BIOM9510
Introductory Biomechanics
Lecture 3
Anne Simmons
a.simmons@unsw.edu.au
This lecture
Forces and movement
Free body diagrams
Upper limb biomechanics
Forces and movement
Action and reaction
Internal and external
Motive and resistive
Force vs pressure
Friction
Centrifugal and centripetal
Work
Power
Energy
Torque and rotation
Action and reaction
If the body is the system, internal forces
produced by muscles cannot cause movement
to the centre of gravity of the system.
Without these internal forces, body segments
movement cannot be initiated,
however, the actual movement of the centre of
gravity has to be cause by external forces.
Therefore it must be generated by the
surrounding environment where the body
system contacts.
Action and reaction
When a body applies a force to the environment,
the environment delivers a counter force in
return called the reaction force
The theory of action and reaction was
described by Sir Isaac Newton in his third law
of motion:
“For every force applied by one body on a second,
the second body applies an equal and opposite force
directed on the first.”
Reaction forces are the forces generated by the
environment which cause movement of the
body.
Action and reaction
Action and reaction
The earth is preventing
the hands from moving
away from the body
So body moves away
from the hands
Internal and external forces
Movement of the body’s centre of gravity (CG)
relative to the environment must be accounted
for by forces external to the system
Muscle forces do not change the CG in the
unsupported body
Internal and external forces
Internal and external forces
Conversely, when the
body is in contact with
the environment, the
CG can change
Motive and resistive forces
External forces can be further categorised
An external force that causes an increase
in speed or change in direction is called a
motive force.
An external force that acts to resist the
motion caused by some other external
force or to decrease the speed of a moving
system is a resistive force.
Motive and resistive forces
Sources of resistive forces within a body system
include:
tension in a muscle acting to resist movement of a
segment as it is acted upon by some force that is
trying to move it
resistance of connective tissue
contact forces such as the touching of two body
segments as they approach one another
Resistive forces help to provide stability of a system
because they restrict excessive movement that could
cause injury.
Motive and resistive forces
An external force that causes an increase in
speed or change in direction is called a
motive force.
A motive force can originate from within the
human body or from outside of it, as long as
the force is external with respect to the
segment (system considered).
Motive forces for segmental movements
include muscle contraction and recoil of
elastic tissue
Motive and resistive forces
The most significant motive force
causing motion of the total body is
the pull of gravity.
Force and pressure
The definition of pressure is the amount of
force acting over a given area
Pressure = Force / Area
The measuring unit is N/m2
Friction
Friction is the force created between two
contacting surfaces that tend to rub or slide
past each other.
Eg it is the resistive force that prevents the
foot from slipping on the ground during
walking and running.
It is also the motive force that propels the
body forward during these activities.
Friction
Friction does not exist unless some sliding tendency
exists or unless actual sliding occurs between two
surfaces.
When one surface exerts a friction force on a second
surface, an equal and opposite friction force is applied
by the second on the first
The greater the force pressing the two surface
together the greater the friction force.
Ie the greater the weight of an object, the greater the
friction force generated when it is sliding on the
surface.
Friction
The friction force depends on the textures of
the surfaces in contact
Increased roughness usually results in
increased friction
Friction
Friction
To quantify the friction force, two facts must
be known:
The normal (perpendicular) force pressing the two
surfaces together
The coefficient of friction for the two surfaces.
The coefficient is dependant on hardness and
surface texture and is the ratio of the friction
force and the normal force forcing the two
surface to contact.
Coefficient of friction = Friction force /
Normal force
Friction
Coefficient of friction = 0 when there is
no friction
= 0.7 rubber on wood
= 0.005 cartilage on cartilage
Centripetal and centrifugal forces
When a body is restricted to traveling in a circular
path around a central axis, it experiences a force
that is directed along the radius toward the
center of the circle.
Centripetal force is responsible for continually
forcing the rotating object to follow a circular
path.
The equal and opposite force is called the
centrifugal force and is the force that the rotating
body exerts along the radius on the central axis.
Centripetal and centrifugal forces
Centripetal and centrifugal forces
Fc = mass x velocity2
radius
Work
Work is the product of force times the
distance through which that force moves
a load.
Work = Force x distance
Measuring unit is joules (1 Nm = 1 J)
Power
Power is the product of force times the
velocity with which that force is applied.
A strong, fast muscle contraction is
more powerful than that same muscle
force applied more slowly.
Power = Work / time or
Power = Force x velocity
Measuring unit is Watts, Joules/sec or
Nm/sec
Energy
Energy is defined as the ability to do
work.
The more energy a body has, the greater
the force with which it can move
something, or the farther it can move it.
There are three forms of energy relevant
to the human body:
kinetic energy,
gravitational potential energy and
elastic potential energy.
Energy
Kinetic energy is the energy a body has
because of its motion.
KE = ½ mass x velocity2
Energy
Gravitational potential energy
Whenever a body or object is in a
position from which it can fall or be
lowered by gravity, it possesses
potential energy due to its height above
the surface on which it will land.
Gravitational PE = weight x height
Energy
Elastic potential energy is the ability of a
body or object to do work while it recoils
after being stretched or compressed or
twisted.
Torque and rotation
When a force is applied to a system and
the system is restricted to moving
around an axis, the body rotates when
the force is applied (if the force does not
act directly through the axis of rotation)
The turning effect is torque
Torque and rotation
the off-axis force is called an eccentric force
the shortest distance from the axis of
rotation to the line of action of the force is
the force arm (or moment arm or torque arm)
the shortest distance is always the line
perpendicular to the force’s line of action.
the greater the force arm distance the
greater the torque produced by the force.
Torque and rotation
Torque is also called moment
Because torque requires a force, the
properties of the torque-producing force
must be considered when dealing with
rotating systems. These are magnitude,
direction, line of action and the point of
application.
Torque and rotation
Torque is produced
by muscles when
they pull on bones
and the result is
rotary motion of the
body segments eg
plantar flexion
Torque and rotation
Torque = force x force arm
Units are Nm
eg
Torque and rotation
Multiple torque forces
Torque and rotation
Because torques are vector quantities, the
direction of the torques on a system is very
important
Use right hand thumb rule
Torque and rotation
Effect of torque
on the difficulty
of a pushup
Torque and rotation
Effect of torque on CG
Exercise 1
What are the units of energy?
Calculate the potential energy of a 70 kg diver on
the 3m platform?
What is the kinetic energy of a 1kg ball travelling
at 10 m/sec?
For each of the figures in Part 1 of the handout,
determine the net torque and the direction of
motion of the system
For each of the figures in Part 2 of the handout,
draw the force arms and calculate the magnitude
and direction of the net torque on the system.
(1cm = 10N of force and 1cm = 1cm of force arm)
Free body diagrams
When a body or some other system is
subjected to external forces, its motion or
shape change is determined by the
combination of all those forces.
In order to visualize and calculate the
effect of all the external forces on the
system, a free body diagram (FBD) is
constructed.
Free body diagrams
FBDs are useful to
determine which forces need to be
altered to change the motion of the
system
keep it motionless
study the stresses and strain placed on
individual body structures and tissues.
Free body diagrams
The system is drawn in a simplified form
often as a stick figure or an outline of the
system.
Tail of the vector is placed at the point of
application
Magnitude and direction of the vectors are
shown accurately
Free body diagrams
Exercise 2
For the three activities below, draw a FBD
that represents the forces in play in the
system.
Overview of lectures so far
Functional anatomy
Some anatomical concepts
Some mechanical concepts
Biomechanics of musculoskeletal systems
Analysis and knowledge of the
mechanisms involved in producing
segmental movements
Elbow as an example
Biomechanics of musculoskeletal systems
Elbow joint
Distal end of the humerus
Proximal end of the ulna
Proximal end of the radius
Biomechanics of musculoskeletal systems
The bony and ligamentous
arrangement of the elbow
joint
Radius is attached to ulna
via annular ligament which
allows pronation and
supination
Movement of ulna is
transferred to radius
Stability of the joint
between the radius and
the humerus is weak
Bones and ligaments of the elbow
Elbow joint - structure
Only movements allowed are flexion and
extension
Achieved by movement of the olecranon
process and coronoid of the ulna around the
trochlea of the humerus
bony structure gives the joint stability
the radial collateral and ulnar collateral
ligaments prevent adduction and abduction of
the joint
Elbow joint - muscles
The anterior and
posterior sides of the
joint are stabilised by
the muscle groups
crossing the joint
Elbow joint - muscles
Elbow flexors are biceps
brachii, brachialis,
brachioradialis
The muscles have different
angles of pull, force arms and
rotary and stabilising
contributions to the elbow
joint
Biceps
origin:
- long head: supraglenoid tuberosity
of the scapula
- short head: tip of the coracoid
process of scapula
insertion:
- bicipital tuberosity of the radius
and lacertus fibrosis
Brachialis
Origin
Distal half of anterior
surface of humerus
Insertion
Coronoid process and
tuberosity of ulna
Brachioradialis
Origin
Proximal 2/3 of lateral
supracondyle ridge of humerus
Insertion
Lateral surface of the distal end
of radius
Elbow joint - muscles
Brachioradialis can
never approach 90° to
the forearm and always
has a small angle of
pull
It is a stabiliser and its
stabilising component
is always greater than
its rotary component
The attachment angle
of the brachialis is
always less than that of
the biceps
Elbow joint - muscles
The biceps is at a more
favourable length when
it achieves a 90°
attachment to the bone
Biceps is a biarticulate
muscle and the length
tension relationship is
improved during
hyperextension of the
shoulder
Brachialis does not have
this ability
Elbow joint - flexion
Brachioradialis and
wrist flexors are
stabilisers
Muscular stability of the
elbow is considered
strong
Biceps and brachialis
are rotators
Elbow joint - extension
Triceps is the main extensor of the
elbow
Attaches to the olecranon process,
proceeds up the humerus attaches
two of its heads to the posterior
humerus and one long head to the
scapula
Two short heads extend the elbow
The longer head is a two joint muscle
that extends the shoulder as well as
the elbow
Triceps
Origin
Long head: infraglenoid tubercle
of scapula
Lateral head: posterior surface of
humerus, superior to radial
groove
Medial head: posterior surface of
humerus, inferior to radial
groove
Insertion
Proximal end of olecranon
process of ulna and fascia of
forearm
Loads transmitted by joints
To calculate the stress and strain on a
structure, the loading by forces and
moments and the mechanical properties of
the materials must be known
Assume negligible deformation
Model and simplify the joint
Calculate the load on the joint
Joint loads in the static case
Forearm is held at
90° to the upper arm
10kg weight held in
the hand (W)
Ignore the weight of
the forearm & hand
Biceps muscle only is
activated (B)
B and W are parallel
to y axis
Moment arms are
20cm and 2cm
Draw a FBD and
calculate load O
Joint loads in the static case
In this case, equilibrium was established by
the activation of the biceps muscle alone
And antagonistic muscle action was not taken
into account
Consider the triceps muscle also involved
Joint loads in the static case
Assume T = 0.25
B and the force
of the triceps is
also in the y
direction
What is the
magnitude of O
now?
Joint loads in the static case
So the joint force now amounts to 1566N with
the humerus pressed against the ulna
The participation of the antagonist increased
the joint force by nearly 75%
Why does the body put up with this increased
load?? Extra stability?? Protection against
sudden release of the load??
Joint loads in the static case
The load on the joint allows an estimation of
the stress on the joint surface
Assume a contact area of 5 cm2, what is the
pressure on the joint surface with a joint force
of 900N?
Joint loads in the static case
Summary
Draw the FBD with magnitudes, directions
and points of application of all forces shown
The magnitude of the muscle force is
calculated from the equilibrium condition of
moments
The direction and magnitude of the joint
force is calculated from the equilibrium
condition of forces
Joint loads in the static case
Interesting observations
The muscle force needed to guarantee
equilibrium is, in general, much larger than the
external force.
This is due to the length of the moment arms.
In the extremities, moment arms of external
forces are comparable to the length of the
bones whereas moment arms for muscles are
comparable to the diameter of the bones.
Joint loads in the static case
Interesting observations (cont)
The magnitude of the joint load is primarily
determined by the muscle force
The external force makes a small contribution
Joint force is minimised when the agonist
muscle alone is activated. Activation of the
antagonist muscle increases the force
disproportionately.
As the shapes of the articulating bones are
generally incongruent, the areas of contact are
small and high compressive stresses on these
areas result
Elbow exercise Part 1
Redo the calculations for holding the weight in the
hand making some assumptions about the weight
of the forearm/hand and its moment arm
Elbow exercise Part 2
Then add the effects of the brachialis and
brachioradialis muscles making more
assumptions about their forces and moment
arms
Elbow exercise Part 3
Redo the calculations for holding the weight in
the hand assuming the forearm/hand weighs
3kg and its CG is 10cm from the axis of rotation
Then add the effects of the brachialis and
brachioradialis muscles assuming the following
Brachialis moment arm is 5cm and its force is
50% of the force of the biceps in the y
direction only
Brachioradialis moment arm is 15cm and its
force is 30% of the force of the biceps at 30°
to the horizontal axis
Compare with results from other analyses
