Dr. Sadiq Jaffar Abass /Al-khwarizmi Engineering Journal, Vol.2, No. 1,PP 1-14  (2006) 
 

 

 1 

                  

                                
                                 Al-khwarizmi 

           Engineering  
            Journal 

 

Al-Khwarizmi Engineering Journal, Vol.2, No.1,pp 1-14, (2006) 

 

 

 

   

 

 

 

 

 Biomechanical Aspects of Shoulder and Hip 

Articulations: A Comparison of Two Ball and Socket Joints 

 
Dr. Akram Abood Jaffar       Dr. Sadiq Jaffar Abass        Mustafa Qusay Ismael 
Department of Human Anatomy             Medical Engineering Department           Medical Engineering Department 

   College of Medicine                              College of Engineering                             College of Engineering 

  Al-Nahrain University                             Al-Nahrain University                               Al-Nahrain University 

 

 

(Received 6 March 2005; accepted 2 October 2005) 

 

 

Abstract:- 

The shoulder and hip joints though essentially both are ball and socket joints, show structural 

variability to serve functional needs.  

This study aims at revealing some of the structural and functional properties of each of the two 

joints regarding the factors that contribute to the stability of any joint in the body, namely: 

bone, ligament, and muscle. 

Twenty dried scapula, hip, humerus, and femur were used. The area of the articular surfaces 

was estimated by molding a sheet of dental wax. Using special graphics software, a novel 

procedure was described to calculate the area under the curve, which was postulated to indicate 

the degree of curvature. Tension test was applied using a testometric machine, which was 

locally modified to suit biological specimens. A finite element analysis was designed to study 

the articulating bones under different loading conditions. 

In the hip joint, the area of the articular surface of the head of the femur and that of the lunate 

showed no significant statistical difference. For the shoulder joint, the articular areas of the 

head of the humerus and the glenoid were statistically different. No statistical significance was 

observed regarding curvature of the articular surfaces within both the hip and shoulder joints; 

however, the values were significantly different between the hip and shoulder. In the tension 

test, the site of rupture of the capsule of the shoulder joint was found to be at its anteroinferior 

part.  

The more contact between the area of the cup and ball, as was demonstrated in the hip joint, 

the more stable the joint. On the contrary, the shoulder articular surfaces have less area of 

contact, which makes it more mobile and decreases stability. The insignificant difference in 

curvature within both joints indicates a good congruity and thus more stability especially 

during joint movement. The curvature difference between the head of femur and the head of 

humerus indicates that the range of motion is quite different for the two joints. Results obtained 

from the finite element analysis were important in understanding the areas of stress 

concentration and were thoroughly explained from the anatomical point of view and linked to 

muscle and joint capsule attachments. The model of the joints developed in this study can be 

used as a computational tool to joint biomechanics and to prosthetic implant analysis.  

Keywords: hip joint, shoulder joint, finite element analysis, biomechanics.



Dr. Sadiq Jaffar Abass /Al-khwarizmi Engineering Journal, Vol.2, No. 1,PP 1-14  (2006) 
 

 

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1.Introduction 

The shoulder and hip joints are synovial 

joints of the ball and socket variety, each is 

formed of a ball–like convex surface being 

fitted into a concave socket. Both joints 

have three degrees of freedom of motion: 

flexion-extension, abduction-adduction, 

and rotation. Each joint has a capsule and 

several associated ligaments. The bones 

articulating in the shoulder joint are the 

head of the humerus and the glenoid cavity 

of the scapula; in the hip joint, the 

articulating bones are the head of the 

femur and the lunate surface of the 

acetabulum of the hip bonei,ii. 

Functionally, the hip joint provides 

stability in addition to providing mobility; 

whereas the shoulder provides primarily 

mobility. The hip joint supports the weight 

of the head, upper extremities, and trunk in 

the erect posture. It also provides a 

pathway for the transmission of forces 

from the pelvis to the lower extremity and 

from the lower extremity to the pelvis. 

Structurally, the pelvis is relatively rigid 

unitary structure, compared with the freely 

moveable, independent structure of the 

scapulaii. Thus, these two joints though 

essentially both are ball and socket joints 

but they bear structural variability to sub 

serve functional needs.  

The hip and shoulder articulations 

were the subject of extensive 

biomechanical studies using a variety of 

methodsiii,iv,v,vi,vii. In this study, the 

shoulder and hip joints will be compared 

for some structural and functional 

properties pertaining to bone, ligament, 

and muscle; the triad that control joint 

stability. Studying the areas and curvatures 

of the articular surfaces should reveal 

some architectural properties pertaining to 

their stability and range of motion. 

Tension test would help to unfold some 

mechanical properties of the joint capsule 

and associated ligaments. Finite element 

analysis (FEA) would help to reveal 

tension and stress pathways across the 

joints. FEA is one of the modern methods 

of human joint stress analysisviii,ix,x,xi. The 

aim of the finite element analysis is to 

develop a three-dimensional model of the 

joints that can be used as a computational 

tool to joint biomechanics and to 

prosthetic implant analysis.  

2.Materials and methods 

A series of 20 isolated dried 

scapula, hip, humerus, and femur were 

used from the inventory of the College of 

Medicine/ Al-Nahrian University. The 

bones belong to adults of the Caucasoid 

race regardless of gender. 

Measurement of the area of the 

articular surfaces 

The areas of the smooth articular 

surface of the head of the humerus, 

glenoid cavity of the scapula, the head of 

the femur, and the lunate surface of the 

acetabulum of the hip bone, which in life 

would have been covered by articular 

cartilage were estimated using a molding 

technique. 

A sheet of dental wax was warmed 

gently until just pliable, molded to the 

contours of the articular surfaces, and 

trimmed exactly around the articular 

margins. The trimmed piece was weighed 

along with a reference piece of wax sheet 

of known area. The surface area of the 

molded wax was calculated from these 

valuesxii.   

The curvature of the articular surfaces 

Each of the heads of the humerus 

and femur was digitally scanned using a 

flat bed scanner. On the scanned profiles, 

20-36 points were allocated on the 

circumference. The curvatures of glenoid 

cavity and lunate surface were treated by 

inserting an amount of children clay into 

the socket, pressed until it took the shape 

of the socket. The molded clay piece was 

then processed in a similar manner as 

indicated for the joint ball.  

Using circumference points, a 

curve was drawn by a Turbo Grapher 

program (TurboGrapher 32bit, Version 

2.135 Copyright ©1996-1999, Jeffrey R. 

Radue ,P.E) from which the area under the 

curve was calculated.  



Dr. Sadiq Jaffar Abass /Al-khwarizmi Engineering Journal, Vol.2, No. 1,PP 1-14  (2006) 
 

 

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Tension test  

A testometric machine (Testometric Co. 

Ltd., England), at the College of 

Engineering/ Department of Medical 

Engineering/ Al-Nahrain University, was 

employed. The machine is originally 

devised for testing the mechanical 

properties of materials such as tension, 

compression, and bending. In this study, 

hooks and metal holders were designed 

to modify the machine so that it will be 

suitable for testing biological material 

(Fig.1).  

Two fresh sheep shoulder joints 

were used to standardize the machine. 

Two adult, male, formalin-fixed human 

shoulder joints were denuded from their 

muscles with care taken not to disrupt 

the capsule. The human joints were 

provided from the teaching material used 

at the College of Medicine/ Al-Nahrain 

University.  

Tension was applied on the joints 

to measure the amount of force required 

before the joint capsule is torn. 

3.FEA study using ANSYS 5.4 

The bones that were used for 

model geometry were cut into slices and 

drawn on a graph paper from which key 

points were determined. These points 

were used to make a closed curve which 

represents the section plane 

circumference then converting this curve 

into area. Relations between section 

planes give the final volume which 

represents the model. After the creation 

of the model, it was meshed to be ready 

for force application and stress analysis. 

Regarding the hip bone, the model  used 

by Jaffar et al.xiii was employed. 

Isotropic material properties were 

used follows: σyield = 85, σultimate =120, 

E=18000 (MPa). The weight was 

regarded as a boundary condition. 

Segment weights expressed in 

percentage of total body weight.were 

usedxiv. 

The applied load was represented 

by the force of muscles and ligaments 

attached to the bones. These forces were 

calculated using the basic equation of 

moment equilibrium (ΣMP=0), Where P 

is the center of rotation. By finding the 

distance between the center of rotation of 

each bone and the point of force action, 

the approximate values of muscle and 

ligament forces were found. 

The major muscles, ligaments 

and reaction forces acting on the 

bonesxv,xiv,xvi were calculated for their 

forces. For each model, the applied 

forces were supposing three body 

weights: 70kg, 90kg, and 110kg (Tables 

1-4). 

4.Results 

Area of the articular surfaces: 
In the hip joint, the mean area of 

the articular surface of the head of the 

femur was 29.8±1.23cm2, the mean area 

of the lunate surface was 24.8±0.75cm2. 

In the shoulder joint, the mean area of 

the articular surface of the head of the 

humerus was19.0±0.88cm2 and the mean 

area of the glenoid cavity was 

5.40±0.30cm2. The difference in the 

mean areas was statistically significant in 

the shoulder joint (t-test, P<0.01). 

Curvature of the articular surfaces 

The means of area under the 

curve of the articular surfaces of the head 

of the femur, lunate surface, head of the 

humerus, and glenoid cavity were 

140.0±5.837, 141.0±6.505, 87.9±3.488, 

and 85.9±1.453 unit area respectively. 

Significant statistical difference existed 

between the means of the area under the 

curve of the two joints, while the same 

parameter did not vary between the ball 

and socket within the same joint (t-test, 

P<0.01). 

Tension test 

The testometric machine worked 

successfully with the sheep material and 

was standardized accordingly. In the 

fixed human joints, increasing the tensile 

force resulted in broken bones before the 

joint capsule was completely torn. The 

maximum force reached before the test 

was stopped was 850N (Fig.2), at this 

point, however, the shoulder joint 



Dr. Sadiq Jaffar Abass /Al-khwarizmi Engineering Journal, Vol.2, No. 1,PP 1-14  (2006) 
 

 

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capsule was partially torn at its 

anteroinferior part. Because of bone 

fragility, the test was not extended for a 

human hip joint since no human fresh 

material could be provided. 

5.Models Analysis 

The results of the FEA were 

represented as a contour and as von 

Mises stresses. The color contours 

represent the range of the stresses, from 

the blue (low value) to the red (high 

value). The area with red color is the 

area at which the stress is in its 

maximum value and it is the first 

probable region to fail when the joint is 

loaded with very high loads. Figures 3-5 

show the color contours of von Mises 

stresses when supposing that 90kg body 

weight material was used. 

For the scapula (Fig.3), the stress 

concentration was in the spine, scapular 

notch close to the neck, superior angle 

and the superior part of the medial 

border. The stress in these regions 

increased with the increase of the body 

weight. Analysis of the scapula for the 

90kg and 110kg body weight, revealed 

that another region of stress 

concentration could be noted, this was 

represented by a beam of stresses 

radiating from the superior-medial aspect 

toward the inferio-lateral border of the 

scapula, adding some stresses in the neck 

and around the glenoid cavity. 

In the humerus (Fig.4), the 

regions that revealed high stresses were 

the greater tubercle and the surgical 

neck. The stresses inside the upper end 

of the humerus if compared with that of 

the scapula were small. 

Regarding the acetabulum, and 

by using the model of Jaffar et al.xiii the 

largest values of stresses for 70kg person 

were distributed in its anterior and 

posterior borders. By increasing the load, 

it was noticed that stresses would be 

concentrated in the superior part of the 

acetabulum. 

In the femur (Fig.5), the stresses 

were concentrated at the upper part of 

the head and neighboring part of the 

neck at all loading conditions. A line of 

high stress can also be noted at the lower 

margin of the neck. The neck of the 

femur, however, demonstrated higher 

stresses than the lower part of the head 

and the regions of the greater and lesser 

trochanters. The stresses of the upper end 

of the femur were higher than those 

recorded for the scapula or the upper end 

of the humerus. 

6.Discussion 

Factors that contribute to the 

stability of any joint in the body are 

bone, ligament, and muscleii. In this 

study, the role of the bony articular 

surfaces in maintaining joint stability 

was studied measuring the area of the 

articular surfaces and calculating the 

degree of curvature.  

 

Areas and curvatures 

The wax technique method used 

to measure the area of articular surfaces 

was simple and required no expensive 

equipment; it could be applied 

particularly to the area measurement of 

highly curved articular surfaces. 

The mean of the areas of articular 

surfaces of the hip joint did not differ 

significantly, while the difference was 

statistically significant for the shoulder 

joint.  The difference in areas of the 

articulating surfaces gives an indication 

of the degree of compatibility of the ball 

with its socket. The ratio of the area of 

articulation of the femur to the lunate 

was (1.2:1). For the shoulder joint, the 

ratio of the area of articulation of the 

humerus to the glenoid of the scapula 

was (3.5:1). The ratio between the areas 

of each ball with its socket was 

comparable with that of the other 

researchersxv. The more contact between 

cup and ball, the more stable the joint is. 

From the above-mentioned ratios, the hip 

is more stable than the shoulder joint. 

The greater mobility of the shoulder 

increases instability and the risk of 

dislocation.  



Dr. Sadiq Jaffar Abass /Al-khwarizmi Engineering Journal, Vol.2, No. 1,PP 1-14  (2006) 
 

 

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Another parameter that plays a 

role in joint stability pertaining to the 

bony factor is the curvature of articular 

surfaces. It is difficult to measure the 

curvature of the articulating surfaces and 

there was no applicable nor a standard 

method to measure it in biological 

specimens. Thus, a simple yet applicable 

method was used in this study to find a 

value that represents the curvature; that 

is the area under the curve. 

The effect of curvature – as a 

parameter or property – indicates the 

degree of congruity of the articular 

surfaces of a joint. In this study, where 

there was no significant difference in 

curvature within both joints, it can be 

concluded that there was a good 

congruity of the joint articular surfaces. 

Congruity implies more stability 

especially during joint movement. The 

effect of congruity of joint surface has a 

less profound significance in static state. 

The significant difference in 

curvature between the two balls (the 

head of hip and the head of humerus) 

and between the two sockets (glenoid 

cavity and the lunate surface) indicates 

that the range of motion is quite different 

for the two joints. 

It should be emphasized that the 

results of this study does not take into 

account the shape and thickness of the 

articular cartilage nor the presence of the 

fibrocartilagenous labrum that surrounds 

the socket of both joints. 

Tension test 

The modifications applied to the 

testometeric machine in this study 

(hooks and metal plates) were suitable 

for joint installation as has been proved 

by the pilot study on the sheep joint. 

However, formalin fixed human bone 

could not withstand the forces applied. 

Formalin fixation changes the tensile 

properties of collagen and renders the 

bone weaker and easy to be brokenxvii. It 

is recommended that the modified 

machine be used on fresh tissue. Since 

no fresh human hip joint could be 

afforded then the test was not extended 

to the hip joint. Future studies on the 

modified machine can implement fresh 

animal joint when no human material 

can be provided.  
In spite of the bone failure when 

testing the human shoulder joint, the 

force which was applied before failure 

was 43% of the desired force and the 

curve obtained was comparable to the 

curve of Kaltsas in shoulder jointxviii. 

The site of rupture of capsule of the 

shoulder joint was at its anteroinferior 

part suggesting that this part of the 

capsule is the weakest. This corresponds 

to the finding that anterior dislocation of 

the shoulder is the most common as is 

always mentioned in literaturexix,xx.     

FEA models 

In the scapula where the stress 

which was concentrated in the scapular 

spine and the region of scapular notch 

close to the neck can be attributed to the 

tensile force applied from the upper 

fibers of trapezius muscle. In the 

superior angle and the superior part of 

the medial border of the scapula, the 

effect of the levator scapula and 

rhomboid minor was the major force 

which causes the reactions and stresses 

in this region.  

The stresses in the neck of the 

scapula and around the glenoid cavity for 

the 90kg and 110kg body weight 

analyses, can be attributed to the reaction 

between the upper medial border at 

which the upper trapezius and the levator 

scapula muscles try to elevate the 

scapula upward, and the infero-lateral 

border at which the load applied is 

represented by the weight of the upper 

limb which pulls the scapula inferiorly. 

In the greater tubercle of the 

humerus, the high stress can be viewed 

as a translation to the effect of the force 

of the joint capsule and the 

coracohumeral ligament, but above all, 

to the rotator cuff muscles. These 

muscles stabilize the joint by pressing 

the head into the glenoid. Three of the 



Dr. Sadiq Jaffar Abass /Al-khwarizmi Engineering Journal, Vol.2, No. 1,PP 1-14  (2006) 
 

 

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four rotator cuff muscles (namely, 

supraspinatus, infraspinatus, and teres 

minor) are attached to the greater 

tubercle very close to the attachment of 

the capsule of the shoulder joint for 

which they provide reinforcementsxxi.  

At the surgical neck of the 

humerus (the narrow region between the 

proximal end and the shaft of the 

humerus, which is the most likely region 

to be fractured in the upper part of the 

humerusxxii), stress concentration 

reflected an internal interaction between 

the loads applied on the humerus 

(represented by the weight of the rest of 

the humerus plus the weight of the 

forearm and hand) and the reaction force 

on the articular surface of the humerus, 

the tension force of the joint capsule, and 

rotator cuff muscles.  

The small stresses inside the 

upper end of the humerus when 

compared with that of the scapula might 

be attributed to thinness of the latter 

bone. However, the fact that only the 

proximal end of the humerus was 

analyzed in this study should not be 

overlooked. The forces that suspend the 

humerus are not only concentrated at its 

proximal end, but there are other 

powerful muscles that suspend the 

humerus yet they have a more distal 

insertion. These muscles are the 

coracobrachialis and deltoid, which are 

attached to the middle of the shaft of the 

humerus (a region which was not 

included in this study). Moreover, biceps 

brachii, another muscle suspending the 

upper limbs in the static position, is not 

attached to the humerus but to the more 

distal radius. The long head of triceps, 

which extends from the scapula to the 

ulna, suspends the limbs at a more distal 

position than the humerusxxi. 

   The intact acetabulum is a 

horseshoe form that wraps around the 

superior, anterior, and posterior aspects 

of the femoral head. In the lightly loaded 

state for the 70kg, the dome of the 

acetabulum is relatively unloaded, and 

the stress is transferred between the 

femoral head and the acetabulum 

through the anterior and posterior 

extensions of the horseshoeiii. When the 

load was progressively increased (for the 

90kg and the 110kg body weight) and 

since the acetabulum is not in continuity 

inferiorly, the stresses will be distributed 

superiorly and the anterior and posterior 

sides of the horseshoe are free to expand 

so that a more congruous seating of the 

femoral head is allowed. This 

phenomenon of deformation under load 

leads to increasing congruity with 

progressive loading. 

In the femur, where stresses 

higher than the humerus and scapula 

were recorded, this is coexistent with the 

fact that the weight-bearing femur is 

subjected to higher force if compared 

with the applied load on the humerus and 

scapula. The concentration of the stress 

at the upper part of the head is consistent 

with the finding that pressure distribution 

in the articular cartilage is mainly 

concentrated in its anterosuperior surface 

when using pressure-sensitive filmiii. The 

concentration of these stresses at the 

neck of the femur even in the slightly 

loaded state explains the predilection of 

the neck to undergo fracture. In older 

subjects, femoral neck fractures, which 

are common, might take place even after 

mirror trippingxxii. The line of high stress 

at the lower margin of the neck is 

compensated in life by the calcar 

femorale, a flange of compact bone 

projecting like a spur into the cancellous 

bone of the neck and adjoining shaft 

from the concavity of their junctionxxiii. 



Dr. Sadiq Jaffar Abass /Al-khwarizmi Engineering Journal, Vol.2, No. 1,PP 1-14  (2006) 
 

 

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Body weight 
(kg) 

Weight of arm, 
forearm and hand (N) 

Upper 
Trapezius (N) 

Levator 
scapulae 

(N) 

Rhomboids 
(N) 

70 39.6 44.5 34.6 19.8 

90 50.9 57.3 44.5 25.4 

110 62.2 69.9 54.4 31 

 

Table (1) Calculated forces acting on the scapula 
 

 

Body weight 
(kg) 

Weight of forearm & hand (N) Coracohumeral 
ligament force (N) 

Reaction 
force (N) 

70 28.5 12.2 4 

90 36.6 15.7 5.2 

110 44.7 19.1 6.4 

 
Table (2) Calculated forces acting on the humerus 

 

Body weight 
(kg) 

1/3 of B.W (N) Abductor muscles 
(N) 

Reaction of ground 
(N) 

70 228.7 22.9 68.6 

90 294 29.4 88.2 

110 359.3 35.9 107.8 

 

Table (3) Calculated forces acting on the femur 
 

 

Body weight 
(kg) 

1/6 of B.W (N) 1/3 of B.W 
(N) 

Force of Sacrotuberous 
ligament. (N) 

70 114.4 228.7 63 

90 147 294 81 

110 179.7 359.3 99 

 

Table (4) Calculated forces acting on the hip bone 



Dr. Sadiq Jaffar Abass /Al-khwarizmi Engineering Journal, Vol.2, No. 1,PP 1-14  (2006) 
 

 

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Fig.1: Reinforced human shoulder joint specimen positioned on the 
testometric machine. Note the metal plate and hooks used to fix and 
reinforce the specimen. 

 

 

0
20 30

55
90

155

250

360

476

600

750

800

850

800

340330315

240
260

230230

175170168

100

50

00

100

200

300

400

500

600

700

800

900

Strain (%)

S
tr

e
s
s
(N

)

 

 Fig.2: Tension test curve of fixed human shoulder joint. Testometric 

machine output curve. 

 

 

 

 



Dr. Sadiq Jaffar Abass /Al-khwarizmi Engineering Journal, Vol.2, No. 1,PP 1-14  (2006) 
 

 

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Fig.3:  von Mises stresses for 90kg body weight of the posterior surface of the 

scapula. 

 

 
 

 

Fig.4: von Mises stresses for 90kg body weight of the posterior surface of the 

Humerus. 



Dr. Sadiq Jaffar Abass /Al-khwarizmi Engineering Journal, Vol.2, No. 1,PP 1-14  (2006) 
 

 

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Fig.5: von Mises stresses for 90kg body weight of the posterior surface of the 

Femur. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



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Company. Philadelphia. 1984; pp.157-178, 255-286. 

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mechanical properties of bovine bone. Biomaterials. 1995; 16:1267-1271 

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replacement. Mechanical engineering publications. London. 1981 



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 جوانب ميكانيكية احيائية لتمفصالت الكتف والورك: مقارنة لمفصلين من نوع
 الكرة والتجويف

 
 مصطفى قصي اسماعيل            د.صادق جعفر عباس               د.أكرم عبود جعفر  

 / كلية الطب             قسم الهندسة الطبية / كلية الهندسة           قسم الهندسة الطبية / كلية الهندسة قسم التشريح 

 جامعة النهرين                              جامعة النهرين                                 جامعة النهرين    

 

 

 :الخالصة
رغم ان مفصلي الكتف والورك ينتميان اساساً الى نوع المفاصل ذات الكرة والتجويف اال انهما 
يظهران تباينات تركيبية لخدمة المتطلبات الوظيفية. تترافق هذه االختالفات التركيبية بين المفصلين 

 ضرورة مع الخواص الميكانيكية التابعة ألي منهما.بال
تهدف هذه الدراسة الى الكشف عن بعض الخواص الميكانيكية والوظيفية لكل من مفصلي الورك 
والكتف. حيث تم سبر الخواص الهندسية التصميمية لسطوح التمفصالت العظمية من خالل دراسة مساحة 

الجهاد للكشف عن بعض الخواص الميكانيكية لمحافظ المفاصل وتقوس هذه السطوح. كما تم استخدام فحص ا
لغرض تحليل العناصر المحددة الظهار مسارات الشد والضغط   واالربطة المرافقة لها. كما تم استخدام نموذج

 عبر المفصلين.
تم استخدام عشرين عظم جاف من كل من لوح الكتف، الحوض، العضد، والفخذ. وتم حساب 

اب المساحة تحت باستخدام قالب من شمع االسنان. كما تم وصف طريقة مبتكرة الحتس مساحات التمفصل
التقوس عن طريق استخدام برامجية خاصة للتعامل مع الرسوم. ونعتقد بأن هذه الطريقة يمكن ان توفر 
مؤشر لدرجة التقوس. كما التجأنا الى تحوير جهاز فحص االجهاد محلياً ليتالئم مع فحوصات النماذج 

قطيع العظام الى شرائح وتحويلها الى صور البايولوجية. اما دراسة تحليل العناصر المحددة فقد صممت بعد ت
 تحت تأثير قوى مختلفة. Ansysرقمية ثالثية االبعاد ليتم تحليلها بواسطة برنامج 

اظهرت النتائج في مفصل الورك بأن مساحة السطوح التمفصلية لرأس عظم الفخذ والسطح الهاللي 
تتابع(. اما بالنسبة لمفصل الكتف، فأن بال 8سم 0،،5±2،،8و  8سم 3،81±2،،8لم تكن مختلفة احصائيا )

و  8سم 5،22±5،،3السطوح التمفصلية لرأس عظم العضد والجوف الحقاني اظهرت اختالفا احصائيا )
 بالتتابع(. 8سم ±5،1،،0

 ،0،2±3،5،5كانت المساحة تحت التقوس للسطح التمفصلي لرأس عظم الفخذ والسطح الهاللي 
بع. اما في مفصل الكتف فقد كانت القيم لراس عظم العضد والجوف وحدة مساحة بالتتا 1،03±3،3،5و 

لم تالحظ فروق احصائية مهمة ضمن  وحدة مساحة بالتتابع. 0،،3±20،3و  ،،،1±،،،2الحقاني 
 مفصلي الورك والكتف، في حين كانت الفروق مهمة احصائياً عند المقارنة بين سطوح المفصلين.

تطبيق فحص االجهاد وذلك لجعل اآللة المستخدمة اكثر مالئمة  تمت مناقشة الصعوبات التي واجهت
للفحوص البايولوجية في المستقبل. ورغم الصعوبات اال ان النتائج اظهرت بأن موقع تمزق محفظة مفصل 

 الكتف كانت عند الجهة االمامية السفلى.
عل المفصل اكثر ان وجود تماس كبير بين مساحة الكرة والتجويف، كما ظهر في مفصل الورك، يج

استقراراً. على العكس من ذلك، فان مساحة التماس للسطوح التمفصلية لمفصل الكتف كانت اقل بكثير مما 
 يقلل من ثبات المفصل.

ان عدم وجود فروق مهمة لتحدب السطوح التمفصلية ضمن مفصلي الكتف والورك يشير الى جودة 
لمفصل. اما اختالف التحدب بين المفصلين فانه يشير الى التطابق وبالتالي ثباتاً اكبر خاصة عند حركة ا

 اختالف مديات الحركة بينهما.
كانت النتائج التي تم التوصل اليها من خالل تحليل العناصر المحددة مهمة في تحديد مناطق تمركز االجهادات 

. ان نماذج وقد تم تفسيرها من وجهة نظر تشريحية وربطها بمناطق اتصال العضالت ومحفظة المفصل
المفاصل التي طورت في هذه الدراسة يمكن ان تستخدم كوسيلة حساب للميكانيك االحيائي للمفاصل وفي 

 تحليل المفاصل الصناعية المغروسة.
  الميكانيكا البيولوجية ،المحددةتحليل العناصر مفصل الورك، مفصل الكتف،  مفتاح الكلمات: