Chapter 4 (Movement Science)
 Newton’s laws of motion help to explain the relationship between forces and
their effect of individual joints, as well as on the entire body.
 Biomechanics is a study of the forces applied to the outside and inside of the
body, and the body’s reaction to these forces.
 Newton’s Laws of Motion: law of inertia, law of acceleration, and law of
action-reaction.
 1st law: a body remains at rest or at a constant linear velocity expect when
compelled by an external force to change states. This means that a force is
required to start, stop, slow down, speed up, or alter the direction of linear
motion. The law also states that a body remains at rest or at a constant
angular velocity around an axis of rotation unless compelled by an external
torque to change its state. This means that a torque is required to start, stop,
slow down, speed up, or alter the direction of rotational motion.
 Static equilibrium: linear and rotational velocities are zero.
 Dynamic equilibrium: linear and rotational velocities are not 0 but are
constant (no acceleration).
 Inertia: the amount of energy required to alter the velocity of a body. The
inertia of a body is directly proportional to its mass.
 COM: point around which an object’s mass is evenly distributed (equal to the
COG). COM changes as a person changes their body position.
 Each body segment also has a COM. This point stays fixed. The COM of the
entire lower extremity changes with a change is spatial configuration.
 COG: point about which the effects of gravity are completely balance.
 Moment of inertia: indicates a body’s resistance to a change in angular
velocity. Unlike its linear counterpart, moment of inertia depends not only on
an object’s mass but also on the distribution of its mass with respect to an
axis of rotation (indicated by the letter I). The ability to actively change an
entire limb’s moment of inertia can profoundly affect the muscle forces and
joint torques necessary for movement (an extend leg has a larger moment of
inertia than a flexed leg).
 Reducing the body’s moment of inertia results in an increased angular
velocity.
 2nd law: linear acceleration of a body is directly proportional t the force
causing it, take place in the same direction in which the force actions and is
inversely proportional to the mass of the body. F (net force)= m*a (this can
be viewed as a cause and effect relationship, where the F is the cause). The
angular counterpart states that a torque which produces an angular
acceleration of a body around an axis of rotation. Angular acceleration of a
body is directly proportional to the torque causing it, takes place in the same
rotary direction in which the torque was applied, and is inversely
proportional to the moment of inertia of the body. T (net torque/moment)=I*
(angular acceleration).
 The primary torque producers are muscles. A contracting biceps muscle
produces a net internal flexion torque at the elbow.
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F*t (impulse)=m*v (momentum). This shows that an application of a linear
impulse leads to a change in linear momentum. Momentum is the quantity of
motion (generally represented by the letter p). An impulse is a force applied
over a period of time. The linear momentum of an object is changed by the
application of a force over a given time. Impulse and momentum are vector
quantities.
Increasing the duration of impact (prolonged eccentric activation) minimizes
the peak external force of the impact.
Impulse-momentum also has an angular counterpart. Application of an
angular impulse (torque*time) leads to a change in angular momentum
(moment of inertia*change in angular velocity).
Newton’s 2nd law can also be restated to provide a work-energy relationship.
This can be used to study human movement by analyzing the extent to which
work causes a change in an object’s energy.
Work occurs when a force or torque operates over a linear or angular
displacement. Work is a produce of the magnitude of force applied against an
object and the linear displacement of the object in the direction of the applied
force. If no movement occurs in the direction of the applied force, no
mechanical work is done. Work is expressed in joules (J).
Energy exists in two forms: potential and kinetic. Potential energy is a
function of the height of an object’s COM within a gravitational field. Kinetic
energy is influenced by the object’s mass and velocity, regardless of the
influence of gravity. An object’s angular kinetic energy is related to its
moment of inertia and it angular velocity (there is no angular correlation to
potential energy). PE=mgh. KE= 1/2mv2.
Energy is the currency for performing work. Energy is the capacity to do
work. To do 100 J of work, you must expend 100 J of energy. A change in KE
of a object is equal to the work done on that object.
The work-energy relationship describes the change in kinetic energy caused
by a force applied over a given displacement. When a quick change in kinetic
energy is required, a very large brake force is applied over a short
displacement. Work and displacement are vector quantities.
The work-energy relationship does not take into account the time over which
the forces or torques are applied. The rate of performing work is defined as
power. The ability of the muscles to generate power is critical to the success
of movement. Average power is work divided by time. Angular power is often
used as a clinical measure of muscle performance. The mechanical power
produced by the quadriceps is equal to the net internal torque produced by
the muscles times the average angular velocity of knee extension.
Power is often used to designate the net transfer of energy between active
muscles and external loads.
Power is the rate of doing work or using energy.
Positive power reflects the rate of work done by concentrically active
muscles against an external load and negative power reflects the rate of work
done by the external load against an eccentrically active muscles.
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3rd law: for every action there is an opposite and equal reaction. This law
implies that every effect one body exerts on another is counteracted by an
effect that the second body exerts on the first. An example of this law is the
reaction force provided by the surface on which one is walking or standing.
The foot produces a force on the ground and the ground exerts a force
(ground reaction force) on the foot that is equal and opposite. The GRF
changes in magnitude, direction, and point of application on the foot
throughout the stand period of gait. The third law has an angular equivalent:
during an isometric exercise, the internal and external torques are equal and
in opposite rotary directions.
Anthropometry: the measurement of certain physical design features of the
human body, such as length, mass, weight, volume, density, center of gravity,
and moment of inertia. Knowledge of these parameters is essential to
conducting kinematic and kinetic analyses for both normal and pathological
movement. Mass and moment of inertia of individuals limb segments are
needed to determine the inertial properties that muscles must overcome to
generate movement (this is relevant to the table that he presented in class
with the location of the COM of each limb from the proximal joint).
The analysis of movement requires that all forces that act on an object be
taken into account. A free-body diagram is used to represent the interaction
between a body and its environment.
Joint reaction force: this force includes joint contact forces as well as the net
effect of all other forces transmitted from one segment to another. Joint
reaction forces are caused in reaction to other forces, such as those produced
by active muscles and gravity. The joint reaction force is usually in the
opposite direction of the muscle force.
Clinically, reducing joint reaction forces is often a major focus in treatment
programs designed to lessen pain and prevent further joint degeneration in
persons with arthritis. This is done by changes in the magnitude of muscle
activity and their activation patterns or through a reduction in weight
transmitted through a joint.
In a free body diagram, the direction of the muscle force is drawn to
correspond to the line of muscle pull and in a direction to generate toque that
opposes the net torque produced by the external force.
Adding forces together uses a process call vector composition. The process of
decomposing a single force into its components is called vector resolution.
Two or more forces are collinear if they share a common line of force. Vector
composition allows several collinear forces to be combined graphically as a
single resultant force (tip-to-tail method).
Forces acting on the body may be coplanar, but they might not always be
collinear.
In may clinical situations knowledge of the effect of the individual
components that produce the resultant force may be more relevant to
understanding the impact of these forces on motion and joint loading.
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The muscle force that is depicted parallel to the forearm compresses and
stabilizes the joint, or in some cases distracts the two joint surfaces (this
component does not produce a torque at the axis of rotation b/c it has no
moment arm). A joint reaction force opposes this parallel force. The Y
component acts perpendicularly to the long axis and it causes rotation at the
axis of rotation.
In a condition of equilibrium, the external torque acts relative to the joints
axis of rotation in an opposite rotary direction as the net internal torque.
The angular position of a joint alters the angle-of-insertion of the muscle.
This explains why people have different strengths in certain parts of a joint’s
ROM.
The external torque around a joint is greatest when the resultant external
force vector intersects the bone or body segment at a right angle.
The associated force and moment arm for any given torque (internal or
external) must intersect each other at a 90-degree angle.
These approaches can be employed to asses 1) the effect of force at an
instant in time (force-acceleration relationship), 2) the effect of a force
applied over an interval of time (impulse-momentum relationship), 3) the
application of force that causes an object to move through some distance
(work-energy relationship).
The assumption that the joint reaction force is in the opposite direction of the
muscle forces holds true for situations in when the mechanical advantage is
less than one (the muscle forces are greater than the external resistance
forces).
Most muscles in the body generate force many times greater than the
externally applied force.
When linear or angular acceleration occurs, a dynamic analysis must be
undertaken.
Kinematic measurement systems:
o Electrogoniometer: measures joint angular rotation during
movement. The axis of rotation of the goniometer is aligned with the
axis of rotation of the joint. This is limited to measuring ROM in one
plane.
o Accelerometer: this device measures acceleration of a object to which
it is attached-either an individual segment or the whole body.
o Imaging Techniques: this is the most widely used method for
collecting data on human motion.
 Photography: displacement data is converted into velocity and
acceleration data.
 Digital videography: reflective markers are used to indicate
anatomic locations for determination of joint angular
displacement.
o Electromagnetic Tracking Devices: measure 6 degrees of freedom,
providing position and orientation data during both static and
dynamic activities.
o Mechanical Devices: measure the applied force by the amount of
strain of deformable material.
o Transducers: an applied force deforms the transducer, resulting in a
change in the voltage in a known manner. One of the most common
known transducers is a force plate (measures the ground reaction
force during waling and running).
o Electromechanical Devices: most common is an isokinetic
dynamometer. This device maintains a constant angular velocity of
the tested limb while measuring the external torque applied to resist
the subject’s produced internal torque.