A look back in time at the
lever and the spine.
The lever as a tool was
probably used for simple things like prying and moving rocks since
time immemorial.
The lever can be seen as a working tool
as long as 5,000 years ago in Egypt.
The shaduf was used by ancient
Egyptians to help farmers get water from the Nile to dry
land to irrigate their crops. The weight at the far end
provided a "see-saw" mechanism which aided the farmer in lifting
the bucket of water to land.
This
riddle actually depicts the aging process of the human spine.
From the book Anatomy and Human
Movement Structure and Function. Palastanga N, Field D, Soames R, 1989, Goodman
writes that the aging of the spine goes from the C-shape type
of posture to the S-shape and back to C-shape in the elderly.
For
3600 years many questions about postural development of man have
remained a mystery. Why do humans develop the S-shape posture
shown? Why does it make them an efficient biped? As
humans age, why does the spine degenerate into the C-shape?
Spinal
biomechanics seeks to solve these questions.
600 B.C.
 The earliest work in spinal anatomy from Greek mythology appears
to be the Riddle of the Sphinx. "What has one voice,
and is four-footed, two footed and three footed?" Upon giving
the wrong answer that person was eaten by the Sphinx.
The
answer: Man (humans). The infant  has a C-shape spine like quadrupeds and crawls on all fours.
Mature humans gain an S-shape spinal posture and walk upright
on two legs. As humans continue to age, the spine returns
to the more C-shape and man now has to walk bent over with a cane
(the third foot). A major biomechanical significance of
this riddle is how to mature from an infant into upright posture
and once there, avoid degenerating into the hunched over spinal
posture.
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300 B.C. Aristotle
Aristotle appears to elevate
the lever from a simple tool to a machine by identifying its mathematical
properties. There doesn't appear to be any evidence of this
occurring prior to the time of Aristotle. In his Quaestiones
Mechanicae he not only refers to levers, but also deduces
the inverse proportionality of forces and distances. He
wrote "...it appears contrary to reason that a large weight should
be set in motion by a small force; yet a weight that cannot be
moved without the aid of a lever can be moved easily with it."
200 B.C.
Archimedes
One hundred years later, Archimedes comments on the efficacy
of the lever by saying "Give me a fulcrum on which to rest and
I will move the earth!"
(The
engraving is from Mechanics Magazine London, 1824.)
Archimedes
derived the formula:
By the sixteenth century, this formula becomes:
Force on Short Arm x Short Arm = Force on Long Arm x Long Arm
This formula becomes known as the condition of/or principle
of rotational equilibrium.
1114 A.D. Bhaskaracharya Second
In
his work, Siddhanta Shiromani, Second describes the concepts in
trigonometry of sine and cosine. These concepts are essential
to mathematically determining forces used and created in lever
systems. This knowledge will not make its way into western
culture until Britain colonizes India and British mathematicians
discover it.
1500's Leonardo
da Vinci
 da Vinci was the first to
accurately describe the human adult S-shape spinal posture with
its curvatures, articulations and number of vertebrae.
He stated “nature cannot give
the power of movement to animals without mechanical means”.
He appears be the first to apply mechanical logic of
lever systems in the understanding of human movement.
He described a
method by which the spine provided stability to the human body. He wrote “You will first make
the spine of the neck with its tendons like the mast of a ship
with its side-riggings (transverse or spinous processes), this
being without the head. Then make the head with its tendons
(muscles that can provide active force of effort) which (attached
to the side riggings) gives it (the head) its movement on its
fulcrum (spinal joints)."
1500's Giovanni
Batista Benedetti
Benedetti's book De
Mechanicis defines the effective lever arm. For
1,700 years, the amount of force applied on the short or long
arm appeared to be the function of the fixed length of force
application to the fulcrum, Benedetti changed that thought.
On page 143 of De
Mechanicis, (1599), Benedetti demonstrates that
as far as rotation about point O is concerned, the oblique force
C, applied at A could be replaced by a vertical force of the
same magnitude applied at I, where OI has the same length at
OT. OT is defined as the perpendicular distance from the
axis to the line of action of the oblique force C.
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Example A
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Example B
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Above are diagrams noting
Benedetti's real significance of torque.
Example A can be expressed
as example B.
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As Benedetti was working
on torque, European colonization of India begins which makes India's
mathematical technology of sine and cosine available to the rest
of the world.
These two events set the
stage for the two greatest principles in biomechanics of lever
systems:
Equilibrium of Rotation
In Benedetti's example, rotation
could be demonstrated three ways:
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Equilibrium:
Force of E x BO (length) = Force of C x OT (length)
OT is defined as the perpendicular
distance from the axis to the line of action of the force.
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2
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Rotation toward Force of E
Force of E x BO (length) > Force of C x OT
(length)
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3
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Rotation toward Force of C
Force of E x BO (length) < Force of C x OT
(length)
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Benedetti's finding of the
effective lever arm relative to biomechanics is important for two
main reasons:
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In human biological study,
when measuring the amount of effort a muscle must produce at
a joint to provide for Equilibrium of Rotation, the effective
effort arm is determined to be the perpendicular distance form
the line of pull of muscle to the joint (fulcrum).
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Once the force of effort
is determined for Equilibrium of Rotation, the mathematics are
then in place to determine the Equilibrium of Translation.
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The effective lever arm OT is the
perpendicular distance from the pull of the muscle (C) to
the joint (O). In the body the typical term for C is force
of effort.
The effective lever arm SB is the
perpendicular distance from the line of pull (E) back to the
joint (O). In the body the typical term for E is force of
resistance.
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If force in the form
of weight was applied to the body at a point with direction,
it was determined that a muscle had a pull across the joint
with a direction of force. Knowing that, the amount
of force that muscle had to pull to keep the system in equilibrium
or not allow any rotation could be easily applied.
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Equilibrium of Translation
In a lever system, the pull
of E and C would exert a force on O and cause it to translate in
that direction. In the study of spinal biomechanics, what
stops translation or keeps stability in the human spine are the
vertebrae.
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Benedetti's Lever example
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The resultant force,
force D, would cause the movement of the lever system components
at the fulcrum in the direction of force D.
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Force E plus Force C
create a combined force at the fulcrum, force D, called the
resultant.
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Equilibrium of Translation
requires that a force, force F, be in place to push back with
the same amount of force of D but in the opposite direction.
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In spinal biomechanical
study, a pair of vertebrae make up a complete lever system.
The resultant force created by the Equilibrium of Rotation
on the superior vertebra is stabilized by the inferior vertebra
and its components (i.e., joints, muscle) to provide the stabilizing
force necessary for Equilibrium of Translation.
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In the study of biomechanics,
the sequence of events in lever system analysis is first to discover
all the factors relative to Equilibrium of Rotation and then from
those findings, proceed to discover all the factors necessary for
Equilibrium of Translation.
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First determine how
much force E is, then how much force C must be to create Equilibrium
of Rotation.
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Next determine the resultant
force D and how much force F is needed opposite the resultant
force to keep the entire lever system in Equilibrium of Translation.
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The biomechanical historical
significance of these two principles is: The Equilibrium of
Rotation demonstrates the initial structures and effort involved
in human movement. The Equilibrium of Translation demonstrates
all structures and effort involved in the human body as it creates
stability for the movement.
Equilibrium of Rotation
Determines how
much muscle effort is required.
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Equilibrium of Translation
Determines how the joint
and tissue provide stability to stop translation.
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How the resultant force
D interacts with the stabilizing force F at the joint is important
to understand the Equilibrium of Translation.
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Using Benedetti's discovery
of the effective lever arm, the classic structural identification
of the three classes of lever systems (1st, 2nd
and 3rd class) can easily be mathematically proven to
be functionally incorrect. We have, to date, been unable to
find any evidence that this have ever been demonstrated in this
manner.
Benedetti's discovery proves
these incorrect.
However, the structural identification
of levers continues to be taught for the next 400 years.
See our functional
identification of lever systems demonstrating mathematical proof
that the current structural teaching of levers is misleading and
can be clearly and functionally defined by applying Benedetti's
effective lever arms.
1600's Rene Descartes
He published Tractus de
Homine et de Formatione Fœtus in 1675. He stated
“The body is a machine (the lever is a machine) made by the hand
of God.” Descartes argued that all of animal physiology could
be explained by mechanics (levers systems force analysis).
From his Meditations
On First Philosophy, he stated “Archimedes, that he might transport
the entire globe from the place it occupied to another, demanded
only a point that was firm and immovable (fulcrum supporting force
of effort and force of resistance); so, also, I shall be entitled
to entertain the highest expectations, if I am fortunate enough
to discover only one thing that is certain and indubitable.”
1600’s Giovanni Alfonso Borelli
Born in 1608, he is considered
to be the Father of Biomechanics for his contributions to the field.
The American Society of Biomechanics annually awards the scientist
contributing the greatest achievement within the field with it's
highest award, the Borelli Award.
Borelli’s knowledge
of mechanics relative to human movement was restricted to the principles
of levers and, as such, it appears to generate his accurate account
of spinal muscle action. He worked in collaboration with Marcello
Malpighi. Malpighi was a professor of theoretical medicine
at the University of Pisa. Malpighi recalled “What progress
I made in philosophizing stems from Borelli. Borelli states
this about Malpighi “I worked hard dissecting living animals at
his home and observing their parts to satisfy his keen curiosity”.
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Marcello Malpighi
(1628-1694)
Anatomist
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Giovanni Alfonso Borelli (1608-1679)
Mathematician
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 Borelli applied these principles of Equilibrium of Rotation
and Equilibrium of Translation to spinal biomechanical analysis.
In his work De Motu Animalium, Borelli illustrates the first
comprehensive accounts of force of effort provided by posterior
spinal musculature in stabilizing a force of resistance. “If
the spine of a stevedore is bent and supports a load of 120 pounds
carried on the neck, the force exerted by Nature in the intervertebral
disks and in the extensor muscles of the spine is equal to 25,585
pounds. At the fifth lumbar the muscular forces are equal
to 413 pounds and the forces exerted by the disc are equal to 1239
pounds."
Click here to see an example from our courses that
depicts the type of anatomical mathematical lever system analysis
resisting
a posterior force that Borelli would have used.
One of the greatest mechanical
features noted of the body, as was shown by his analysis, was that
the muscles act with short lever arms so the joint transmits a force
that is a magnitude greater than the weight of the load. Borelli
overturned older concepts of muscle action, which was that long
lever arms allowed weak muscles to move heavy objects.
Equilibrium of Rotation
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Archimedes demonstrated
the lever arm for force was bigger than the arm used for resistance.
It took little force or move a large resistance. For
1,800 years it is believed this is apparently the lever system
used by the body to lift and move things.
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Borelli showed the spine
as he set it up, used a lever arm shorter than the resistance
arm and the body actually used more force than the force of
the weight of the object lifted or moved. This was against
common thinking.
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Borelli wrote “Galen also
states that a tendon (muscle working on joint) is like a lever.
He thinks that, consequently, a small force of the animal faculty
(muscle effort) can pull and move heavy weights. This general
opinion and surprisingly, to my knowledge, has been questioned by
nobody. Who indeed would be stupid enough to look for a machine
to move a very light weight with a great force i.e. use a machine
or contrivance not to save forces but rather to spend forces?
This seems strange and against commons sense, I agree, but I can
convincingly demonstrate that this is what happens and given, permission,
that the upholders of the opposite opinion have been mistaken.”
Dr Scherger`s
demonstration of Borelli's Analysis
Borelli's Analysis
Borelli demonstrated a Stevedore
with a weight carried at the neck that each vertebral joint (individual
lever system) in the lower back used an effective effort arm (created
by the position of the muscle relative to the disc or fulcrum) that
was shorter than the effective resistance arm (created by the position
of the weight relative to the disc or fulcrum). This lever
system requires more effort than the weight of resistance which
ran against common thought. Why use an ineffective lever system?
In our courses we demonstrate
many reasons why you should not use the spine in this manner.
1900’s
In their paper
“ The History of Spinal Biomehanics” Abhay Sanan and Setti S. Rengachary. Neurosurgery
39(4): 657-668; discussion 668-669. 1996, they write that
the type of lever systems analysis that Borelli performs disappears
from science until 1935. Then Freidrich Pauwels demonstrates
that forces into a hip joint constitute not only the weight of the
upper trunk on the hip, but also the additional force of effort
required to stabilize the upper trunk mass
Click here
to see an example from our courses that depict the type of anatomical
mathematical lever system
analysis of the hip that Pauwels would have used.
Present History
We find current science is
just beginning to return to the level that Borelli left it.
Examples:
1995:
A paper by K.P. Granata and
W.S. Marras: The Influence of trunk muscle coactivity on dynamic
spinal loads. Spine April 15; 20(8):913-919, 1995,
finds that there must be another greater force at the fulcrum
than just the weight of the trunk and it must come from the cocontraction
of muscle. What they are speculating about is the force of
effort and resultant force that Borelli did his work on 400 years
ago.
2002
The authors of the following
paper suggests there is a need to put the spinal joints into equilibrium.
Serpil Acar, B. Grilli, S.L.: Distributed
Body Weight over the Whole Spine for Improved Inference in Spine
Modelling. Comput Methods Biomech Biomed Engin Feb; 5(1):81-90,
2002. In Borelli's work he demonstrates the spine in equilibrium.
Working to the posterior, as Borelli demonstrated, there are no
cocontractions that would supply active force of effort needed to
put the spine into equilibrium and hence has already performed the
work that these authors suggest needs to be done.
Note!! It
is an extremely difficult anatomical mathematical lever system analysis
to put the spine into equilibrium when resisting a force of resistance
anterior to the spine. This is something neither Borelli nor
anyone we are aware of has ever attempted. We demonstrated
the procedures necessary to do this in our courses.
2003
John Scherger, D.C., applies
the two principals (Equilibrium of Rotation and Equilibrium of Translation)
to study and develop many concepts in human spinal posture.
An example of a major prevailing
concept of thought at this time was that the upright S-shaped posture,
first identified by da Vinci, was the best mechanical (mathematically
efficient) position to exist upright in gravity.
Using the the principle of
Equilibrium of Translation, Scherger demonstrates that the S-shaped
spine upright under gravity is a complex and unstable position due
to shear forces at the fulcrum (vertebral joint). He further
develops mathematical necessity for stabilization for translational
equilibrium.
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Disc and facets are needed for
complex Equilibrium of Translation stabilization.
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The true stability and secret
of the human S-shaped posture is revealed when it performs discretionary
movements like sitting up supine or then upright moving forward
against a resistance.
It is during movement that
shearing is eliminated and the vertebral bodies are able to line
up providing, at each fulcrum (vertebral joint) a simple mechanically
efficient third force required for equilibrium of stabilization.
John Scherger submits his
two courses to the National Strength and Conditioning Association.
These courses underwent a peer review process for over a year before
finally being accepted for continuing education credits.
Course #1
Spinal Fitness in Sports Medicine
Series: Kinesiological Analysis of Human Spinal Development &
Function in Earth's Gravity. Volume1.
Course #2
Spinal Fitness
Series - Spinal Core Stability Training & Treatment: The Restoration
& Preservation of Proper Structure & Function. Volume 2.
Both courses were peer reviewed
by scientists from the National Strength and Conditioning Association.
In our courses we present
many premises related to spinal biomechanics, spinal structure and
function, spinal postural adaptation, spinal training and spinal
treatment. In all of those premises we present mathematical
proofs. In the preface to On Spirals Archimedes
it is stated Archimedes was in the habit of sending statements of
his latest theorems, but without proofs. Apparently some of
those that had received his theorems claimed the results as their
own. He then sent those individuals theorems, some of which
were false “so that those who claim to discover everything, but
produce no proofs of the same, may be confuted as having pretended
to discover the impossible”.
A 1740 engraving of Archimedes planning the defenses
of Syracuse. The Greek writing on his cap is  (Archimedes
the geometer).
In the tradition
of Archimedes we have taken the time and effort necessary in our
courses to provide anatomical mathematical proofs of all theorems.
Click here
to see some examples of our
theorems and the accompanied anatomical mathematical proofs.
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