Stress Distribution and Optimum Design of Polypropylene and Laminated Transtibial Prosthetic Sockets. FEM and Experimental Implementations

Content

ABSTRACT I

Chapter 1: Introduction and Literature Survey
1.1. General
1.2. The Effect of Stiffness
1.3. Literature Review
1.4. Concluding Remarks
1.5. Objectives of Work

References

Chapter 2: Theoretical Analysis
2.1. Gait cycle
2.2. Ground Reaction Forces (GRFs)
2.3. Socket Stress Distribution
2.3.1. Introduction
2.3.2. Socket Stress Distribution Using ANSYS Package
2.4. Design Specifications of below the Knee Prosthetic Socket
2.4.1. Introduction
2.4.2. Finite Element Model
2.4.3. Alternate Designs
2.5. The Effect of Varying Modulus of Elasticity on Polypropylene Socket
2.5.1 Finite Element Model
2.5.2 Alternate Analyses

References

Chapter 3: Experimental work
3.1. Introduction
3.2 Prosthetic Socket Manufacturing
3.2.1 Polypropylene Socket Manufacturing
3.2.2. Laminated Socket Manufacturing
3.3. The Tested Sockets
3.4. Testing the Samples
3.4.1 Testometric Machine
3.4.2 Compression Test
3.4.3 Flexural Test
3.4.4 Tensile Test

References

Chapter 4: Results and discussions
4.1 The Results of Socket Stress Distribution
4.2. The Results of Design Specifications of below the Knee Prosthetic Socket
4-3. The Results of the Effect of Varying Modulus of Elasticity on PP Socket
4.4. Experimental Work Results
4.4.1 Compression Test Results
3.3.2 Flexural Test Results
4.3.3. Tensile Test Results

References

Chapter 5: Conclusions and Suggested Future Work
5.1 Conclusions
5.2. Suggested Future Works

References

Appendices

References

ABSTRACT

This study presents analyses for below knee prosthetic socket of a human. Socket stress distribution is performed on three types of socket, polypropylene (5mm), polypropylene (3mm) and a standard laminate (3mm) sockets to determine the stresses path through the prosthetic socket during the gait cycle. It is found that heel strike phase is the critical phase. The stresses increase at the socket base while the maximum deflection is maximum at the patellar region of the socket. This work is achieved by finite element program, ANSYS.

The development of design specifications of a below the knee prosthetic socket is presented in this study for successful ambulation and comfort. Seven different design models are created by changing the socket wall thickness and the material. Polypropylene socket gives the best results with regard to the allowable deflection for the regions of the pressure relief areas of the stump.

The effect of varying the modulus of elasticity on the polypropylene socket is considered in this study. Three models are analyzed with different tensile creep moduli during different periods. It is found that the polypropylene socket will enlarge in size with time.

An experimental study is conducted to compare the strength of five prosthetic sockets made of different materials. Compression, three-point flexural and tensile tests are implemented by the Testometric machine. The laminate sockets have larger compressive stiffness than polypropylene while polypropylene has larger flexural stiffness than the tested laminates except for socket No.5.

Chapter 1: Introduction and Literature Survey

1.1. General

Humans have perfect mobility with amazing control systems; they are extremely versatile with smooth locomotion. However, comprehensive understanding of the human locomotion is still not entirely analyzed. Therefore, much attention has been paid to investigate biped locomotion systems such as orthoses, prostheses, biped robots, etc. [21-34].

An amputation, especially at any level below the knee, does not usually present a particularly disabling condition. With modern prostheses and treatment methods, below knee amputees who have no complicating medical problems can do most of the things he or she could do before amputation.

Of special importance here is the use of "transtibial" in place of "below the knee" to identify an amputation between the knee and the ankle. This term has been adopted to avoid confusion with disarticulation at the ankle (Syme's amputation) and amputations through the foot [1].

In recent years, there has arisen an aversion to the use of the word ''stump'' in referring to that part of the limb that is left after amputation. Amputations are caused by accidents, disease and congenital disorders. The accidents most likely to result in amputations are war accident, followed by traffic, farm and industrial accidents.

Amputations in the case of disease are performed as a lifesaving measure. The diseases that cause most amputations are a peripheral vascular disease (poor circulation of the blood) and cancer.

Congenital disorders or defective limbs present at birth are not amputations, but rather are a lack of part or all of a limb. A person with a limb deficiency can usually be helped by using an artificial limb. Sometimes amputation of parts of a deformed limb or some other types of surgery is desirable before the application of an artificial limb.

Surgeons preserve the knee joint whenever it is practical to do so. Very short stump makes fitting extremely difficult and very long below-knee stumps are prone to circulation problems.

The Syme's amputation, which is essentially the removal of the foot at the ankle, usually results in a stump that will bear a substantial part of the body weight over the end.

The artificial leg resembles the normal leg in many ways. For lower extremity prosthesis, the major components, which are shown in Figure (1-1), are:

Abbildung in dieser Leseprobe nicht enthalten

- The Socket

The socket represents the component of the prosthesis which holds the stump of the amputee and is shaped so that there is total contact over the entire surface area of the stump [2].

- The Suspension Mechanism

Suspension systems all serve a similar function of suspending the socket when the prosthetic unit is not in contact with the ground. These systems include a supracondylar cuff, supracondylar suspension, supracondylar/suprapatellar suspension and thigh corset. The supracondylar cuff is a strap positioned superiorly over and encircling the femoral condyles. The supracondylar suspension system includes medial and lateral walls of the socket extended above the femoral condyles. the supracondylar/suprapatellar suspension includes the same features as the supracondylar suspension system plus an additional anterior wall covering the knee. The thigh corset consists of metal hinges that are attached to the socket and a leather thigh corset that is strapped around the thigh. The hinges located near the knee joint principally, allow movement in the sagittal plane only. Figure (1-2) shows the suspension systems.

Abbildung in dieser Leseprobe nicht enthalten

- The Shank (Pylon)

The shank can be divided into plastic tube and metal tube. The shanks have progressed from simple static shell to dynamic devices that allow axial rotation and absorb, store and release energy.

- The Couplings

The almost universal standardization of coupling components of below keen prosthetics allows for the easy interchanging of components.

- The Prosthetic Foot

Prosthetic feet have been categorized as either articulated or non- articulated, as well as energy storing feet. However, despite these differences, all prosthetic feet serve the basic function of providing a solid base of support during standing and during the stance phase of gait. The development of these prosthetic devices has evolved from numerous generations of prosthetic feet design. The first generation is characterized by articulated and non–articulated feet that provide a stable base of support, with some ability to absorb energy during initial heel contact. The second generation of prosthetic feet was designed initially for young active amputees who participate in reactional activities and require a higher level of performance. The design of this particular foot was based on the principle of storing energy as the foot lifts off the ground. The prosthetic foot of this generation is commonly referred to as the energy storing prosthetic foot.

A prosthetic foot consists of a heel, ankle adaptor and a cosmosis. These components vary in geometry, orientation and material composition in each prosthesis, according to their specific function. Figure (1-3) shows the general components of prosthetic feet.

Abbildung in dieser Leseprobe nicht enthalten

Figure (1-3) The components of prosthetic foot

1.2. TheEffectof Stiffness

Stiffness is the ability of the material to maintain its shape when acted upon by a load. There are three reasons why stiffness is important. One is concerned with stable deflections another with the absorption of energy and the third with failure by instability.

Patients expect to receive a prosthesis with proper fit. Despite the best efforts of the prosthetist, the prosthesis is rejected due to the inability of the patient's residual limb to tolerate normal and appropriate socket pressures. The socket wall can be aligned away from the body tissue relieving the pressure at these locations. This requires the stiffness of the socket material at the pressure relief areas to be less than other regions of the socket which should be supported by a larger stiffness of the socket material.

1.3. Literature Review

The major components that were used in the construction of a prosthesis included wood, aluminium and iron or metal with leather parts acting as suspension systems. Between 484 B.C. and 1800 A.D., metal prosthesis made of static and preset components were used as a means of protection and also served for aesthetic purposes. Until World War II, the major advancements in prosthetics were the result of individual contributions by such people as, James Potts, 1816; Perin Andriannzoon; professor Antenreith, 1818, and Verdayen, 1826. With the end of the Second World War and a sudden increase in the amputee population, there was an increased interest in the development of new prosthetic feet and related components [2].

Appoldt and Bennett [3], found the loading on an above-knee fibreglass socket by building the socket with the pressure transducers incorporated. Unfortunately, their results are only accurate for the single socket used in the experiment. This is due to all modern sockets having different geometries and external loads due to differences in the amputees. Bielefeldt and Schreck [4] investigated the difference in loading of four different material sockets, during stance phase, for the same patient. Their sockets were built with transducers incorporated. Ross Stewart [5] developed finite element model for above-knee prosthetic socket using the PAL2 program. The external forces were found for the prosthetic leg, while the characteristics for the socket loading were assumed. Fiberglass and polypropylene sockets were used in this analysis. S.A. Hale [6] examined the kinetics of walking at different walking speeds for above-knee amputee prosthetic leg. Three subjects were filmed at three self-selecting walking speeds (slow, natural and fast). The swing phases were analyzed in details using the inverse dynamic approach. He concluded that the increase in walking speed results in a decrease in the prosthetic leg swing time, and these times are longer than normal subjects walking at comparable speeds. Charles et al. [7] evaluated the characteristics of suction sock suspension for above-knee prostheses. Fourteen silicone sleeves were fabricated for seven different above knee amputees. It was found that above-knee suction sock suspension provides a very functional, durable means of suspending an above-knee prosthesis with the advantage of suction while negating the need for good manual dexterity and increased exertion. There was one disadvantage encountered which was the volume fluctuation of the stump. Joshua S. Rovick & Dudley [8] developed a new rapid prototyping method for fabrication of prosthetic socket. The system, referred to as SQUIRT shape, fabricates sockets by extruding a continuous bead of molten plastic and laying it down in the desired socket form. This technique eliminates intermediary steps (e.g., fabrication of plaster blanks and carving of socket positives) used in contemporary CAD/CAM prosthetics, and enables the socket to be fabricated in a single operation. Judy Van Rooyen [9] studied the material fatigue in the prosthetic SACH foot. Three samples of SACH foot were selected for testing by fatigue tester to evaluate its effect on mechanical characteristics of SACH foot. In addition, shock test was implemented on three samples of SACH foot to evaluate the shock absorption energy. Kazuko L. Shem et al. [10] measured the interface pressures between the residual limb and the socket in 13 transtibial amputees who use prostheses with thigh lacers. A Rincoe Socket Fitting System was used to measure static pressures at the interface between the stump and the socket. He found that the interface pressures with a thigh lacer are lower than the pressure without a thigh lacer.

S. Guard [11] studied the mechanical characteristics of vertical shock absorbing pylons for lower-limb prostheses. He performed static and dynamic tests on 3 commercially available vertical shock pylons which are similar in design. They have spring-like nature with considerable damping, and they shorten telescopically in response to axial loading. The results showed that the 3 tested pylons have significantly different mechanical characteristics. Tai-Ming Chu and Rong Fing [12] performed experimental stress analysis on five different custom-made Ankle-Foot Orthoses (AFOs). The biaxial rosette strain gauges were used in the analysis. The results revealed that peak stresses in the orthoses occur in the neck region. Daniel et al. [13] developed anatomical data from magnetic resonance images of a single subject to produce a generic mathematical model of the residual soft tissues and skeletal structure. The model was employed to theoretically evaluate the mechanical behaviour of tissues, predict interface stresses and aid in shaping the socket. Derek W. Potter [14] performed a comparison study between NPO and SAFE feet. The two prosthetic feet were compared in four main categories: time-distance parameters, gait curve patterns, gait curve parameters and a subjective questionnaire. Daniel Rihs & Ivan Polizz [15] analyzed the characteristics of different types of prosthetic feet. He explained the role of materials used in the construction of the prosthetic feet and performed a torsional and impact tests on different prosthetic feet for comparative results. Tara Ziolo et al [16] performed a research concerning the design of a mechanical cycle fatigue to assess prosthetic feet as a predictor of field service life. A finite element model was created for the NPO foot and analyzed the model by FE program under fatigue loading. Michael Hillery & Siobhan Strike [17] designed dynamic response prosthesis for natural and fast walking. A visual basic computer program was developed for the calculation of the deflection and the strain energy of the prosthesis for any particular loading. Ming Zhang [18] developed a finite element model based on the three-dimensional geometry of the residual limb and the internal bone structure of below-knee amputees. The shape of the residual limb was obtained from a digitizer. The contact between the residual limb and the socket was introduced in the model analysis. Tracy L. Beil & Glenn M. Street [19] measured the interface pressures between the stump and socket during ambulation. The test socket was instrumented with five sensors. It was found that the positive pressures during stance phase reduce the limb volume, while the negative pressures during the swing phase increase the limb volume. Joan E. Sanders [20] evaluated the mechanical properties of 15 elastometric liner products used in limb prosthetics under compressive, frictional, shear and tensile loading condition. All tests were conducted at load levels comparable to interface stress measurements reported on transition amputee subjects.

1.4. Concluding Remarks

Most researchers concentrated their investigations on the followings:

1. The interface pressure distribution between the socket and the stump.
2. The manufacturing process of the prosthetic socket. They try to make use of the computer for manufacturing the socket accurately, getting rid of the prosthetist tiring.
3. They do not pay attention to the strengths of the material of the sockets.
4. Construction of the pylons and the feet.
5. Studying the effect of suspension systems on the residual limb.

The current work will be directed to study the followings:

1. Asymmetry in socket shape.
2. Design specifications of the sockets. This requires giving the pressure relief areas of the socket specific flexibility.
3. Experimental comparative studying of the compressive and flexural stiffness of polypropylene and laminate sockets to understand the behaviour of these materials under these loads.

1.5. Objectives of Work

The objectives of the current work are to study the followings:

1. Analysis of the socket stress distribution during the three phases of gait cycle using the commercial package, ANSYS.
2. Design of below the knee prosthetic socket using FEM.
3. Investigating the effect of varying the modulus of elasticity on the polypropylene socket.
4. Experimental investigation of the mechanical properties of different types of prosthetic sockets used in Iraq under bending, compression and tensile loads.

References

[1] Alvin, Mulinburg and A. Bennet Wilson. A manual for below-knee amputees (1996)

[2] Karl F. Zabjek. Analyse biomécanique des pieds sach et seattle-light durant la locomotion chez les personnes âgées amputées du membre inférieur. MSc Thesis, Université de Sherbrooke (1997)

[3] Appoldt and Bennet. A preliminary report on dynamic socket pressures. Bull Prosthetic Res. (1967)

[4] Bielefeldt and Schreck. The altered alignment influence on above knee prosthesis socket pressure distribution. International Series on Biomechanics, VIIa, 387-393 (1981)

[5] Ross Stewart. Stress Paths of AK Prosthetic Socket. Monash Rehabilitation Technology Research Unit; Research (1991)

[6] S. A. Hale. The effect of walking speed on the joint displacement patterns and forces and moments acting on the above knee amputee prosthetic leg. Journal of Rehabilitation Research and Developments, Vol.3, No.2, pp. 51-78 (1991)

[7] Charles J. Dietzen, Jerald Harshberger and Rama D. Pidikiti. suction sock suspension for above knee prostheses. Journal of Rehabilitation Research and Developments, Vol.3, No.2, pp. 90-93 (1991)

[8] Joshua S. Rovick and Dudley S. Childress. An additive fabrication technique for the cam of prosthetic sockets. (VA Project Number: A711-DA) (1995)

[9] Jody Van Rooyen. Material fatigue in the prosthetic sach foot: effects on mechanical characteristics and gait. Monash Rehabilitation Technology Research Unit (1997)

[10] Kazuko L. Shem, James W. Breakey and Peter. Pressure at the residual limb-socket interface in transtibial amputees with thigh lacer-slide joints. Journal of Rehabilitation Research and Developments, Vol.10, No.3, pp.51-55 (1998)

[11] S. Gard. Mechanical characterization of vertical shock-absorbing pylons for lower limb prostheses. North American Congress on Biomechanics (1998)

[12] Tai-Ming Chu and Rong Feng. Determination of stress distribution in various ankle-foot orthoses: experimental stress analysis. JPO, Vol.10, No.1, pp.11-16 (1998)

[13] Daniel, Thomas and Bill Roger. Location anatomical landmarks for prosthetic design using ensemble neural networks. The University of Texas Health Science Center at San Antonio Department of rehabilitation Medicine (1999)

[14] Derek. W. Potter. Gait analysis of a new low cost foot prosthetic for use in developing countries. Thesis, Queen's University at Kongston (2000)

[15] Daniel Rihs and Ivan Polizz. Prosthetic foot design. Monash Rehabilitation Technology Research Unit (2001)

[16] Tara Ziolo, Radovan Zdero and J. Timothy. The NPO fatigue tester: the design and development of a new device for testing prosthetic feet. Human Mobility Research Center (AMRC) (2001)

[17] Michael Hillery and Siobhan Strike. Dynamic response of lower limb prostheses. University of Limeric (2001)

[18] Ming Zhang. State of the art research in lower limb prosthetics biomechanics-socket interface. Journal of Rehabilitation Research and Developments. Vol.38, No.3, pp.55-66 (2001)

[19] Tracy L. Beil and Glenn M. Street. Interface pressures during ambulation using suction and vacuum-assisted prosthetic sockets. Journal of Rehabilitation Research and Developments, Vol.39, No.6, pp.693-700 (2002)

[20] Joan E. Sanders. Testing of elastometric liners used in lower prosthetics: classification of 15 products by mechanical performance. Journal of Rehabilitation Research and Developments, Vol.41, No.4, pp591-602 (2004)

[21] Hayder F. N. Al-Shuka. An overview on balancing and stabilization control of biped robots. Munich, GRIN Verlag (2017). http://www.grin.com/en/e-book/375226/an-overview-on-balancing-and-stabilization-control-of-biped-robots.

[22] Hayder F. N. Al-Shuka. On local approximation-based adaptive control with applications to robotic manipulators and biped robot,' International Journal of Dynamics and Control, Springer, pp. 1-15 (2017)

[23] Hayder F. N. Al-Shuka, Burkhard J. Corves, Wen-Hong Zhu, and Bram Vanderborght. Multi-level control of zero moment point-based biped humanoid robots: a review. Robotica, Cambridge Press, vol. 34, No. 11, pp. 2440-2466 (2016)

[24] Hayder F. N. Al-Shuka. Modeling, walking pattern generators and adaptive control of biped robot,’ PhD Thesis, RWTH Aachen University, Mechanical Engineering, IGM, Germany (2014)

[25] Hayder F. N. Al-Shuka, Burkhard J. Corves, Bram Vanderborght and Wen-Hong Zhu. Zero-moment point-based biped robot with different walking patterns. International Journal of Intelligent Systems and Applications, Vol. 07, No. 1, pp. 31-41 (2015)

[26] Hayder F. N. Al-Shuka, Burkhard J. Corves, Wen-Hong Zhu and Bram Vanderborght. A simple algorithm for generating stable biped walking patterns. International Journal of Computer Applications, Vol. 101, No. 4, pp. 29-33 (Sep. 2014)

[27] Hayder F. N. Al-Shuka, B. Corves and Wen-Hong Zhu. Dynamic modeling of biped robot using Lagrangian and recursive Newton-Euler formulations. International Journal of Computer Applications, Vol. 101, No. 3, pp. 1-8 (Sep. 2014)

[28] Hayder F. N. Al-Shuka , F. Allmendinger, B. Corves and Wen-Hong Zhu. Modeling, stability and walking pattern generators of biped robots: a review. Robotica, Cambridge Press, Vol. 32, No. 6, pp. 907-934 (Sep. 2014)

[29] Hayder F. N. Al-Shuka, B. Corves and Wen-Hong Zhu. Function approximation technique-based adaptive virtual decomposition control for a serial-chain manipulator. Robotica, Cambridge Press, Vol. 32, No. 3, pp. 375-399 (May 2014)

[30] Hayder F. N. Al-Shuka and B. Corves. On the walking pattern generators of biped robot. Journal of Automation and Control, Vol.1, No. 2, pp.149-156 (March 2013)

[31] H. F. N. Al-Shuka, B. Corves and W-. H. Zhu. On the dynamic optimization of biped robot,” Lecture Notes on Software Engineering, Vol. 1, No. 3, pp. 237-243 (June 2013)

[32]

Abbildung in dieser Leseprobe nicht enthalten

Hayder F. N. Al-Shuka, Burkhard J. Corves, Bram Vanderborght, and Wen-Hong Zhu. Finite difference-based suboptimal trajectory planning of biped robot with continuous dynamic response. International Journal of Modeling and Optimization, Vol.3, No. 4, pp.337-343 (August 2013).

[33] Samira K. Radhi and Hayder F.N. Al-Shuka. Analysis of below knee prosthetic socket. Journal of Engineering and Development, Vol. 12, No.2, pp. 127-136 (June 2008)

[34] Muhsin J. Jweeg, Samira K. Radhi and Hayder F.N. Al-Shuka. An experimental comparative study between polypropylene and laminated lower limb prosthetic socket. Al-Khwarizmi Engineering Journal, Vol.3, No.1, pp.40-47 (2007)

Chapter 2: Theoretical Analysis

2.1. Gait cycle

The motion of walking is divided into two phases for each step. These are the stance phase and the swing phase. The stance phase takes approximately 63% of the total time of the step. This value varies for each subject. Stance phase starts with heel contact. After heel contact, the leg and foot pivot about the heel until the foot is flat. After this, pivot point moves forward along the foot [1, 2, 10-23].

The body now starts to move ahead of the foot and the leg is pivoting at the toe break. The ankle angle now increases. There has been little knee movement up until now. As the thigh and body increase in forwarding speed, the knee starts to bend lifting the foot and shank. Thus, the swing phase starts.

As the leg continues to move forward, gravity counteracts the knee moment until the leg is straight again, in a pendulum type motion at which point heel strike occurs again. Figure (2-1) shows the gait phases [1].

Stance Swing

time time

Stride time

Figure (2-1) Gait phases [2]

2.2. Ground Reaction Forces (GRFs)

The ground reaction force is the main force acting on the body during walking. It consists of a vertical component and two horizontal components (Rx, Ry, Rz). Figure (2-2) shows the components of ground reaction forces

These forces are found by having a subject walking across a force plate. A force plate is an instrument which provides readings of the forces and moments applied to its top surface while the foot of the subject is in contact with the plate.

Data of GRFs are readily available and these are usually in the form of a percentage of the body weight versus phases of gait. Tables (2-1) and (2-2) show the values of vertical and horizontal GRFs respectively. The lateral component has been neglected as it is insignificant compared with the vertical force [1].

Table (2-1) the values of vertical force for heel strike, mid- stance and push-off [1].

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Table (2-2) The values of horizontal force for heel strike, mid-stance and push-off [1].

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§ The minus sign means that the direction of horizontal force is opposite to the direction of walking.

2.3. Socket Stress Distribution

2.3.1. Introduction

When the socket is loaded by the stumps normally, the load will be transferred non-uniformly. This is due to parts of the stump carrying a higher load than other parts of the stump. Parts of the stump such as bones and tendons can support more loads than skin and muscles. During gait, the load transfer distribution also varies. There is no definite pressure distribution between the socket and the stump.

The PTB (Patellar Tendon Bearing) socket, used in Iraq, uses the design criterion which states that load increases on the patellar ligament with minimum contact pressure placed over the sensitive areas.

Interfacial pressure measurements require a proper measurement technique, including the use of transducers and their placements at the prosthetic interface. The experimental data of pressure distribution at the residual limb and socket interface are taken from reference [3]. Figure (2-3) shows the location of pressure measurement sites used in reference [3]. The testing procedure includes four subjects wearing PTB sockets. Each subject is required to walk with the prosthesis for at least 15 minutes to become accustomed to the test socket. The tests are divided into static (standing) and dynamic (walking) stages. The average value of l is 88mm of four subjects having (98, 113, 60 and 80mm) respectively.

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Figure (2-3 ) Pressure transducer locations[3]

2.3.2. Socket Stress Distribution Using ANSYS Package

2.3.2.1. Finite Element Model

The prosthetic socket is not a simple shape to be modeled with finite elements. Due to its unique geometry, no simplification of the shape or symmetrical shape is possible.

The rigid socket shape is measured using the soft (inner) socket for correct shape reproduction. The soft socket is broken into rings of 10mm height. The shape of each cross-section of the ring is sized. This builds up a three-dimensional socket shape. The shape of the laminated socket is different from polypropylene socket at the bottom base. Figure (2-4) shows the models.

(a) Polypropylene socket (b) Laminated socket

(c) Top view (d) Top view

Figure (2-4) Finite element models of prosthetic socket by ANSYS

2.3.2.2. Material Properties

The prosthetic socket may be manufactured from polypropylene (thermoplastic material) or composite materials (laminates). The sockets used in the analysis are polypropylene (5mm thickness), polypropylene (3mm thickness) and laminate (3mm) sockets (2-layers perlon, 6-layers fiberglass and 2-layers perlon) with orthocryl resin. The mechanical properties of polypropylene are measured experimentally, as it will be seen later, while the mechanical properties of the laminate socket are taken from reference [1]. Table (2-3) shows the material properties of polypropylene and the laminate.

Table (2-3) The Material Properties

Abbildung in dieser Leseprobe nicht enthalten

× Reference No.[1]

¤ Reference No.[4]

2.3.2.3. Element Types

For polypropylene, the element type used is SHELL63. It is an elastic shell element that has six degrees of freedom at each node, translations the nodal x, y and z directions and rotation about the nodal x, y and z-axes. Additionally, SHELL63 is capable of capturing complicated curvilinear geometry and is capable of carrying both in-plane and normal loads.

For the laminated socket, SHELL 63 is used for socket frame. The bottom base of the laminated socket consists of a solid cylinder of 20 mm radius and 20 mm height. SOLID 92 elements are chosen to mesh the volume of a solid cylinder. It is a 10-noded tetrahedral element having 3 degrees (Ux, Uy, Uz) of freedom at each node. Optimal meshing is used to mesh the surface areas of the sockets.

2.3.2.4. Loading

Tables (2-4), (2-5) and (2-6) show the average values of pressure between the socket and the stump at heel strike, mid-stance and push-off respectively[3]; the details of the interface pressure values of the four subjects are listed in part two of Appendix (B). From the results of pressure values for the four subjects, it is possible to conclude that there is no definite relationship between the pressure values and the socket height. Therefore, the averaged pressure values at each transducer for the four subjects will be used in the FE model. In effect, every person has his particular pressure distribution because there are factors which affect this distribution such as, the shape of the stump, alignment and thigh muscle strength. The averaged body weight is 75.5 Kg for body weights of four subjects (76.2, 75.4, 87 and 62.8 kg). The pressure distribution between each transducer is assumed linear. The pressure applied to the socket is as the pressure on the area of definite width with of (1mm).The effect of GRFs on the socket will be explained in the next article. Figure (2-5) and (2-6) shows the loads which are applied on the sockets.

Table (2-4) The average pressure values in (kPa) at heel strike

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Table (2-5) The average pressure values in (kPa) at mid-stance

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Table (2-6) The average pressure values in (kPa) at push-off

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2.5.2.5. The Effect of GRFs on the Socket

The polypropylene socket base is different from the laminated socket, as shown in Figure (2-4). For the laminated socket, a cross-section at a distance 20 mm from the base is taken. Therefore, the boundary conditions for the laminated socket base are built in. For polypropylene socket, the inner steel ring at the base is built in, because of the bolt passing through it, while the outer ring of the base is under pressure produced by GRFs.

2.3.2.5.1. Pressures Produced by GRFs at Heel Strike for Polypropylene Socket

From Tables (3-1) and (3-2), the vertical and horizontal forces of ground reaction forces at heel contact are :

Fy = (1.3) (75.5) (9.81) = 926.851 N (1)

Fx = -(0.2) (75.5) (9.81) = -148.131 N (2)

The maxim angle at heel strike is 30º [3], assuming that the length of the shank is 250 mm. Figure (2-7) shows the geometry of the foot-shank and the location of GRFs.

The force components are transferred to the socket base as a vertical load and a moment about the center of the socket base . The horizontal force affects the bolt mainly which fastens the socket to the shank .

The moment at the end of the shank is :

+ ΣM+ Fy (L'sin30º)- Fx (L'cos30º) = 0 (3)

where,

M : moment at the end of the shank .

Fx: horizontal force of GRFs .

Fy : Vertical force of GRFs.

L' : length of the shank .

This moment is applied to the socket base as a distributed pressure along the base area. From Equation (3), the (ΣM=-83785.072 N. mm).

At the end of the shank, the resultant force which is parallel to the shank produced by Fx and Fy is :

Fy' = Fycos30º + Fx sin 30º

= (962.851) (cos30º) + (148.131) (sin30º)

= 907.918 N

PFy' = (Fy') (4) / п(Do2-Di2)

= (907.918) (4)/п(702-302) = 0.288 N/mm2

2.3.2.5.2. Pressures Produced by GRFs at Mid-stance for Polypropylene Socket

From Tables (3-1) and (3-2), the vertical and horizontal forces of ground reaction forces at mid-stance phase are :

Fy = 0.7 (75.5) (9.81) = 518.458 N

Fx = -0.04(75.5)(9.81) = 29.626 N

Figure (2-8) shows the geometry of foot –shank and the affected forces .

+ ΣM = 29.626 (250) – 518.458(60)

= -23700.98 N. mm

PFy = Fy (4) / п (Do2-Di2)

= (518.458)(4)/ п (702-302 )=0.165 N/mm2

2.3.2.5.3. Pressures Produced by GRFs at Push–off for Polypropylene Socket

From Tables (2-1) and (2-2), the vertical and horizontal forces of ground reaction forces at push-off phase are:

Fy = (1.1)(75.5)(9.81) = 814.72 N

Fx = (0.15) (75.5) (9.81) = 111.098 N

Figure (2-9) shows the geometry of the foot – shank and the affected forces assuming that the length of the shank is 250mm.

By analysis, the forces along x' and y' axes are :

Fy' = (814.72)(cos70º) +(111.098)(sin70º)=383.048 N

Fx' = (814.72)(sin70º)-(111.098)(cos70º) =727.588 N

+ ΣM + 383.048(250)-(727.588)(250) = 0

ΣM = 86135 N. mm

PFy' = (383.048)(4)/ п (702-302)=0.121 N/mm2

Abbildung in dieser Leseprobe nicht enthalten

2.4. Design Specifications of below the Knee Prosthetic Socket

2.4.1. Introduction

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