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Biomechanics Lecture
STABILITY & EQUILIBRIUM
NEWTON’S LAWS OF MOTION
1. Law of Inertia
A body continues in a state of rest or uniform motion unless a force/torque
acts upon it.
2. Law of Acceleration
The acceleration of a body is directly proportional to the force/torque acting upon it, in the same direction as the force/torque and inversely proportional to the mass/moment of inertia of the body.
3. Law of Reaction
When a force/torque is applied to one body by another, the second body will exert an equal and opposite force/torque on the first.
TERMINOLOGY
All human movement involves the rotation of body
segments about their joint axes
Force: •  Is a linear measurement. •  Newton’s 2nd Law: Force = mass x acceleration •  It will cause a body to move in a straight line (Accelerates an object).
•  Force as the cause of movement Torque: •  Is rotational force
•  It will cause a body to rotate about a fulcrum.
•  Is the vector equal to the magnitude of the force x moment arm
(perpendicular distance between the line of action of the force and the axis
of rotation)
The Skeletal System
•  Provides shape to the body
•  Facilitates movement
through a network of
different types of joint
•  Provides attachments for
muscles, ligaments and joint
capsules
•  Absorbs or dissipates stress
generated by movement or
external force
•  Protects vital organs
Hinge joints: bending
and straightening
Pivot joints: some
rotational movement
Ball and socket
joints: forwards,
backwards, sideways,
rotational movement
Ellipsoidal joints: all
movement but no
pivoting
Shape of bones related to their function
Ball and Socket : Flexibility
Pelvis: Stability
Bones and Forces
•  The shape of bones affects the
mechanics of movement by altering
the line of force of muscles and
their tendons
•  The processes of the vertebrae
extend the area of the bone
available for tissue attachment but
also facilitate the turning moments
produced by muscles by
lengthening the lever arm
•  Long curved bones in the body
function to dissipate forces
Joints
•  Bones covered with
cartilage to reduce friction
when joint surfaces worn,
loss of low friction
impedes movement
•  Synovial membrane lines
the joint and seals to
capsule
•  Synovial fluid to lubricate
joint. •  Ligaments to support and
limit the joints movement
When joint is ‘close
packed’ it is most stable
Internal and External Forces
•  Always forces acting on the body: sometimes facilitating
movement, sometimes resisting movement and sometimes can
damage
•  Internal forces: muscle contraction
•  External force: gravity •  The body is a series of long and short bones connected at joints.
Each joint’s design allows for movement in specific directions
•  Forces are transmitted in straight lines. Long joints of the body
are curved, and this means the forces will meet tissue, but some
force will have been dissipated
•  Absorbed forces form elastic (Potential) energy which can be
released as Kinetic energy when the bone returns to shape. The Free Body diagram to identify forces
involved
Determining the force exerted
by a runner on the ground
•  Used by
biomechanists to aid
analysis: identifies the
forces involved
(considered) in the
action
•  Only show forces
acting on the ‘system’
from the surroundings
and not those within the
‘system’
Force/Torque Relationships
•  Actions are produced by the interaction of forces
associated with external loads and muscle activity
•  Human movement is the consequence of an imbalance
between the components of these forces: leading to rotation
•  Torque = perpendicular distance to line of action of force
and axis of rotation x magnitude of force (r x F)
•  Torque is often represented as a curved arrow Levers
•  A lever is: A rigid bar that rotates around a fixed
point (fulcrum)
•  In biomechanics, the rigid bar could be a bony
segment in the body, while the fulcrum could be a
joint.
•  There are three distinct forms of levers that
depend on the relative position of the fulcrum
(Class I, Class II and Class III)
•  We see examples of levers in the body
Anatomical Levers
•  In the human body, most lever systems are third
class
•  Arrangement promotes
–  Range of motion
–  Angular speed
•  Forces generated must be in excess of the
resistance force
•  Two components of muscular force
–  rotary and parallel component Forearm as a Class III Lever
•  The force lies
between the fulcrum
and the resistance
F
Application of muscle force!
• Muscle insertion
lies closer to the joint
axis than the load
•  Tissue loading is
large
Joint!
R
Weight of arm!
Mechanical Advantage=resistance/force
Mechanical Advantage=force arm/resistance arm
No Mechanical Advantage, Speed advantage
• The advantage for
the muscle is that the
distance and velocity
of shortening during
contraction are
smaller
STABILITY & EQUILIBRIUM
1. Gravity 2. Measurement of Centre of Gravity!
3. Principles of Equilibrium
4. The Standing posture
5.  Maintaining the Standing posture
1. GRAVITY - An ever-present force
Acceleration of Gravity = 9·8 m/s2 (on earth)
- Directed vertically (to centre of earth)
- Acts on a Mass to give Weight
weight = mass x gravity
- Acts through Centre of Gravity (mass)
Compared to weight on earth, bodies weigh:
On the Moon - 17 %
On Jupiter
- 250 %
Weightlessness
The downward directed
weight vector originates
from a point: The centre of mass CoM
The point at which
the mass of an object
is evenly distributed
The CoM of an object is the
geometrical centre of that object if
it is symmetrical and regular
(cube,cylinder,cone). Body segments are approximated
in this way
Centre of Gravity
•  The CoG is sometimes explained as the point at which the
force of gravity is said to act
•  The CoG of the body as a whole can be thought of as the
point about which the mass of all body segments is evenly
distributed
•  During standing, this is thought to be at the second sacral
vertebra, inside the pelvis (See Skeleton, forces, torques)
•  When the configuration of the body changes, the CoG will
shift and can be outside the body
Changing position of CoG
•  For eg, if both arms are elevated to a
horizontal position during stance
•  CoG moves forward and upward
relative to its location in the
anatomical position
•  These types of changes are important
to consider when thinking about the
balance and equilibrium in different
postures
Centre of Gravity with Age
C of G = (0.557 x height) + 1.4 cm from soles of feet
Locating the Human Body
Center of Gravity
Reaction board:
•  requires a scale, a platform & rigid board
with sharp supports on either end.
Segmental method:
•  uses data for average locations of individual
body segments CGs as related to a
percentage of segment length
Determination of Centre of Gravity in Frontal & Sagital planes
Calculation of Centre of Gravity
from Anthropometric data
Models of the human body
(a) The Hanavan model (b) The Hatze model
Computed CoM
Balance, Equilibrium and Stability
•  Balance: the line of gravity is within
the base of support
•  Equilibrium: when all the resultant
forces and moments acting on a body
are equal to zero
•  Stability: if after a displacement by
force the body returns to its original
starting position it is said to be stable
When forces are balanced: there is equilibrium: terminal velocity
Acceleration due to gravity
towards the ground
Opposed by air resistance
Stability and Balance
Stability:
•  Factors that affect:
–  Mass, friction, center of gravity & base of
support
Balance:
•  Foot position affects standing balance
Base of Support (Standing)
CoM projection
Base of Support
•  Every object (apart from during weightlessness etc)
has to rest on a supporting surface
•  The surface area of the part which is involved in
support of the object is the Base of Support.
•  The shape and size of the base of support depends
- on the posture that the body adopts (lying,
standing)
- on the position of the feet and hands or use of
extra support (eg crutches)
For example, when standing, the BoS is between and
underneath the feet
3. Stability & Equilibrium
To be stable :
  Centre of Gravity must fall over the base of support
  Any other forces must be cancelled out