Biomechanics

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Biomechanics
2
Basic definitions

• Rigid body Does not deform or deforms so little
  under load that small deformations are
  negligible. (bone)
• Deformable body Deforms (intervertebral discs)
• Force The physical quantity that changes the
  state of rest or state of uniform motion of a
  body and/or deforms its shape. (Newton, 1N moves
  1kg at 1m/s2)
• Resultant force vector sum of all forces.
• Mass Amount of matter in object. (kg)
• Velocity rate of positional or angular change
  of objects position with time. (m/s for linear,
  rad/s for angular)

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Basic definitions

• Acceleration rate at which velocity changes
  with time. (m/s2 for linear, rad/s2 for angular.)
• Moment A measure of the ability of a force to
  generate rotational motion. (Nm)
• Instantaneous axis of rotation (IAR)
• Moment arm is shortest distance between IAR and
  point of load application.
• Magnitude of the moment is calculated by force
  times its moment arm.
• Torque A rotational moment.
• Mechanical equilibrium sum of all
  forces/moments equals zero.

4
Basic definitions

• Degrees of freedom (DOF) The number of
  parameters that it takes to uniquely specify the
  position and movement of a body.

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Basic definition

• Scalar quantity
• Only magnitude
• Temperature (Celsius), mass (Kg)
• Vector
• Magnitude direction
• Velocity, force, moment
• Four characteristics
• Magnitude (length), direction (head), point of
  application (tail) line of action (orientation)

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Vectors Forces Parallelogram law of vector
addition
Corollary to parallelogram law would mean that
any vector may be broken into component forces
along any specified mutually perpendicular
coordinate axes.
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Parallelogram law of vector addition

• FFx Fy Fz
• Magnitude of force (F)
• Pythagorean theorem
• F2 Fx2 Fy2 Fz2

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Vectors Forces
Joint shear force
Deltoid muscle force
Joint compressive force
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Moment
That action of a force applied to an object
which tends to rotate the object about an axis
is called moment
Mo F x d (N.m) F x l sin?
Moment arm
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Equilibrium
An object is said to be in equilibrium if sum of
all forces and moments acting on the object is
zero
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Free-body analysis

• Use the following steps
• Identify the system (objectives, knowns,
  assumptions)
• Select a coordinate system
• Isolate the free bodies
• Apply Newtons laws (?F 0, ?E 0)

From Brinker
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Forces in free-body analysis

• Split into components along x and y axis
• Fx F cos ?
• Fy F sin ?

Fy
F
?
Fx
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Example Calculate the biceps force necessary to
suspend the weight of the forearm (20N) with the
elbow flexed at 90 degrees assuming that the
biceps insertion is 5 cm distal to the elbow, and
the center of gravity of the forearm is 15 cm
distal to the elbow

• Solution
• ?Mj 0
• -B(0.05)20(.15) 0
• 0.05B 3
• B 60N
• ?Fy 0
• J B 20 0
• J 20 B
• J - 40N

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Kinesiology
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Basic Concepts

• Kinematics
• Concerned with geometric and time-dependent
  aspects of motion without regard to responsible
  forces.
• Involves relationships between position,
  velocity, and acceleration.
• Six degrees of freedom
• Range of Motion
• Kinetics (forces)
• Analysis of effects of forces or moments that are
  responsible for the motion.
• Joint Stability
• Bony configuration
• Ligaments
• Muscles

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Rolling Contact
?
??
o
?
O

• The contact points on the two surfaces have zero
  relative velocity , no slip
• Tire marks on the surface
• The ICR is on the surface of the object

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Pure Sliding Contact
?
o
?
?
?

• Spinning motion (tires on icy road)
• The ICR is the center of axis

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Rolling and Sliding Contact
?
o
o
P

• The relative velocity at the contact point is not
  zero
• The ICR is between the geometric center the
  point of contact
• Car is moving tires will leave behind skid
  marks

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Motion at the articulating surfaces of
diarthrodial joint

• All diarthrodial joint motion consists of both
  rolling and sliding motion
• In the hip shoulder sliding motion predominates
  over rolling motion
• In the knee both rolling sliding motion occurs
  simultaneously

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Instant center of Rotation

• When a rigid body is rotating translating at
  the same time its motion at any instant of time
  can be described as rotation around a moving
  center of rotation (Instant Center of Rotation or
  ICR)

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ShoulderKinematics

• Normal arm elevation averages 170
• The plane of the scapula is 30 to 50 anterior
  to coronal plane of the body
• 2 of glenohumeral motion occurs for each 1 of
  scapulothoracic motion (21 ratio) during
  elevation

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Scapulo-thoracic Motion
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ShoulderKinetics

• Zero position (Saha) 165º of abduction in
  scapular plane minimizes the deforming forces
  around the shoulder and can be used to reduce
  dislocation fracture dislocations around the
  shoulder.

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Free body analysis of shoulder

• Deltoid Force
• ?Mo 0
• 3D 0.05 W (30) 0
• D 0.5 W

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ShoulderStability

• Passive Constraints
• Conformity of the radii of curvature
• Negative intra-articular pressure
• Static Constraints
• Middle GH ligament
• Inferior translation in adducted externally
  rotated shoulder
• Inferior GH ligament
• Primary stabilizer (anterior band) of the
  abducted externally rotated shoulder against
  AP translation
• Primary restrain to inferior translation in 90
  degree abduction
• Dynamic Constraint (Rotator cuff)

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Contributors to shoulder stability
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Static stabilizer IGHL
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Static stabilizer IGHL
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Muscular Activity in Shoulder

• Elevation
• Both supraspinatus deltoid are necessary for
  elevation
• 97 of supraspinatus force is directed towards
  compression of glenohumeral joint

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Muscular Activity in ShoulderElevation
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ElbowKinematics
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ElbowKinematics

• Axis of Motion
• Flexion-Extension
• Line drawn from the inferior aspect of the medial
  epicondyle through the center of the lateral
  epicondyle
• Forearm Rotation
• Capitellum radial head extending to the distal
  ulna (defines a cone)

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Elbow Axis of Motion
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ElbowStability

• Medial side (Valgus)
• Elbow Flexion (90º)
• gt50 by the medial collateral ligament
  (especially the anterior oblique band)
• 30 by radial head
• Elbow Extension
• Equal contribution by the shape of the
  articulation, medial collateral ligament
  anterior joint capsule

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ElbowStability

• Lateral side (Varus)
• Elbow Flexion (90º)
• 78 by the joint articulation
• 9 by lateral collateral ligament (Ulna band)
• 13 by joint capsule
• Elbow Extension
• 54 by joint articulation
• 32 by capsule
• 14 by LCL

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ElbowKinetics

• Muscle forces that act about the elbow have short
  lever arms, they are relatively inefficient
  kinetically but very efficient kinematically
• Small muscle excursion can produce a large arc of
  motion

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Free body analysis of elbow

• Biceps Force
• ?Mo 0
• - 5 B 15 W 0
• B 3 W

Because of the close insertion of biceps to the
joint it is relatively inefficient and support
3-times weight of the arm
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SpineKinematics Motion Segment
The motion segment is the basic anatomical unit
of the spine. Comprises of two adjacent
vertebrae their intervening soft tissue
including the disk
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SpineKinematics

• Two types of motion
• Translation
• Rotation
• Three axis of motion
• Translation rotation are often coupled

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Spine BiomechanicsIntervertebral Disk

• Collagen fiber orientation
• About 35 resistance to torque is provided by the
  disk

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Spine BiomechanicsIntradiskal Pressure
Nachemsom
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Spine BiomechanicsVertebral Body

• Resists compressive forces
• Bone mineral content is a good predictor of the
  ultimate strength
• Flexion forces tend to cause anterior collapse
  where the trabeculae are weak

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Spine BiomechanicsVertebral Body
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Spine BiomechanicsPosterior Elements, Facet
Joints ligaments

• Lumbar facets contribute to 40 resistance to
  torsional loads
• Posterior ligaments are primarily tensile
  load-bearing structures resists 20 of
  torsional loads

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Spine BiomechanicsPosterior Elements, Facet
Joints ligaments
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Spine BiomechanicsSpinal Motion
C5 -6
L4-5
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Spine BiomechanicsCervical Spine Motion

• 60 of the axial rotation of the cervical spine
  occurs at upper region (occiput- C1 C2)
• Most of the motion of flexion-extension is in the
  central region
• Largest range highest incidence of spondylosis
  is found at C5 C6 level

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Spine BiomechanicsLocation of Instantaneous Axis
of Rotation in lumbar spine
N
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Spine BiomechanicsBack Muscle Activity
Very little
280 N
2080 N
3300 N
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Hip BiomechanicsKinematics

• Normal Motion
• Flexion-Extension Arc 120º - 140º
• Abduction-Adduction Arc 60º - 80º
• Rotation Arc 60º - 90º
• Total motion reaches 240º - 300º
• Putting on shocks and shoes requires a total
  motion of 160º - 170º

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Hip BiomechanicsKinematics
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Hip BiomechanicsKinetics
Fj FAB 5/6W 0
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Illustration of Forces operating on the
hipExplanation using a simple balance
M Abductor force K Body weight R Joint
reaction force
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Hip BiomechanicsKinetics

• Joint reaction force is result of contraction of
  muscles crossing the hip
• During quiet single-leg stance, the forces
  transmitted across the hip joint are estimated to
  be 2 to 2.8 times the body weight

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Hip BiomechanicsKinetics

• During two legged stance, the forces are about
  half that in a single-leg stance
• Getting in out of the bed, raising onto a bed
  pan, transferring to a wheelchair all involve
  high forces of at least 2 times body weight

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Hip BiomechanicsKinetics

• Reducing Joint Reaction Force
• Increasing abductor moment arm
• Lateralization of greater trochanter
• Restoring the offset
• Decreasing the medial moment arm
• Medialization of acetabulum
• Shifting the body weight over the hip (lurch)
• Decreasing W
• Using Cane in the contralateral hand

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Hip BiomechanicsReducing Joint Reaction
ForceLurch on the affected side
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Hip BiomechanicsKinetics

• A properly used cane can reduce the total forces
  up to 40 crutches from 30 to 50
• Instrumented hip prosthesis have measured joint
  forces lower than predicted on mathematical
  models
• They have indicated rotational torques generated
  by out-of-plane loads at the hip joint

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Hip BiomechanicsReducing Joint Reaction
ForceUsing a cane
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Hip BiomechanicsInfluence of Neck-Shaft Angle

• Varus angulation
• Decrease joint reaction force
• Increase shear across the neck
• Shortening of abductor resting length causing
  limp
• Valgus angulation
• Increases joint reaction force
• Decrease shear across the neck

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Hip BiomechanicsIncreased Joint Reaction
ForceValgus angulation
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Knee BiomechanicsKinematics

• Sagittal Motion
• Normal motion
• Extension 0º - 20º of recurvatum
• Flexion 125º - 165º
• Function ROM
• 3º - 4º of extension to 140º flexion

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Knee BiomechanicsKinematics Sagittal Motion
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Knee BiomechanicsKinematics Sagittal Motion

• Normal walking the knee is flexed to 15º at heel
  strike has a maximum flexion of 65º in swing.
• With sprinting the knee is flexed about 35º at
  foot strike and requires about 130º of flexion in
  swing
• Most competitive athletic activities require 130º
  of flexion
• Getting in and out of chair requires 115º of
  flexion

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Knee BiomechanicsKinematics Intra-articular
Motion

• Both rolling sliding
• In Rolling translation of the joint axis equaling
  that of the contact point on the articular
  surface
• In Sliding the joint axis remains stationary
  while the articular contact points translate

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Knee BiomechanicsKinematics Intra-articular
Motion

• Rolling is most prominent in the initial 15
  degrees of motion (RS 12)
• As flexion advances sliding becomes more
  prominent (RS 14)

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Knee BiomechanicsRelationship between ICR
Surface Contact Point
ICR
Contact Point
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ICR in the Knee
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Knee BiomechanicsKinematics Intra-articular
Motion

• In the normal knee as the femur rolls and glides
  on the tibial surface, the instantaneous
  directional lines generated always remain
  parallel to the tibial surface
• If the relationship between the ICR and surface
  contact point is altered femoral movement will be
  directed into the plateau, crushing the surface
  or away from plateau producing lift-off

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Knee BiomechanicsRelationship between ICR
Surface Contact PointAbnormal contact point or
ICR

• Internal derangement
• Nonphysiological ligament reconstruction
• Knee brace

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Knee BiomechanicsKinetics

• Anterior Cruciate Ligament
• The fibers as they pass from origin to insertion
  rotate approximately 90º
• This leads to differential tension in the fibers
  and causes the ligament to twist in flexion

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Knee BiomechanicsACL
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Knee BiomechanicsACL PCL

• ACL two bundles
• Anteromedial (tight in flexion)
• Posterolateral (tight in extension)
• PCL two bundles
• Anterolateral (tight in flexion)
• Posteromedial (tight in extension

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Knee BiomechanicsAP Translation Restrain

• Anterior Translation
• Primary ACL
• Secondary deep MCL
• Posterior Translation
• Primary PCL
• SecondaryLCL, posterolateral complex
  superficial MCL

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Knee BiomechanicsAP Translation Restrain

• In the absence of ACL the posterior horn of
  medial meniscus acts as a wedge to resists
  anterior tibial translation
• There is 0.5 cm of excursion of the medial
  meniscus and 1.1 cm of excursion of the lateral
  meniscus during 0 120 degree arc of knee motion

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Knee BiomechanicsAP Translation Restrain
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Knee Biomechanics

• The ultimate strength of ACL in a young patient
  is about 1750 N
• ACL fails by serial tearing at elongation strain
  of 10 15
• PCL deficiency leads to increased contact
  pressure in the medial compartment
  patellofemoral joint

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Knee Biomechanics4-Bar Cruciate Linkage
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Knee Biomechanics4-Bar Cruciate Linkage

• In full extension the ACL is parallel with the
  roof of the intercondylar notch
• In full flexion the PCL link is parallel to the
  notch
• The center of rotation in the 4-bar linkage model
  is where the 2 cruciate ligaments cross

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Knee BiomechanicsVarus - Valgus Restrain

• Varus Angulation
• Primary LCL
• Secondary Posterolateral capsule
• Valgus Angulation
• Primary Superficial Deep MCL

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Knee BiomechanicsRotational Restrain

• Internal Rotation
• Primary Superficial deep MCL
• Secondary ACL
• External Rotation
• Primary LCL, posterolateral complex and
  popliteofibular ligament
• Secondary PCL

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Knee BiomechanicsPatellofemoral Joint

• The patella increases the mechanical advantage of
  the extensor muscles by increasing the moment arm
• The quadriceps force decreases by 15 to 30
  after patellectomy
• Joint compressive forces at PF joint
• Normal Walking half BW
• Stairs 2.5 to 3.3 BW
• Deep Knee Bends 7 8 BW

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Free Body Diagram for the Knee
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BiomechanicsAnkle Joint
Axis of Motion
85
BiomechanicsAnkle Joint

• Motion of the talus takes place primarily in the
  sagittal planes about a transverse axis that
  deviates posteriorly from the frontal plane on
  the lateral side
• The ICR falls within the talus throughout the
  full range of ankle motion

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BiomechanicsAnkle Joint

• The forces acting on the ankle joint can rise to
  levels exceeding five time BW
• The fibulotalar joint transmits approximately one
  sixth of the force

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Biomechanics of the FootThe stabilizing
Mechanisms

• Static
• Arches of the foot
• Longitudinal (medial lateral)
• Transverse
• Plantar aponeurosis (windlass mechanism)
• Dynamic
• Intrinsic muscles
• Posterior anterior tibial peroneus longus

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Biomechanics of the FootThe stabilizing
Mechanisms
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Biomechanics of the FootThe stabilizing
Mechanisms

• The longitudinal arches are not intrinsically
  stable and are stabilized by heavy ligamentous
  structures
• The plantar calcaneonavicular (spring) ligament
  is the most important ligament supporting the
  medial arch

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Biomechanics of the FootWindlass Mechanism
Increases the arch height as the toes
dorsiflex Passively inverts the calcaneus
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Biomechanics of the FootThe subtalar Joint
Axis of Motion
23º in transverse plane
41º in sagittal plane
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Biomechanics of the FootThe subtalar Joint

• Coupled Motion
• Inversion, plantar flexion adduction
  (supination)
• Eversion, dorsiflexion abduction (pronation)

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Biomechanics of the FootRelationship of muscles
about the ankle subtalar joints
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Biomechanics of the Ankle FootRelationship to
Gait
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Biomechanics of the Ankle FootRelationship to
Gait

• Heel Strike
• Tibia rotates internally
• Subtalar joint everts
• Transverse tarsal joints are parallel
• Foot is flexible
• Absorbs shock

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Biomechanics of the Ankle FootRelationship to
Gait

• Push-off
• Tibia rotates externally
• Subtalar joint inverts
• Transverse tarsal joints are not parallel
  locked
• Rigid lever arm for push-off

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Biomechanics of the Ankle FootLoad Distribution

• During standing loads are distributed equally on
  the heel ball of the foot, the hallux bears
  twice the load of any MT
• During walking most load is transmitted through
  2nd MT
• Loads within the foot are generally transmitted
  from talus to calcaneus to navicular. Only
  minimal forces are transmitted laterally

98
Following patellectomy, the power of extension is
reportedly decreased by approximately 30
(Figure). This biomechanical effect is caused by

• posterior shift of the center rotation of the
  knee joint.
• an increase in anterior translation of the tibia.
• a reduction in the quadriceps force production.
• a reduction in the moment are m(t).
• a reduction in moment arm m(q).

99
The facet joints contribute what percentage of
the torsional load resistance in the lumbar spine?

• 5
• 20
• 40
• 75
• 95

100
In Figure 18, the foot is secured in a traction
apparatus with a 15-lb weight attached. Each
pulley weighs 1 lb. Assuming frictionless
pulleys, what is the longitudinal traction on the
leg?

• 12 lb
• 15 lb
• 20 lb
• 29 lb
• 30 lb

101
An idealized diagram of loads across the hip
joint is shown in Figure 7. The loads across the
hip joint may vary from three to five times body
weight during walking or stair climbing. The
most important factor that contributes to this
finding is the

• modulus of bone in the femoral head.
• moment at the center of rotation because of the
  action of the gluteal muscles.
• resultant force vector because of the contact
  across the acetabulum.
• contact area of the femoral head on the
  acetabulum.
• ground reactive force.

102
Which of the following factors is used to
determine torsional rigidity of a long bone
fracture under internal or external fixation?

• Bone rotation versus torque applied
• Bone deflection versus bending moment applied
• Axial displacement versus tension applied
• Lateral translation versus shear force applied
• Fracture gap closing versus compressive force
  applied