Levers
Movement
in the body is produced by a system of levers. These series of
levers work together to produce coordinated action, some by actual
movement (dynamic) and others by stabilization (static).
 Definitions
 Lever: Rigid bar that turns about an axis of rotation or
a fulcrum (A)
 Motive Force (F): effort or exertion applied to cause movement
against resistance or weight
 Resistive Force (R): opposes motive force
First Class Lever
 axis is placed between force and resistance
 examples: crowbar, seesaw, scissors
 examples in body:
 elbow
extension
 triceps applying
force to olecranon (F) in extending the nonsupported forearm
(R) at the elbow (A)
 flexing muscle
 agonist (F) and antagonist (R) muscle groups are simultaneously
contracting on either side of a joint axis (A).
 lever characteristics
 balanced movement
 axis is midway between force and resistance
 e.g.: seesaw
 speed and range of motion
 axis is close to force
 e.g.: elbow extension
 force
 axis is close to resistance
Second Class Lever
 resistance is between axis and force
 classic examples: wheelbarrow, nutcracker
 complex example: rowing
 paddle in water acts as slipping axis (A)
 boat resistance is resistive force (R)
 rower is motive force (F)
 relatively few examples in body
 plantar flexion of foot to raise body up on toes
 ball of foot (A) serves fulcrum as ankle plantar flexors
apply force to calcaneus (F) to lift resistance of body at tibial
articulation (R) with foot.
 entire body during pushup
 foot is axis of rotation (A) when reaction force of ground
pushing against hands (F) lifts weight of body's center of gravity
(R).
 lever characteristics
 produces force: large resistance can be moved by a relatively
small force
 weight machines: more resistance needed, lower inertia, smoother
feel.
Third Class Lever
 force is placed between the axis and resistance
 examples:
 tongs: food (R) is supported by grip on handles (F) while
axis is on opposite end.
 shovelling: dirt on shovel (R) is lifted by force to handle
by hand (F) while upper hand on end of shovel handle serves as
axis (A)
 rowing: oar is moved through water (R) by pulling on middle
of oar (F) while holding end of oar with opposite hand (A).
 Note: shovelling and rowing actions can also be first class
lever systems if the hand closes to the force remains stationary
(A) and the hand on the far end of the shovel or oar is moved
(F).
 batting: ball is hit (R) by moving bat toward ball with hand
of far arm (F) while supporting lower portion of bat with hand
of near arm (A).
 example in body
 most levers in body are third class
 elbow flexion
 Biceps and brachialis pull ulna (F)
lifting the forearm, hand, and any load (R) at the elbow (A).
 knee flexion
 hamstring contract (F) to flex the lower leg (R) at the knee
(A).
 lever characteristics
 produces speed and range of motion
 requires relatively great force to move even small resistances
 weight machines: less resistance required, greater inertia
 harder to start and stop movement
Lever Arm Length
 Definitions
 Resistance Arm: distance between axis and point of resistance
application.
 Force Arm: distance between axis and point of force.
 Formula
F 
x 
FA 
= 
R 
x 
RA 
Force 
x 
Force Arm 
= 
Resistance 
x 
Resistance Arm 
Initial Example 

Change insertion 1 cm 

Change point of resistance 1 cm 
F x 2 cm 
= 
10 kg x 9 cm 
2 F 
= 
90 kg 
F 
= 
45 kg 


F x 3 cm 
= 
10 kg x 9 cm 
3 F 
= 
90 kg 
F 
= 
30 kg 


F x 2 cm 
= 
10 kg x 8 cm 
2 F 
= 
80 kg 
F 
= 
40 kg 

 Lever characteristics
 Long resistance arm: speed and range of movement
 Short resistance arm: force
 Mechanical advantage
 Motive force arm length / Resistive force arm length
 No mechanical advantage if quotient = 1 (same length):
 If quotient >1: mechanical advantage in force
 If quotient <1: mechanical advantage in speed and range
of motion
 Lever length of resistive forces
 Center of gravity of body segment (eg: forearm in arm curl,
body during pushup, etc.)
 Center of gravity of any additional weight. (eg: handle on
barbell, sand bag on back, etc.)
 Perpendicular distance from fulcrum
 When calculating forces applied to levers, the Perpendicular
Distance from the fulcrum needs to be measured.
 Torque = Force x Perpendicular Distance.
 The physical distance and the perpendicular distance are
the same only when force is being applied at a right angle (perpendicular)
to the lever.
 Perpendicular distance can be calculated by multiplying the
physical distance x sine of the angle of force application. Also
see Force Vectors and example below.
Variable Resistance Levers

Resistive force (R) is initially relatively short [close to fulcrum
(A)]. 


As motive force (F) acts on lever, resistive arm becomes physically
longer, yet its perpendicular distance remains constant. In contrast,
motive torque diminishes, requiring progressively greater motive
force throughout movement. 

Even though the physical distance between (R) resistive force
and (A) fulcrum increases approximately 2 fold, perpendicular
distance is the same. You can more clearly see this by drawing
a line in the direction of (R) resistive force and a parallel
line through (A) fulcrum. Since gravity acts on the weight in
our diagram, the (R) resistive force is downward, so both lines
will be drawn vertically. The distance between the lines (perpendicular
distance) are the same in each diagram, therefore the resistive
torque remains constant.
In contrast, although the physical distance between (F) motive
force and (A) fulcrum do not change, their perpendicular distance
decrease. To see this, draw a line in the direction of the (F)
motive force and a parallel line through the (A) fulcrum. But
in this case, the distance between the lines (perpendicular distance)
decrease, therefore the motive torque diminishes as it moved
downward, requiring greater (F) motive forces to raise the (R)
resistive forces.

