta)=1

Therefore, Torque, T=412*0.8636*1 = 355.8 Nm

So, Torque required on standing as a function of knee angle= 355.5 Nm at Force=412N

Max Torque = F(max)*L*sin(theta)= 550*0.8636*1 = 474.98Nm

Min Torque = F(min)*L*Sin(theta)=350*0.8636*1 = 302.26 Nm

The movement starts with the knee at ninety degrees (or close to that) in the deep squat, and

ends with the knee angle at zero degrees when standing.

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Now if we want the amputee using this prosthesis to stand up in 1 second, then the average

angular velocity will be 90 deg/sec. Since, the start and end velocity equals to zero, so the peak

angular velocity will probably be 90*2 = 180 deg/sec.

=> 360 deg = 1 revolution per sec

=> 180 deg = 0.5 revolution per sec

=> 0.5 revolution per sec

=> 0.5 * 60 = 1 sec* 60

=> 30 revolutions per min

So, we have approximately 30 revolutions per minute (RPM=30)

Angular velocity, ω =30 RPM = 30*2π/60 = 3.142 rad/sec

Power generated, P= Torque * Angular velocity = 355.8*3.142 = 1117.93 watts

So, our human knee design generated power equal to 1117.93 watts.

When this power generation is compared to Seimen Motors (Z39-LE90SM4P), it produces

equal to 53 RPM and can deliver torque up to 199 Nm which generates power of 1256 watts.

To incorporate this design in human prosthetic knee, the speed of motor is kept low by Seimens

motors. This is because human muscles (electric motors) delivers lower force at higher speed.

By using this knowledge, spring was incorporated in the design where the joints move. This

method of design is called ‘series-elastic actuator’. Other way is to put elasticity in foot, which

is usually done in BIOM foot.

Spring stiffness takes was equal to 0.024Nm/Kg-deg [8]. Material selected was Cobalt-

Chromimum having elastic modulus equal to 7-30 MPa, and a density equal to 8.5g/cm3.

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4.2 Stress Analysis

Figure 23(a): Original Model Figure 23(b): Analyzed Model

Model Information:

Before performing stress analysis in SolidWorks, we need to model the system. Based on our

assumption of materials and measurements, the SolidWorks determine the volumetric

measurement as well as weight analysis of the parts designed.

Linear stress analysis with SolidWorks simulation enables engineers to quickly and efficiently

validate quality, performance, and safety—all while creating their design.

Linear stress analysis calculates the stresses and deformations of geometry given three basic

assumptions: (1) The part or assembly under load deforms with small rotations and

displacements. (2) The product loading is static (ignores inertia) and constant over time. (3)

The material has a constant stress strain relationship (Hooke’s law). SolidWorks simulation

uses finite element analysis (FEA) methods to discretize design components into solid, shell,

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or beam elements and uses linear stress analysis to determine the response of parts and

assemblies due to the effect of:

Forces

Pressures

Accelerations

Temperatures

Contact between components

Loads can be imported from thermal, flow, and motion Simulation studies to perform

multiphysics analysis.

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Model name: KneeModelel

Current Configuration: Default

Solid Bodies

Document Name and Reference

Treated As Volumetric Properties Document Path/Date

Modified

Fillet1

Solid Body

Mass:0.155208 kg Volume:2.01569e-005 m^3

Density:7700 kg/m^3 Weight:1.52104 N

C:\Users\sggau\Desktop\Ahmed\2.SLDPRT

Nov 23 04:51:20 2016

Boss-Extrude2

Solid Body

Mass:1.68352 kg Volume:0.000218639 m^3



Nov 23 04:51:26 2016

Page - 47 - of 89

Revolve2

Solid Body

Mass:0.0647815 kg Volume:8.41319e-006 m^3



Nov 23 04:51:29 2016

Cut-Extrude1

Solid Body

Mass:0.0112543 kg Volume:1.4616e-006 m^3



Nov 23 04:51:33 2016

Kes-Ekstrüzyon2

Solid Body

Mass:0.149435 kg Volume:1.94071e-005 m^3



Nov 23 04:51:41 2016

Cut-Extrude3

Solid Body

Mass:8.45831 kg Volume:0.00109848 m^3


C:\Users\sggau\Desktop\Ahmed\foot.SLDPRT

Nov 23 04:50:51 2016

Boss-Extrude1

Solid Body

Mass:0.273048 kg Volume:3.54607e-005 m^3


C:\Users\sggau\Desktop\Ahmed\rood.SLDPRT

Nov 23 04:50:58 2016

Figure 24: Knee Model Information

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Table 2: Study Properties

Study name Static 1

Analysis type Static

Mesh type Solid Mesh

Thermal Effect: On

Thermal option Include temperature loads

Zero strain temperature 298 Kelvin

Include fluid pressure effects from SOLIDWORKS Flow Simulation

Off

Solver type FFEPlus

Inplane Effect: Off

Soft Spring: Off

Inertial Relief: Off

Incompatible bonding options Automatic

Large displacement Off

Compute free body forces On

Friction Off

Use Adaptive Method: Off

Result folder SOLIDWORKS document (C:\Users\sggau\Desktop\Solidoworks - Practice)

Table 3: Units of measurements used

Unit system: SI (MKS)

Length/Displacement mm

Temperature Kelvin

Angular velocity Rad/sec

Pressure/Stress N/m^2

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Model Reference Properties Components

Name: Alloy Steel Model type: Linear Elastic Isotropic

Default failure criterion:

Max von Mises Stress

Yield strength: 6.20422e+008 N/m^2 Tensile strength: 7.23826e+008 N/m^2 Elastic modulus: 2.1e+011 N/m^2

Poisson's ratio: 0.28 Mass density: 7700 kg/m^3

Shear modulus: 7.9e+010 N/m^2 Thermal expansion

coefficient: 1.3e-005 /Kelvin

SolidBody 1(Fillet1)(2-1), SolidBody 1(Boss-Extrude2)(3-1), SolidBody 1(Revolve2)(4-1), SolidBody 1(Cut-Extrude1)(5-2), SolidBody 1(Kes-Ekstrüzyon2)(6-1), SolidBody 1(Cut-Extrude3)(foot-1), SolidBody 1(Boss-Extrude1)(rood-1)

Curve Data:N/A

Figure 25: Material Properties

Fixture name Fixture Image Fixture Details

Fixed-1

Entities: 4 face(s) Type: Fixed Geometry

Resultant Forces Components X Y Z Resultant

Reaction force(N) -891.47 251.541 7.341 926.308

Reaction Moment(N.m) 0 0 0 0

Figure 26: Load and Fixtures

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Load name Load Image Load Details

Force-1

Entities: 7 face(s) Type: Apply normal force

Value: 412 N

Figure 27: Connector

Calculation of Spring stiffness:

The embedded springs not only must provide the vertical displacement for the hip joint, but

also must act as a shock absorber against the ground reaction impact. In order to choose a

correct spring, stiffness of the spring is calculated using Hooke’s Law:

𝐹 = 𝑘𝑥 𝑜𝑟 𝑘 =𝐹

𝑥

Spring needs to resist half of the Ground Reaction Force (GRF) since one leg is being

considered. The displacement of the spring is equal or less than the displacement of the hip

Connector Name Connector Details Connector Image

Spring Connector-1

Entities: 2 vertex(s) Type: Spring(Two

locations)(Compression & Extension)

Axial stiffness value: 0.024 N/m Tangential Stiffness: 0.024 N/m Rotational stiffness

value: 0 N.m/rad

Pre-compression value: 2.2e+006 N

Spring Connector-1

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joint, which is 71 mm. [19] The ground reaction force is 412 N. Therefore, the optimal stiffness

of the spring is 0.0024 N/m has been taken.

Mesh Information:

Contact Contact Image Contact Properties

Global Contact

Type: Bonded Components: 1 component(s)

Options: Compatible mesh

Total Nodes 149115

Total Elements 92224

Maximum Aspect Ratio 43.566

% of elements with Aspect Ratio < 3 98.4

% of elements with Aspect Ratio > 10 0.0813

% of distorted elements(Jacobian) 0

Time to complete mesh(hh;mm;ss): 00:00:09

Computer name:

Figure 28: Mesh Information


Mesher Used: Curvature-based mesh

Jacobian points 4 Points

Maximum element size 12.9024 mm

Minimum element size 0.645118 mm

Mesh Quality High

Remesh failed parts with incompatible mesh On

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Figure 29: Solid Mesh (Knee Model)

Resultant Data

Table 4: Resultant Force

Selection set

Units Sum X Sum Y Sum Z Resultant

Entire Model N -891.47 251.541 7.341 926.308

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Figure 30: Stress Analysis

The maximum stress the knee model can handle is equal to 2.19992e+006 N/m^2 and minimum

stress the knee model can handle is equal to 4.09813e-009 N/m^2.

Name Type Min Max

Strain1 ESTRN: Equivalent Strain 1.31581e-020 Element: 80351

9.88103e-006 Element: 86927

Name Type Min Max

Stress1 VON: von Mises Stress 4.09813e-009 N/m^2 Node: 132576

2.19992e+006 N/m^2 Node: 144447

Assem-1237654_KneeModel_Ah1-Static 1-Stress-Stress1

Page - 54 - of 89

Name Type Min Max

Assem-1237654_KneeModel

Figure 31: Strain Analysis

The maximum stress the knee model can handle is equal to 9.88103e-006 N/m^2 and minimum

stress the knee model can handle is equal to 1.31581e-020 N/m^2.

Factor of Safety:

The factor of safety is the factor of ignorance. If the stress on one part at a critical location is

known precisely i.e. applied stress (Sapp), and the material’s strength i.e. allowable stress is

known with precision and the allowable stress (Sallow) is greater than applied stress, then that

part will not fail. However, in real world all the aspects of design have some degree of

uncertainty and therefore factor of safety is needed. In practical, factor of safety is used in one

of three ways: (a) it can be used to reduce allowable strength such as yield strength of material

to a lower level of comparison with applied strength, (b) it can be used to increase the applied

Page - 55 - of 89

stress for comparison with allowable stress, (c) it can be used as a comparison for the ratio of

allowable stress to applied stress.

𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦, 𝐹𝑆 =𝑆𝑎𝑙𝑙𝑜𝑤𝑒𝑑

𝑆𝑎𝑝𝑝𝑙𝑖𝑒𝑑

𝑆𝑎𝑙𝑙𝑜𝑤𝑒𝑑 = 8.2𝑒 + 008 𝑁/𝑚2= Maximum stress

𝑆𝑎𝑝𝑝𝑙𝑖𝑒𝑑 = 6.2𝑒 + 008 𝑁/𝑚2 = Material Yield Strength

𝐹𝑆 = 8.2𝑒 + 008

6.2𝑒 + 008= 1.3

Figure 32: Factor of Safety

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4.3 Motion Analysis

4.3.1 Description of our Problem statement

Our problem describes the mechanism of a human leg (knee). So therefore, we plot our study

around knee mechanism" reacting forces and moment".

Assumptions:

We start our study by assuming that the human want sitting and his knee perpendicular to his leg.

Figure 33: Human (knee) Position while sitting

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Figure 34: Face 1 and Face 2 are perpendicular to each other

Considering the assumption of sitting, the below knee (tibia) and the above knee (femur or

thigh) are perpendicular to each other.

Then we assume that the knee rotates with limited angle between 0 to 90 degree, so we added

a virtual motor to make this rotation.

Figure 35: Virtual position of motor

And we added force 412N on thigh perpendicular to knee with a distance equal to 868 mm.

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Figure 36: Moment analysis around knee

Figure 37(a): Leg (femur & tibia) Figure 37(b): Knee Joint

Figure 37(c): Knee bonded with thigh acting as Human Femur

Modeling Information:

We simplify our problem by neglecting weight of modeling parts and concentrate all weight at

force 412N.

Units have been kept in SI (MKS) system and the material properties have been excluded.

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Figure 38: Units of the measurement

Graphs 1: Torque vs Time

Graph no.1 plot the relation between torque and time, since our calculation duration was 5

second, we found that the maximum torque came at the converting from inertia state to dynamic

state.

Max. Torque at force equal to 412 N = 352878 N.mm

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Graphs 2: Torque and Angular Displacement vs Time

Graph no.2 plot the relation between torque and angular displacement. We found that max.

torque achieved at angle equal zero (inertia state).

We check our calculation by calculate the error percentage.

Since;

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝑒𝑟𝑟𝑜𝑟 =|𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 𝐴𝑐𝑡𝑢𝑎𝑙|

𝐴𝑐𝑡𝑢𝑎𝑙𝑋 100%

Theortical "actual": torque= force *distance*cos.angle

Where force =412N, Distance =868mm, Angle=zero.

We used cos. and not sin. because we take the horizontal axis our datum axis

Therefore; Torque theoretical = 412*868*1

Torque theoretical = 357616 N.mm & Torque measured = 352878 N.mm

Therefore; error percentage = 1.32%

This is an accepted error because error is smaller than 10%

Also, we used 25 frame per second (means calculation repeating 25 time every 1 sec.), we can

use more frames per second to get more accurate result, if the result wasn't accepted.

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Graph 3: Torque vs Angle of Rotations (Various angles at 0, 30, 60,90 degrees)

Standing position represents the angle of zero degree. From the graph, we can see that the

maximum torque was obtained there. As the motion reaches towards sitting position, i.e. the

angle of rotation keeps on increasing, the value of torque decreases.

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CHAPTER 5: CONCLUSIONS

The static structural analysis of the knee joint has a great significance, as these analytical results

provide us a wider knowledge about the mechanical behavior of the knee. Performing stress

analysis as a simulation method instead of intrusive methods is one of the important part of

biomechanical study for different 3D models. The study reveals that the stress analysis work

performed will help us to obtain a rough geometry of the knee joint. The stress and motion

analysis has been done on the designed human knee model. From the analysis, several

conclusions are made which are listed below.

Table 5: Stress Analysis comparison with Knee model and Biological Knee Implant

Stress

Strain

Load

Resultant force

Material

Safety Factor

Knee Model

2.19992e+006 N/m2

9.88104e-009 N/m2

926.308 N

Biological Knee Implant

3.52e+005 to 5.62e+007 MPa

Alloy Steel

412 N 686.7 N

1.3 5.05

Page - 63 - of 89

Figure 39: Distribution of Stress on Knee Model

From the figure, we can see that the stress and tension has been evenly distributed in the femoral

(above knee component) and tibial (below knee component). The above figure shows in more

details the distribution of stress and displacements in the prosthetic knee model, therefore it

can be analyzed the greater stresses are generated in this component and even its distribution

is uniform, it has higher values toward the center of the element, due to the weight of the tibial

component and the loads applied in this.

The motion study allows observing the approximate behavior that the ligaments have after a

knee replacement. The mechanical behavior of medial collateral ligament is simulated through

linear springs (spring stiffness=0.024 Nm/Kg deg). It is considered that in the finite element

study (FES), the joint had a hinge type behavior, in which the tibia and corresponding

component remained fixed on the environment, whereas the femur presented the rotation of the

structure, contrary to the motion analysis. The analysis was developed with a 0° flexion with

an equivalent distributed load of 84 kg (412Nx2) in the perpendicular direction of the femoral

Page - 64 - of 89

component. Figure below shows the applied load along with weight of the human body on the

knee model.

Figure 40: Applied and Distributed Load on Knee Model

Table 6: Motion Analysis Data for Knee model

Future Work:

The future work will be modelling the knee model design into a 3-D model and apply the

motion analysis data. And finally develop the prototype of the affordable knee design.

REFERENCES

Mass

Min Mass

Max Mass

Leg Length

Torque

Angular Velocity

Power generated

Spring stiffness

Material

Pressure

Alloy Steel

2.25 Mpa

200x103 Nmm

53 RPM

1256 watts

352878 Nmm

30 RPM/3.142 rad/sec

1117.93 watts

0.024 Nm/Kg-deg

Knee Model Seimen/BIOM Foot

85 Kg

71 Kg

112 Kg

868 mm

Page - 65 - of 89

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Page LXX of 89

APPENDICES

Appendix 1: Designing Knee Joint Parts Using SolidWorks

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A) Appendix 2: Assemble of all the Parts Using SolidWorks

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Final Assembly of Knee Joint Model

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Appendix 3: Stress Analysis

Simulation of KneeModel Date: Wednesday, November 23, 2016 Designer: Solidworks Study name: Static 1 Analysis type: Static

Table of Contents Description .......................................... 78

Assumptions ......................................... 79

Model Information .......... Error! Bookmark not defined.

Study Properties .................................... 80

Units .................................................. 80

Material Properties ................................. 81

Loads and Fixtures ................................. 82

Connector Definitions.............................. 83

Contact Information ............................... 83

Mesh information ................................... 84

Sensor Details ....................................... 88

Resultant Forces .................................... 88

Beams................................................. 88

Study Results .... Error! Bookmark not defined.

Conclusion ....... Error! Bookmark not defined.

Description No Data

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Assumptions

Original Model

Model Analyzed

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Study Properties Study name Static 1

Analysis type Static


Thermal Effect: On

Thermal option Include temperature loads

Zero strain temperature 298 Kelvin

Include fluid pressure effects from SOLIDWORKS Flow Simulation

Off

Solver type FFEPlus

Inplane Effect: Off

Soft Spring: Off

Inertial Relief: Off

Incompatible bonding options Automatic

Large displacement Off

Compute free body forces On

Friction Off

Use Adaptive Method: Off

Result folder SOLIDWORKS document (C:\Users\sggau\Desktop\Solidoworks - Practise)

Units Unit system: SI (MKS)

Length/Displacement mm

Temperature Kelvin

Angular velocity Rad/sec

Pressure/Stress N/m^2

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Material Properties

Model Reference Properties Components

Name: Alloy Steel Model type: Linear Elastic

Isotropic Default failure

criterion: Max von Mises Stress

Yield strength: 6.20422e+008 N/m^2

Tensile strength: 7.23826e+008 N/m^2

Elastic modulus: 2.1e+011 N/m^2 Poisson's ratio: 0.28

Mass density: 7700 kg/m^3 Shear modulus: 7.9e+010 N/m^2

Thermal expansion coefficient:

1.3e-005 /Kelvin

SolidBody 1(Fillet1)(2-1), SolidBody 1(Boss-Extrude2)(3-1), SolidBody 1(Revolve2)(4-1), SolidBody 1(Cut-Extrude1)(5-2), SolidBody 1(Kes-Ekstrüzyon2)(6-1), SolidBody 1(Cut-Extrude3)(foot-1), SolidBody 1(Boss-Extrude1)(rood-1)

Curve Data:N/A

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Loads and Fixtures

Load name Load Image Load Details

Force-1

Entities: 7 face(s) Type: Apply normal force

Value: 412 N

Fixture name Fixture Image Fixture Details

Fixed-1

Entities: 4 face(s) Type: Fixed Geometry

Resultant Forces Components X Y Z Resultant

Reaction force(N) -891.47 251.541 7.341 926.308

Reaction Moment(N.m) 0 0 0 0

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Connector Definitions

Connector Name Connector Details Connector Image

Spring Connector-1

Entities: 2 vertex(s) Type: Spring(Two

locations)(Compression & Extension)

Axial stiffness value: 0.024 N/m Tangential Stiffness: 0.024 N/m Rotational stiffness

value: 0 N.m/rad

Pre-compression value:

2.2e+006 N

Spring Connector-1

Contact Information

Contact Contact Image Contact Properties

Global Contact

Type: Bonded Components: 1

component(s) Options: Compatible

mesh

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Mesh information Mesh type Solid Mesh

Mesher Used: Curvature-based mesh

Jacobian points 4 Points

Maximum element size 12.9024 mm

Minimum element size 0.645118 mm

Mesh Quality High

Remesh failed parts with incompatible mesh On

Mesh information - Details

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Mesh Control Information:

Mesh Control Name Mesh Control Image Mesh Control Details

Control-1

Entities: 1 component(s) Units: mm Size: 6.45123

Ratio: 1.5

Total Nodes 149115

Total Elements 92224

Maximum Aspect Ratio 43.566

% of elements with Aspect Ratio < 3 98.4

% of elements with Aspect Ratio > 10 0.0813

% of distorted elements(Jacobian) 0

Time to complete mesh(hh;mm;ss): 00:00:09

Computer name:

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Control-2


Ratio: 1.5

Control-3


Ratio: 1.5

Control-4


Ratio: 1.5

Control-5


Ratio: 1.5

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Control-6


Ratio: 1.5

Control-7


Ratio: 1.5

Control-8


Ratio: 1.5

Control-9


Ratio: 1.5

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Sensor Details No Data

Resultant Forces

Reaction forces

Selection set Units Sum X Sum Y Sum Z Resultant

Entire Model N -891.47 251.541 7.341 926.308

Reaction Moments

Selection set Units Sum X Sum Y Sum Z Resultant

Entire Model N.m 0 0 0 0

Beams No Data

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Appendix 4: Motion Analysis