Download Collins_PTI_BiomechanicsGuestLecture - Patho-DPT

Biomechanics Guest Lecture
PT Interventions I
Sean Collins
Objective
• Describe biomechanical principles during
joint movement and functional activities.
(CAPTE CC-5.20)
– Will be broken down to 7 need to know
questions & answers……
But first… some preliminaries
• Biomechanics (application of mechanics to biological systems)
– Systems are well defined and isolated for
computational reasons
– Therefore requires assumptions
– Does not only include musculoskeletal systems
• Kinesiology (Study of movement)
– Systems exist as they are, can be well defined
but less emphasis is placed on isolation
– Still requires assumptions
– Tends to focus on neuro musculoskeletal
systems
…more preliminaries
• Kinetics – quantification of forces (as scalars or vectors)
• Kinematics – quantification of motion (vectors)
• Perspective
– Biomechanics – isolate from the get go to try
to understand isolated components and then
bring to whole
– Kinesiology – take in the whole and dig into
isolated components as necessary to
understand the whole
Fundamentals - Summary
• Human movement occurs due to forces created by
muscles (Fm) acting on levers created by bones
and joints and is therefore rotational movement
– Even if we move through space in a line – there are
many sets of isolated rotational movements allowing
this to occur
– Whole muscle factors – Length Tension; Force
Velocity
• Rotational movement is created by torque
• Torque = F * pD (pD = Perpendicular Distance)
• Human movement is therefore the sum of of all
Torques
Mechanics
All motion is subject to
laws and principles of
force and motion
F = ma
Fundamental quantities:
Mass (m), Length (l), Time (t)
(also consider electric charge &
temperature)
Force = m (l x t-2)
Why study mechanics?
Biomechanics
The study of mechanics applied
to living things
Statics: all force acting on a
body are balanced
– Equilibrium (F1=F2)
Dynamics: deals with
unbalanced forces
• (F1 ≠ F2) -> Δ acceleration
Kinematics and Kinetics
Kinematics: geometry of motion
• Describe time, displacement, velocity, & acceleration
• Linear -motion in straight line; Angular - rotating
Kinetics: forces that produce or change motion
• Linear – causes of linear motion; Angular – causes of angular motion
Laws of Motion
The Law of Inertia:
Acceleration requires Force
Law of Acceleration:
• From: F = ma
• Derive: a = F/m
Equal and opposite:
F = -F (equal, opposite,
collinear)
Angular Displacement
• The skeleton is a system
of levers that rotate about
fixed points when force is
applied.
• Particles near axis have
displacement less than
those farther away.
• Degrees:
– Used most frequently
in measuring angular
displacement.
Angular Velocity
• C traveled farther than
A or B
• C moved a greater
linear velocity than A or
B
• All three have the same
angular velocity, but
linear velocity of the
circular motion is
proportional to the
length of the lever
Analytical Tool: Vector analysis
• In biomechanics - Vector’s typically represent
a Force and depicts its magnitude, direction,
and point of application (note – can present
quantities derived from Force (i.e. velocity)
– Most simply represented as an arrow
– Length is proportional to magnitude
– Direction determined by its direction
– Point of application considered conceptually
Scalar vs Vector Quantities
Scalar: magnitude alone
– Described by magnitude (Size or amount)
– Ex. Speed of 8 km/hr
Vector: magnitude and direction (minimally)
– Described by magnitude and direction
– Ex. Velocity of 8 km/hr heading northwest
Vector Quantities
• Equal if magnitude & direction are equal
• Which of these vectors are equal?
A.
B.
C.
D.
E.
F.
Combination of Vectors
• Vectors may be combined:
– addition, subtraction, or multiplication
• New vector called the resultant (R)
Fig 10.2
Vector R can be achieved by different combination
Combination of Vectors
Fig 10.3
What is an example of combining
vectors in biomechanics?
• Every movement you observe is caused by resultant
muscle force vectors – so what of “abnormal”
movements?
Resolution of Vectors
• Any vector may be broken down into
component vectors in a coordinate system (i.e.
Cartesian coordinate system)
– Components are at right angles to one another
– Coordinate system can be local or global
• 2 vector components – 2 d planes
• 3 vector components – 3 d space
Resolution of
Vectors
• What is the vertical
velocity (A)?
• What is the horizontal
velocity (B)?
• A & B are components
of resultant (R)
Fig 10.4
Location of Vectors in Space
For 2 d (2 vector) planar analysis:
• Horizontal line is the x axis
• Vertical line is the y axis
• Coordinates for a point are represented by two
numbers (x,y) (13,5)
From Vectors to Movement
• Vectors represent muscle force
• Muscle forces act on bony lever systems and create
Torque (also called Moments)
• Torque is an angular (rotary) force and results in angular
movement
• Human movement is the sum of all Torques acting at all
joints
Force Vectors
• Force is a vector quantity
– Magnitude
– Direction
– Point of Application
• For a weight lifter to lift a 250 N barbell
– Lifter must apply a force greater than 250 N,
in an upward direction, through the center of
gravity of the barbell
Point of Application
• Point at which force is applied to an object
• Where gravity is concerned, this point is always
through the center of gravity
• For muscular force, that point is assumed to be
the muscle’s attachment to a bony lever
• Technically, it is the point of intersection of
– line of force and
– mechanical axis of the bone
Direction
• Direction of a force is
along its action line
• Direction of muscular
force vector is the
direction of line of pull of
the muscle
• Direction of gravity is
vertically downward
• Gravity is a downwarddirected vector starting at
the center of gravity of
the object
Direction of Muscular
Force Vector
• Muscle angle of pull: the angle between the line
of pull and the portion of mechanical axis
between the point of application and the joint
Fig 12.1
Angle of Pull
• Force may be resolved into a vertical and a
horizontal component
• Size of each depends on angle of pull
• A muscle’s angle of pull changes with every
degree of joint motion
• So do the horizontal & vertical components
• The larger the angle (00 - 900), the greater the
vertical and less the horizontal components
Angle of Pull
• As seen here, the patella
creates a larger moment
arm (the perpendicular
distance from the line of
action to the axis of the
joint)
• The patella allows this
joint to favor
rotary/angular/ movement
force.
• Without it the force from
the quads would be
redirected towards the
joint.
Angle of Pull
• Vertical component is perpendicular to the
lever, and is called the rotary component
(aka angular force or movement force)
• Horizontal component is parallel to the lever,
and is called the nonrotary component (aka
stabilizing force)
• Most resting muscles have an angle of pull <
900
Rotary vs. Nonrotary Components
Angle of pull < 900
• As the angle of pull gets
smaller, the moment arm
decreases.
• Nonrotary force is directed
toward fulcrum
• Stabilizing effect
– Helps maintain integrity of
the joint
– Almost all of the force
generated is directed back
to the joint, pulling the
bones together
Fig 12.1a
Rotary vs. Nonrotary Components
Angle of pull > 900
• Nonrotary force is directed
away fulcrum
• Dislocating component
– It is called a dislocating force
because the force generated is
directed away from the joint
• Muscle is at limit of shortening
range and does not exert much
force (Reminder: active
insuficiency)
Fig 12.1c
Rotary vs. Nonrotary Components
Angle of pull = 900
• Force is all rotary/angular force
• The moment arm is at its greatest length
Angle of pull = 450
• Rotary & nonrotary components are equal
Muscular force functions:
• Movement
• Stabilization
Drawing Vectors
1. Note the Axis of the Joint
2. Draw the Horizontal component
- Parallel to Lever
- Start at muscle intertions
* 90˚ all rotary (movement force)
* > 90˚ Distracting (force generated away form
joint)
* < 90˚ Compressive (force generated towards
joint)
3. Draw Vertical Component
- Perpendicular
- Start at muscle insertions
4. Draw vectors ONLY long enough to make a perpendicular
angle to the resultant vector.
Torque or Moment
• The turning effect of an rotary force
• Equals the product of the force
magnitude and the length of the
moment arm
• Moment arm (later will divide the
moment arm into the “effort” and
“resistance” arm in certain situations) is
the perpendicular distance form the line
of force to the axis of rotation
• Torque be modified by changing either
force or moment arm
Fig 13.2
Length of Moment Arm
• Perpendicular distance
from the direction of force
to the axis of rotation
• At 450 moment arm is no
longer the length of the
forearm
• Can be calculated using
trigonometry
Fig 13.3
Length of Moment Arm
• In the body, weight of a
segment cannot be altered
instantaneously
• Therefore, torque of a
segment due to
gravitational force can be
changed only by changing
the length of the moment
arm
d
Fig 13.4
W
d
W
Gluteus Medius
Hamstrings
Summation of Torques
Movement is equal to the sum of
Torques and Forces
Forces that result in balanced
torque do not produce rotary
motion (i.e. a balanced scale);
but the forces are summed and
can produce linear motion (i.e.
a canoe)
Forces that result in an imbalance
of Torque produce rotary
motion (i.e. elbow flexion)
Objects undergoing Rotary motion
may exert Force that produces
Linear motion (i.e. push up)
Principle of Torques
• Resultant torques of a force system must be equal to the sum
of the torques of the individual forces of the system about the
same point
• Must consider both magnitude and direction
– In Biomechanics - Torques can be named by the movement
– Biceps brachii creates an elbow flexion torque; Hamstrings
create a knee flexion torque
– When you know the movement a muscle creates as an
agonist, you know the Torque its Force vector tends to
create at that joint
Force Couple
• The effect of parallel forces acting in
opposite direction
Fig 13.6 & 13.7
THE LEVER
• A rigid bar that can rotate about a fixed
point when a force is applied to overcome
a resistance
• They are used to;
– overcome a resistance larger than the
magnitude of the effort applied
– increase the speed and range of motion
through which a resistance can be moved
External Levers
• Using a small force to overcome a large
resistance
– Ex. a crowbar
• Using a large ROM to overcome a small
resistance
– Ex. Hitting a golf ball
• Used to balance a force and a load
– Ex. a seesaw
Anatomical Levers
•
•
•
•
Nearly every bone is a lever
The joint is the fulcrum
Contracting muscles are the force
Do not necessarily resemble bars
– Ex. skull, scapula, vertebrae
• The resistance point may be difficult to identify
• May be difficult to determine resistance
– weight, antagonistic muscles & fasciae
Lever Arms
• Portion of lever between
fulcrum & force points
Effort arm (EA):
• Perpendicular distance
between fulcrum & line of
force of effort
Resistance arm (RA):
• Perpendicular distance
between fulcrum & line of
resistance force
Classification of Levers
Three points on the lever have been identified
1. Fulcrum
2. Effort point
3. Resistance point
• There are three possible arrangements of these point
• That arrangement is the basis for the classification of levers
(based on mechanical advantage due to the moment arm of
the effort or the resistance).
First-Class Levers
R
E
A
Fig 13.12
E = Effort
A = Axis or fulcrum
R = Resistance or weight
Second-Class Levers
R
A
E
E = Effort
A = Axis or fulcrum
R = Resistance or weight
Fig 13.13
Third-Class Levers
R
A
E
Fig 13.14
E = Effort
A = Axis or fulcrum
R = Resistance or weight
The Principle of Levers
Any lever will balance when the product of the
effort and the effort arm equals the product of
the resistance and the resistance arm (Note
this is a balanced torque system since E x EA =
Torque E; R x RA = Torque R
E x EA = R x RA
-> no rotation
Fig 13.16
Relation of Speed to Range
in Movements of Levers
• In angular movements,
speed and range are
interdependent
• Note – this is the same
concept as discussed for
angular displacement
and angular velocity
Mechanical Advantage of Levers
• Ability to magnify force
• The “output” relative to its “input”
• Ratio of resistance overcome to effort applied
MA = R / E
*MA = Mechanical Advantage
• Since the balanced lever equation is,
R / E = EA / RA
• Then MA = EA / RA (Greater #, greater MA)
• Used for comparisons – which of two or more possibilities gives
the greatest MA? (Example – squat bar position)
Q1 Define: concentric, eccentric, isometric,
isotonic, isokinetic exercise. Be able to give
examples of each.
•
•
•
•
Concentric: Tm > Te
Eccentric: Tm < Te
Isometric: Tm = Te
Isotonic: Speed varies (The T inequality varies
throughout the ROM and therefore the Speed
Varies (assumes the F is constant and pD is
changing))
• Isokinetic: Speed is constant (The T inequality is
held constant by varying Te: a machine adjusts its
force during the ROM; Tm, and Fm can vary
greatly while maintaining the same speed of
motion)
Q2: How do these exercises vary in terms of peak
torque that can be produced?
Eccentric > Isometric > Concentric
But some thoughts –
1.Peak Torque of the muscle is always
produced at the optimal combination of peak
Fm (length tension; and force velocity needs
to be considered) and peak dD for the joint /
muscle system
2.This cascade really refers to our ability to
generate peak Tm to resist Te – So - we will
always move less than we can hold, and hold
less than we can allow to drop
Q3: How does the velocity of the exercise affect the
peak torque of each of these types of exercise?
• Focus on the “Peak” of Peak Torque here –
• Then: Force – Velocity relationship
– Peak Fm (and therefore Peak Tm) is inversely
proportional to Velocity (but not linear)
• In most circumstances the Fm & Tm “Cause”
a particular Velocity
• At times we consider – if we want to move at
X Velocity – how much Fm and Tm can be
maximally produced
Q4: What is the difference between open
kinematic chain vs closed kinematic chain;
“Normal action”vs “Reverse action”? Be able
to give examples of each.
• Open kinematic chain: distal end of UE or LE is not
interacting with a force other than gravity
• Closed kinematic chain: distal end of UE of LE is interacting
with a force other than gravity (large mass – rigid system)
• “Normal” action –for lower extremity typically normal actions if
closed chain; for upper extremity typically normal if open
chain
• Normal also involves an assumption of the normally moving
element (bone) in the lever system
• Reverse action – Stabilizing the “normally” moving element
– I.e. – stabilize the radius/ulna and move the humerus with the
bicep; fix the humerus and move the sternum with the pec major
Q5: What is an agonist, antagonist,
cocontraction, synergist, active insufficiency,
passive insufficiency. Be able to give examples
of each.
• Agonist – one muscle creating Fm, Tm for motion
• Synergists – muscles creating Fm that creates the
Sum of Tm that creates a particular movement (we
sort of clump them in usual use – biceps, triceps,
quadriceps, hamstrings; but then there is also another
level of synergist – “hamstrings and glut max for hip
extension)
• Anatagonists – muscles that create opposite Fm, Tm
of the syngerstic agonists, so if biceps create Fm, Tm;
Triceps create –Fm, -Tm
• Active / Passive insufficiency – Refers specifically to
muscles that cross > 1 joint
– Active – length tension (Fm) issues associated with >1
joint muscles
– Passive – length and therefore ROM issues associated
with > 1 joint muscles
Q6: Define the three types of levers?
• Define the types in terms of EF, RF, EA,
RA, and mechanical advantage. Be
able to sketch and give examples of
each. Define in terms of concentric,
eccentric and isometric exercise.
• EF – Effort Force --- Fm
• RF – Resistance Force ---- Fe or Fm if
antagonist
• EA = pD of the Effort Force
• RA = pD of the Resistance Force
• MA = EA / RA
Q7: Do lever arms change in concentric vs
eccentric motions? How?
• Define in terms of concentric, eccentric and isometric
exercise.
• Do they change? Depends on who you ask and what
your assumptions are – if you “Define” Effort as that
force creating motion – then the lever system changes
with Eccentric vs. Concentric actions.
• However, if you Define Effort in a human system as
that which requires Fm and therefore Bioenergetics,
then the lever system does not change with Eccentric
vs. Concentric actions.
• My thoughts – understand it both ways – know the
assumptions, and focus on understanding and what
Forces and pD’s are creating what Torques
Discussion Questions
• Why is walking down stairs more difficult
than up for someone with patellofemoral
problems?
• Why is standing up from a commode seat
easier than from a low toilet?
• Why is sitting easier than standing from
the seated position?
• What changes in sit to stand make the
exercise more challenging? In what way?
Discussion Questions
• How do you position an ankle weight to
decrease the hip flexion torque requirements
despite using the same load?
• How does a rigid ankle foot orthosis help
control knee flexion during stance?
• Why does a person with severe COPD need
to lean forward and support their upper
extremities to breath when the diaphragm is
flat?