Physics 160 Biomechanics
Torque
Questions to Think About
• What factors affect a muscle’s
functional strength (i.e. ability to
control rotation) at a joint?
• Why should a worker keep an
object being lifted close to his torso
in the transverse plane?
• What allows us to walk across the
room?
Torque
Torque is the measure of the extent to which a force will
cause an object to rotate. It is the product of the force and the
force’s moment arm.
T= F ⋅ d ⊥
T torque in [ N ⋅ m]
F = force in [ N ]
d ⊥ = moment arm in [m]
Torque is a vector quantity that lies along the axis of rotation.
Line of Action of a Force
• The line of action of a force is the imaginary line that
extends from the force vector in both directions.
• It’s the line that the force pushes or pulls along.
Line of action of F
F
Moment Arm
• Shortest distance from a force’s line of action to the
axis of rotation
• Moment arm is always perpendicular to the line of
action and passes through the axis of rotation
Computing the Moment Arm
• Determined by:
– Distance d from axis of rotation to point at
which force is applied
– Angle at which force is applied
d┴=d sinθ
θ
Axis of rotation
d
F
Line of Action
The line of action of the three
forearm muscles. The
brachialis (BRA) is a large
muscle, but it has the smallest
moment arm, giving it the
poorest mechanical
advantage. The biceps brachii
(BIC) also has a large crosssection and has a longer
moment arm, but the
brachioradialis (BRD), with its
smaller cross-section, has the
longest moment arm, giving it
the best mechanical
advantage in this position.
Example
If the force due to the
biceps shown is 100N
and the moment arm is
1.5 cm. What is the
torque produced by the
biceps?
Torque due to Muscles
A muscle with a small moment arm (A) needs to
produce more force to generate the same torque as a
muscle with a larger moment arm (B).
Moment Arms
The magnitude of the moment arm of the biceps
muscle changes throughout the range of motion.
Positive and Negative Torque
• Positive torque tends to cause counterclockwise
rotation
• Negative torque tends to cause clockwise rotation
Example
Find the torque produced by each child if the angle
of the teeter totter with the horizontal is 25o.
Example
Using the anthropometric data given in Appendix D
determine if the two forces shown below create
torques equal in magnitude?
Resultant Joint Torque
• The effects of all forces acting across a joint can be
duplicated exactly by the combination of:
– A resultant joint force acting at the joint center
– A resultant joint torque acting about the axis of
rotation through the joint center.
• Resultant joint force = the vector sum of all forces
acting across a joint.
• Resultant joint torque = the sum of the torques about
the joint axis due to these forces.
• Note: Forces that do not act across the joint are not
included (e.g. weight)
Shoulder girdle muscle forces
Segmental Representation of the Body
Segment com’s
are marked
with an “X”,
total body com
is the black dot
Torques during a Squat
Joint forces are Fx and FY, W is the weight of each
segment and M denotes the torques acting at the joints.
Levers
• A lever is a simple machine
consisting of a relatively
rigid barlike body that can
be made to rotate about an
axis or fulcrum
• There are first, second and
third class levers depending
on the relative positions of
F, the applied force, R, the
resistance and the fulcrum.
F
R
First class
R
F
Second class
F
R
Third class
Mechanical Advantage
• The mechanical
advantage of a lever
is the ratio of the
moment arm of the
force to the moment
arm of the resistance.
• An anatomical lever
showing the
resistance arm, effort
arm, and fulcrum
(elbow joint).
First Class Levers
• Effort force and resistance force on opposite sides of
the fulcrum
• A first-class lever in which the mechanical advantage
is less than 1, that is, the effort arm is less than the
resistance arm. The linear distance moved by the
effort force, however, is less than that moved by the
resistance force in the same time.
First Class Levers
An anatomical firstclass lever in which
the weight of the
head is the
resistance force, the
splenius muscles
provide the effort
force, and the
fulcrum is the atlantooccipital joint.
Second Class Levers
The effort force and the
resistance force act on
the same side of the
fulcrum. The resistance
force is between the
fulcrum and the effort
force.
Mechanical advantage
is greater than 1.
Third Class Levers
The effort force and the
resistance force act on the
same side of the fulcrum.
The effort force is between
the fulcrum and the
resistance force.
The arm held in flexion at the
elbow is an anatomical thirdclass lever: The resistance
force is the weight of the
arm, the fulcrum is the elbow
joint, and the effort force is
provided by the elbow flexor
muscles.
Levers
• 1st Class: Mechanical Advantage (MA) varies
• 2nd Class: Favors the effort force
– MA > 1 (i.e., a smaller effort force can balance a
larger resistive force)
• 3rd Class: Favors range and speed of movement.
– MA < 1
• The majority of musculoskeletal systems are in
third-class levers.