Biomechanics Guest LecturePT 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 = maFundamental quantities:

Mass (m), Length (l), Time (t)(also consider electric charge &

temperature)

Force = m (l x t-2)Why study mechanics?

BiomechanicsThe study of mechanics applied

to living thingsStatics: all force acting on a

body are balanced– Equilibrium (F1=F2)

Dynamics: deals with unbalanced forces

• (F1 ≠ F2) -> Δ acceleration

Kinematics and KineticsKinematics: 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 MotionThe 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 downward-directed 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 ComponentsAngle 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 ComponentsAngle of pull = 900

• Force is all rotary/angular force• The moment arm is at its greatest lengthAngle of pull = 450

• Rotary & nonrotary components are equalMuscular force functions:• Movement• Stabilization

Drawing Vectors1. Note the Axis of the Joint2. 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

Fig 13.4W

d

W

d

Gluteus Medius

Hamstrings

Summation of TorquesMovement 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 LeversThree points on the lever have been identified

1. Fulcrum2. Effort point3. 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

RE A

Fig 13.12

E = EffortA = Axis or fulcrumR = Resistance or weight

Second-Class Levers

R

EA

Fig 13.13

E = EffortA = Axis or fulcrumR = Resistance or weight

Third-Class Levers

Fig 13.14

R

EA

E = EffortA = Axis or fulcrumR = Resistance or weight

The Principle of LeversAny 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 > ConcentricBut 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?