Chapter 13:
Equilibrium and
Human Movement
Basic Biomechanics, 4th edition
Susan J. Hall
Objectives
• Define torque, quantify resultant torques, and identify
the factors that affect resultant joint torques
• Identify the mechanical advantages associated with
the different classes of levers and explain the concept
of leverage within the human body
• Solve basic quantitative problems using the equations
of static equilibrium
• Define center of gravity and explain the significance of
center of gravity location in the human body
• Explain how mechanical factors affect the body’s
stability
Equilibrium
Torque
Torque: the rotary effect
of a force about an
axis
• Aka Moment of Force
• Torque is product of
force and force’s
moment arm
• T = Fd
Equilibrium
Torque
• T = Fd
Moment arm: the
perpendicular distance
from force’s line of
action to axis of rotation
Moment arm sometimes
referred to as force arm
A force directed through
axis of rotation (centric)
causes no rotation.
Equilibrium
Torque
• In the body, moment
arm of muscle is the
perpendicular
distance between
muscle's line of pull
and joint center
• Largest moment
arm at an angle of
pull ~900
Equilibrium
Torque
When is the moment arm the greatest?
Equilibrium
Torque
• Force couple is two
equal and opposite
parallel eccentric forces
exerted simultaneously
on opposite sides of the
axis of rotation.
• Torque generated by a
couple is sum of
products of each force
and its moment arm.
Equilibrium
Torque
• Torque (Fd ) is a vector quantity, has
magnitude and direction
– counterclockwise (+) & clockwise (-)
Resultant Joint Torques
• Product of muscle
tension and muscle
moment arm produces
a torque at the joint
crossed by the muscle
– Sum of 3 elbow
flexor torques
• Antagonist create
torque in opposite
direction.
• Mvmt depends on net
torque.
Resultant Joint Torques
• Tension in antagonist
controls velocity &
enhances joint
stability.
• Concentric: when
muscle torque & joint
movement in same
direction.
• Eccentric: when
muscle torque & joint
movement opposite.
Resultant Joint Torques
• Concentric and eccentric
complicated in two joint muscles
• Two joint muscles
– Concentric at one joint
– Eccentric at a second joint
– Can you give an example?
• 3 factors that affect net joint
torques: segment weight, motion
of segment, external forces
• How does speed affect net joint
torques?
Levers
Lever: a rigid barlike body that rotates about an axis
Fulcrum: the point of support, or axis of rotation
First class lever: Force – Axis - Resistance
Second class lever: Axis – Resistance - Force
Third class level: Axis – Force - Resistance
Most levers within the body are third class
First Class Levers
Key Term
• First-class lever: A lever for which the muscle
force and resistive force act on opposite sides
of the fulcrum.
Figure 4.3
O = fulcrum; FM =
muscle force; FR =
resistive force; MM
= moment arm of
the muscle force;
MR = moment arm
of the resistive
force.
Mechanical
advantage = MM
/MR = 5 cm/40 cm =
0.125, which, being
less than 1.0, is a
disadvantage.
The depiction is of a
first-class lever
because muscle
force and resistive
force act on
opposite sides of the
fulcrum.
Second Class Levers
Key Term
• Second-class lever: A lever for which the
muscle force and resistive force act on the
same side of the fulcrum, with the muscle
force acting through a moment arm longer
than that through which the resistive force
acts.
• Due to its mechanical advantage, the
required muscle force is smaller than the
resistive force.
– The slide shows plantar
flexion against resistance
(e.g., a standing heel raise
exercise).
– FM = muscle force; FR =
resistive force; MM = moment
arm of the muscle force; MR
= moment arm of the resistive
force.
– When the body is raised, the
ball of the foot, the point
about which the foot rotates,
is the fulcrum (O).
– Because MM is greater than
MR, FM is less than FR.
Figure 4.4
Third Class Levers
Key Term
• Third-class lever: A lever for which the muscle
force and resistive force act on the same side
of the fulcrum, with the muscle force acting
through a moment arm shorter than that through
which the resistive force acts.
• The mechanical advantage is thus less than 1.0,
so the muscle force has to be greater than the
resistive force to produce torque equal to that
produced by the resistive force.
Figure 4.5
– The slide shows
elbow flexion
against resistance
(e.g., a biceps curl
exercise).
– FM = muscle force;
FR = resistive force;
MM = moment arm
of the muscle force;
MR = moment
arm of the resistive
force.
– Because MM is
much smaller than
MR, FM must be
much greater than
FR.
Functions of Levers
Machines function in four ways:
1. To balance multiple forces.
2. To enhance force in attempt to reduce the
total force needed to overcome a resistance.
3. To enhance range of motion and speed of
movement so that a resistance may be
moved farther or faster.
4. To alter the resulting direction of the applied
force.
R. T. Floyd, Manual of Structural Kinesiology.
Functions of Levers
Lever system can serve one of two purposes
• If moment arm of applied force > moment arm
of resistance, force magnified.
• If resistance arm > force arm, range of
motion magnified.
Susan J. Hall. Basic Biomechanics.
Mechanical advantage = Moment arm (force)
Moment arm (resistance)
Anatomical Levers
• In the human body,
most lever systems
are third class
(MA<1).
• Arrangement
promotes
– Range of motion
– Angular speed
• Forces generated
must be in excess of
the resistance force
Analysis of Anatomical Levers
• Force of muscle group
represented by Force
Vector (Fm).
• The Angle of Pull of
muscle is angle Fm makes
with longitudinal axis of
bone to which it attaches
(axis side).
• Force Vector (Fm) can be
resolved into two
perpendicular
components.
Figure 6-20
Analysis of Anatomical Levers
• Two components of muscular force (Fm )
1. Rotary: part of Fm that acts to rotate the lever.
2. Parallel: part of Fm directed parallel to bone.
• Stabilizing: parallel component directed toward
joint center.
• Dislocating: parallel component directed away
from joint center.
Figure 6-21
Analysis of Anatomical Levers
• As Force Vector (Fm)
approaches 90 to
longitudinal axis of bone,
its rotary component
becomes larger &
dislocating or stabilizing
becomes smaller.
• When angle is 90 to
bone, the rotary force is
100% of muscular force.
Figure 13-14
Equations of Static Equilibrium
Principle of Levers
Static Equilibrium:
• Three conditions for static equilibrium:
1. Fv = 0, sum of vertical forces
2. Fh = 0, sum of horizontal forces
3. T = 0, sum of torques
So, torques on one side (+) = torques on other (-)
Force (+) x moment arm = Force (-) x moment arm
Principle of Levers
Force x Force Arm = Resistance x Resistance Arm
Static Equilibrium
• Second Class Lever
mechanical advantage is
always > 1 because FA >
RA.
• Push up is a second class
lever.
– If you have a long torso,
short legs, A, B or C?
– If you have long legs,
short torso, A, B or C?
Static Equilibrium
• Third class lever
mechanical advantage
always < 1 because FA
always < RA.
• Leg extension is a third
class lever
– If you have long legs
are you A, B, or C?
– If you have short
legs are you A, B or
C?
Equations of Dynamic Equilibrium
Bodies in motion considered to be in state of
dynamic equilibrium.
Dynamic equilibrium: concept indicating a
balance between applied forces and inertial
forces of a body in motion.
• Fx - māx = 0
• Fy - māy = 0
• TG - ī = 0
D’Alembert’s principle: “elevator experience”
Dynamic
Equilibrium
• As elevator accelerates
upward, inertial force in
opposite direction
created by BW force on
plate increases.
• As elevator accelerates
downward, inertial force
decreases BW on plate.
• Body weight remains
constant, inertia varies
reaction force.
Center of Gravity (CG)
Center of Mass
Center of Mass / Center of
Gravity: a unique point around
which body’s mass equally
distributed in all directions.
• The CG of a symmetrical
object of homogeneous
density, is the exact center of
the object
• When mass distribution in
object is not constant, CG
shifts in the direction of greater
mass.
Center of Gravity
• For one-segment object, balance point in 3 different planes
•A body behaves as though all mass concentrated at the CG.
• As a projectile, the body’s CG follows a parabolic trajectory,
regardless of changes of body segment configuration.
Center of Gravity
• Path of CG may be an index of performance
proficiency in several sports.
Locating the Human Body
Center of Gravity
Locating the CG for a body
containing two or more
moveable, interconnected
segments more difficult
than for non-segmented.
Reaction board:
• requires a scale, a
platform & rigid board
with sharp supports on
either end.
Locating the Human Body
Center of Gravity
Segmental method:
• uses data for average
locations of individual
body segments CGs as
related to a percentage of
segment length
Appendix D. Hall, p. 527.
SEGMENT
MALES
FEMALES
Head/neck
55.0
55.0
Trunk
63.0
56.9
Upper arm
43.6
45.8
Forearm
43.0
43.4
Hand
46.8
46.8
Thigh
43.3
42.8
Lower leg
43.4
41.9
Foot
50.0
50.0
Expressed in percentages of segment
length; measured from proximal end.
Stability and Balance
Balance: the ability to control equilibrium, static
or dynamic.
To achieve balance, hence equilibrium, need
to maximize stability.
Stability and Balance
Stability: resistance to a change in the body’s
acceleration; resistance to disturbance in
body’s equilibrium (static or dynamic).
– Examples when stability desirable?
– Examples when minimum stability desired?
Stability and Balance
Factors that affect balance
– Mass: greater mass greater balance
– Friction
– Height of center of gravity: lower greater balance
– Base of support: larger greater balance
– Base of support related to CG
Summary
• A muscle develops tension and produces
torque at the joint that it crosses.
• Muscle and bones function as levers.
• The angle of muscle pull on a bone produces
rotary and parallel components of force
• When a body is motionless, it is in static
equilibrium.
• The behavior of a body is greatly influenced
by location of center of gravity.
• Stability is resistance to disruption of
equilibrium