Chap. 5

1
Chap. 5 Applications of Statics to Biomechanics
2
5.1 Skeletal Joints

• Skeletal joints
• Synarthroidal joints no relative motion
  between the two bones
• Amphiarthroidal joints slight relative motion
  (e.g. vertebrae)
• Diarthroidal joints various relative motions
• articular cavities, ligamentous capsules,
  synovial membranes, synovial fluid
• Diarthroidal joints
• gliding vertebral facets
• hinge elbow, ankle
• pivot proximal radioulnar
• condyloid weist
• saddle carpometacarpal of thumb
• ball-and-socket shoulder, hip

3
5.2 Skeletal Muscles

• Skeletal muscles
• smooth muscles
• cardiac muscles
• Viscoelastic viscous elastic
• Sliding-filament theory muscle contraction
• Muscle contraction
• concentric contraction shortening contraction
• (e.g. biceps during forearm flexion)
• eccentric contraction lengthening contraction
• (eg. biceps during forearm extension)
• Functions
• agonist causing movement via concentric
  contraction
• antagonist controlling movement via eccentric
  contraction

4
5.3 Basic Considerations

• Forces in Biomechanics
• internal forces muscle, ligaments, tendons,
  joints, etc.
• external forces gravity force, buoyancy force,
  electromagnetic force, etc.
• In general, unknowns in static problems are
  joint reaction forces and muscle tensions.
• Mechanical analysis of a joint
• 1. Vector characteristics of muscle tension
• 2. Proper locations of muscle attachments
• 3. Mass of the body segments
• 4. CG of the body segments
• 5. Anatomical axis of rotation

5
5.4 Basic Assumptions and Limitations

• Statically determinate problems
• Basic assumptions and limitations to apply
  statics
• 1. The anatomical axes if rotation of joints are
  known.
• 2. The locations of muscle attachments are known.
• 3. The line of action of muscle tension is known.
• 4. Segmental weights and their CGs are known.
• 5. Frictional factors at the joints are
  negligible.
• 6. Dynamic aspects of the problems will be
  ignored.
• 7. Only 2-D problems will be considered.
• Anthropometric data about body segments
• (Chaffin and Andersson, 1991 Roiebuck, 1995
  Winter, 1990)

6
5.5 Mechanics of the elbow

• Elbow joint
• humeroulnar joint hinge
• (only uniaxial rotation, i.e. flexion and
  extension)
• humeroradial joint hinge
• proximal radioulnar joint pivot
• (pronation and supination)
• Brachii
• biceps brachii most powerful flexor of the
  elbow joint
• triceps brachii to control elbow extension
• Common injuries
• fractures mainly epicondyles of the humerus
• dislocations
• tennis elbow repeated pronation and
  supination of the elbow

7
5.5 Mechanics of the elbow

• Example 5.1 Elbow joint

Therefore,
8
5.5 Mechanics of the elbow

• Example 5.1 Elbow joint

• Statically indeterminate prob.
• 1) using cross-sectional areas of muscles
• 2) using EMG measurements
• 3) optimization techniques

9

• Statically indeterminate prob.
• 1) using cross-sectional areas of muscles
• 2) using EMG measurements
• 3) optimization techniques

1) Using cross-sectional areas of muscles or
using EMG measurements
Then,
2) k21 and k31 can also be obtained from EMG.
3) Optimization techniques To minimize the forces
exerted, joint moments and work done by the
muscle for the max muscle contraction efficiency.
10
5.6 Mechanics of Shoulder

• Shoulder joint ball-and-socket joint
• Flexion and extension, abduction and adduction,
  medial and lateral rotation
• Susceptible to instability and injury

11
5.6 Mechanics of Shoulder

• Example 5.2 shoulder joint in dumbbell exercises

A the attachment of the deltoid muscle C CG of
the dumbbell FM deltoid muscle tension FJ joint
reaction force at the shoulder tension
The components of the muscle force
The components of the joint reaction force
12
5.6 Mechanics of Shoulder

• Example 5.2 shoulder joint in dumbbell exercises

Then,
a15cm, b30cm, c60cm, 15o, W40N, Wo60N
Stabilizing component
Avg ROM 230o in flexion-extension, 170o in
ab/adduction
13
5.7 Mechanics of Spinal Column

• Spinal Column most complex in musculoskeletal
  system
• major functions
• to protect spinal cord
• to support the head, neck and upper extremities
• to transfer loads from head and trunk to the
  pelvis
• Configurations
• Cervical
• Thoracic
• Lumbar
• Sacral
• Coccygeal

C6-C7 Flexion/extension
Cervical Flexion/extension
Cervical Flexion/extension
14
5.7 Mechanics of Spinal Column

• Spinal muscles most complex in musculoskeletal
  system
• Intravertebral disc stability
• most vulnerable to many injuries
• Spinal cord injury

15
5.7 Mechanics of Spinal Column

• Example 5.3 Spine

16
5.7 Mechanics of Spinal Column

• Example 5.4 Spine by the weight lifting

17
5.8 Mechanics of the Hip

• Hip joint
• Ball-and-socket joint
• a great deal of mobility
• Diarthroidal joint

18
5.8 Mechanics of the Hip

• Hip muscles

flexors extensors
anterior
posterior
Hip muscles (1) psoas, (2) iliacus, (3) tensor
fascia latae, (4) rectus femoris, (5) sartorius,
(6) gracilis, (7) gluteus minimus, (8) pectineus,
(9) adductors, (10), (11) gluteus maximus, (12)
lateral rotators, (13) biceps femoris, (14)
semitendinosus
19
5.8 Mechanics of the Hip

• Example 5.5 one-leg stance (based on free body
  diagram of leg)

20
5.8 Mechanics of the Hip

• Example 5.5 one-leg stance (based on free body
  diagram of the upper body)

Concurrent system
21
5.8 Mechanics of the Hip

• Remarks
• Carrying a load on one hand results in greater
  hip joint forces and muscle forces.
• Carrying loads using both hands is effective in
  reducing required musculoskeletal forces.
• While carrying a load on one side, people tend
  to lean toward the other side. This brings the CG
  of the upper body and the load closer to the
  midline of the body, thereby reducing the length
  of the moment arm of the resultant gravitational
  forces.
• People with weak hip abductor muscles or the
  painful hip joint usually lean toward the weaker
  side and walk with abductor gait, reducing the
  moment arm toward the midline of the body.
• Abductor gait can be corrected more effectively
  with a cane held in a hand opposite to the weak
  hip, as compared to the cane held in the hand on
  the same side as the weak hip.

22
5.9 Mechanics of the Knee

• largest joint of the body
• modified hinge joint (flexion-extension,
  internal-external rotation)
• essential for human locomotion
• most knee injuries ligament, cartilage on
  medial side

(1) femur, (2) medial condyle, (3) lateral
condyle, (4) medial meniscus, (5) lateral
meniscus, (6) tibial collateral ligament, (7)
fibular collateral ligament, (10) quadriceps
tendon, (11) patella, (12) patellar legament
(1) Rectus femoris, (2) vastus nedialis, (3)
vastus intermedius, (4) vastus lateralis, (5)
patellar ligament, (6) semitendinosus, (7)
semimembranosus, (8) biceps femoris, (9)
gastrocnemius
23
5.9 Mechanics of the Knee

• Example 5.6

24
5.10 Mechanics of the Ankle

• Anatomy

(1) gastrocnemius, (2) soleus, (3) Achiiles
tendon, (4) tibialis anterior, (5) extensor
digitorum longus, (6) extensor hallucis longus
(7) peroneus longus, (8) peroneus brevis
(1) tibia, (2) fibula, (3) medial malleolus, (4)
lateral malleollus, (5) tallus, (6) calcaneus
flexors extensors
25
5.10 Mechanics of the Ankle

• Anatomy

W ground reaction force as the body force FM
tensile force by the gastrocnemius and soleus FJ
ankle joint reaction force