Biomechanics History ( Biyomekanik Tarihi )

Biomechanics History

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!"

This image has been resized.Click to view original image

(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.

Example A

Example B

Above are diagrams noting Benedetti's real significance of torque.

Example A can be expressed as example B.

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
• Equilibrium of Translation

Equilibrium of Rotation

In Benedetti's example, rotation could be demonstrated three ways:

1

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.

2

Rotation toward Force of E

Force of E x BO (length) > Force of C x OT (length)
3

Rotation toward Force of C

Force of E x BO (length) < Force of C x OT (length)

Benedetti's finding of the effective lever arm relative to biomechanics is important for two main reasons:

1. 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).
2. Once the force of effort is determined for Equilibrium of Rotation, the mathematics are then in place to determine the Equilibrium of Translation.

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.

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.

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.

Benedetti's Lever example

The resultant force, force D, would cause the movement of the lever system components at the fulcrum in the direction of force D.

Force E plus Force C create a combined force at the fulcrum, force D, called the resultant.

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.

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.

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.

First determine how much force E is, then how much force C must be to create Equilibrium of Rotation.

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.

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.

Equilibrium of Translation

Determines how the joint and tissue provide stability to stop translation.

How the resultant force D interacts with the stabilizing force F at the joint is important to understand the Equilibrium of Translation.

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.