Download principle of moments


Lever: A simple machine consisting of a rigid bar
that turns about an axis of rotation or a fulcrum (A).
An effort or exertion (F) is applied to cause
movement against resistance or weight (R).
Resistive Force (R) opposes motive force


Levers utilize torque to assist us in lifting or moving objects.
Torque is the cross product between a force and the
distance of the force from a fulcrum (the central point about
which the system turns). The cross product takes only the
component of the force acting perpendicular to the
distance. Using trigonometry the torque is defined as:
Torque = Force × Distance to fulcrum × sin (θ)
Remember that work was
also force multiplied by the
distance, but it was the dot
product and used the cosine
of the angle between the
force and distance: force ×
distance × cos(θ)



For a lever in mechanical equilibrium, sum of all
the torques acting is zero or the total
anticlockwise moment (torque) is equal to the
total clockwise moment.
According to principle of moments equilibrium is
established when the sum of the moments of the
forces acting in a clockwise direction is equal to
the sum of the moments of the forces acting in a
counterclockwise direction
Therefore, a lever will balance or turn uniformly
about the point of support when the product of
the force and force arm equals the product of
the resistance and resistance arm

According to the principle of lever, ∑τ=0
Anticlockwise torques = clockwise torques
Effort Х Effort arm = Resistance Х load arm
Effort arm = Resistance
Load arm
Effort

M. A. =
Load
Effort
= Effort arm
Load arm
If the effort is farther from the fulcrum than the load
(effort arm >load arm) then the lever is a force
multiplier.
If the effort is closer to the lever than the load (load
arm> effort arm) then the lever is a speed
multiplier.

Class 1:
In this case fulcrum, i.e. axis of
rotation is located between force
and resistance. Force arm (FA) is
greater than resistance arm (RA)
and the lever is at mechanical
advantage e.g. seesaw.
In seesaw, the load is the person
that goes up, and the effort applied
is the weight of the person that goes
down. The fulcrum is in the center in
between them
Class II:
Here the fulcrum is at one end of
the lever, the force is applied to
the other end and the load is
situated in between. Hence force
arm is (FA) is greater than
resistance arm and the lever is at
mechanical advantage
 Examples:
wheel barrow, nut
cracker



Class III:
A class three lever has the effort between he
fulcrum and the load. Here RA is larger than FA and
hence lever is at mechanical disadvantage
because the force required to counter the load is
higher
Although it requires relatively great force to move
even small resistances, it can produce speed and
range of motion



The arrangement of muscles, bones and joints in
the body form lever systems
For understanding one should know about the
point of muscle insertion, its distance from the
fulcrum. Force developed by the muscle-tendon
complex produces a torque around the joint.
Center of the joint (elbow, shoulder, knee or hip
acts as the axis of rotation
Muscles operate by applying tension to their points
of insertion into bones. Most muscles act in pairs
known as antagonistic pairs. Each muscle in the
pair acts in the opposite way to the other


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The lever system amplifies the
movement of the muscle so that
short, relatively slow movements of
the
muscle
produce
faster
movements.
Movement in the body is produced
by a system of levers. These series of
levers work together to produce
coordinated action
Let’s look at various levers in the
body
Nodding the head employs a first-class lever. The head acts
as resistance. The counteracting force comes from the
muscle of neck and upper back. They prevent the head
from falling forward. The atlanto-occipital joint of head and
spinal
column
is
the
fulcrum
Forearm extension


Triceps applying force to olecranon (F) in
extending the non-supported forearm (R) at the
elbow (A)
In extending the fore-arm, as in boxing, a lever of
the first order is illustrated; the hand being the
weight, the extensor of the elbow the power, and
that joint the fulcrum placed between the weight
and power.



Flexion or bending of the arm forms a lever of third
class
The biceps (flexor) muscles in front of the upper
arm act when lifting the forearm; and, as they are
situated between the fulcrum (elbow joint) and
weight (of the forearm), a lever of the third order is
brought into action
The biceps muscles of the arm may contract only
about 10cm, but the hand will move about 60cm.
A small contraction of the biceps (the effort) can
produce a large movement of the forearm (load)
around the elbow joint (fulcrum)

When the elbow is straightened in
raising the body on the hands, then
the weight falls at the elbow,
between the extensor muscle,
which is still the power, and the
hand, which is now the fulcrum;
and the second order of levers is
illustrated



When the arm (right/left) is at
right angle to body, a third
kind of lever is illustrated
Deltoid muscle is attached
to the upper arm and spans
the shoulder joint
When the foot is raised as in
working a pedal, the weight is
at the center of foot, and the
ankle-joint is the fulcrum of a
lever of the first order

When we rise on tiptoe it is the
muscles of the calf which raise
the heel, the fulcrum is at the
toes, and the weight of the
body falls on the ankle after
the fashion of a lever of the
second order

Most levers in the body are third order levers
designed to maximize the speed rather than
maximize the force



Suppose a person is holding his/her forearm in a horizontal
position with the upper arm vertical
The biceps muscle pulls the arm upwards by muscle contraction
with a force F, the opposing force is the weight of the arm W at
its center of gravity (CG)
The weight of the average person’s forearm (and hand) is about
2% of the total body weight. Say if a person weighs 72kg then the
weight of his forearm is about 1.44kg
Sum of clockwise torques=
Sum of anticlockwise torques
14W=4F
F=14W/4
For W= 15N, F= 52.5 N

Let’ complicate the problem. Suppose now the
person is holding a ball with weight of 44N



The force in the biceps is quite
large about twenty six times the
weight of the arm and about
ten times the weight of the ball
For mechanical equilibrium, the
forces must balance. This means
that 383N upward force must be
balanced by the downward
forces
Therefore a 324N downward
force is exerted on the elbow
due to weight of the bone in the
upper arm
The lower arm can be hold by the biceps muscle at different angles q.
What muscle forces are required for the different arm positions?

The force developed by biceps is independent of
the angle between the lower and upper arm