Tuesday, November 10, 2015

Biomechanics of Human Anatomy- Three Classes of Levers

Biomechanics refers to the study of the mechanical principles of living organisms, particularly their movement and structure. In the human body this is known as kinesiology.

Most movements of the musculoskeletal structure  are determined by the three classes of levers.
Levers are classified by the relative positions of the fulcrum and the input and output forces. It is common to call the input force the effort and the output force the load or the resistance. This allows the identification of three classes of levers by the relative locations of the fulcrum, the resistance and the effort:

 Class 1: Fulcrum in the middle: the effort is applied on one side of the fulcrum and the resistance on the other side, for example, a seesaw, a crowbar or a pair of scissors. Mechanical advantage may be greater or less than 1.

Class 2: Resistance in the middle: the effort is applied on one side of the resistance and the fulcrum is located on the other side, for example, a wheelbarrow, a nutcracker, a bottle opener or the brake pedal of a car. Mechanical advantage is always greater than 1.

Class 3: Effort in the middle: the resistance is on one side of the effort and the fulcrum is located on the other side, for example, a pair of tweezers or the human mandible. Mechanical advantage is always less than 1.

Sunday, November 1, 2015

The Canon of Polykleitos

Artistic Anatomy and the Canon of Polykleitos 

The Doryphoros

The art of ancient Greece has inspired and influenced the cultural ethos of western and eastern civilization  through the centuries. The reawakening of the European renaissance during the middle ages was due in a large part to a emerging middle class with the accompanying commerce that encouraged new technologies. One aspect of this phenomena was increased scholarly interest in the unearthing of greek and roman antiquities and manuscripts, and the idea that by reverse engineering the technologies and processes the ancients used in fabricating these works( as well as architectural creations) those scholars might learn the secrets of the ancients and thereby increase their own commercial potentials.
Since that time, scholars have gleaned and reconstructed amazing amounts of data from literally shards of pottery and through cross referencing existent manuscripts and artifacts, have been able to replicate techniques the ancients used. One such example is the Canon of Polykleitos, a so called guide or manual on sculpting and drawing the human body,  by the renowned  fourth century BCE sculptor Polykleitos. Elements of this Canon have come down to us through the commentaries of  Greek and Roman scholarly manuscripts, among them Chrysippus, Galen, Pausanias and Pliny. In addition to these written commentaries we also have the sculptures of the artist himself from which to understand his process.
The renowned Greek sculptor Polykleitos designed a sculptural work as a demonstration of his written treatise, entitled the "Kanon" (or Canon, translated as "measure" or "rule"), exemplifying what he considered to be the perfectly harmonious and balanced proportions of the human body in the sculpted form.
Sometime in the 2nd century CE, the Greek medical writer Galen wrote about the Doryphoros as the perfect visual expression of the Greeks' search for harmony and beauty, which is rendered in the perfectly proportioned sculpted male nude:
Chrysippos holds beauty to consist not in the commensurability or "symmetria" [ie proportions] of the constituent elements [of the body], but in the commensurability of the parts, such as that of finger to finger, and of all the fingers to the palm and wrist, and of those to the forearm, and of the forearm to the upper arm, and in fact, of everything to everything else, just as it is written in the Canon of Polyclitus. For having taught us in that work all the proportions of the body, Polyclitus supported his treatise with a work: he made a statue according to the tenets of his treatise, and called the statue, like the work, the 'Canon'
Polykleitos is known as the best sculptor of men, with the primary subjects of his works being male athletes with idealized body proportions. He was interested with the mathematical proportions of the human form, which led him to write an essay the Kanon, on the proportions of humans. The Doryphoros is an illustration of his writings in Kanon on the symmetria between the body parts. Polykleitos achieved a balance between muscular tensions and relaxation due to the chiastic principle that he relied on. “Scholars agree that Polykleitos based his calculations on a single module, perhaps the terminal section of the little finger, to determine the corresponding measurements of each body part”.
The first datable professional treatise on sculpture was the Canon of Polyclitus, probably written during the third quarter of the fifth century B.C. The Canon was the most renowned ancient treatise on art, and enough information is preserved about it in extant ancient texts to enable us to form some conception of its content. The aim of the Canon, was not simply to explain a statue but also to achieve to kallos, "the beautiful” and to eu (the perfect or the good) in it. The secret of achieving to kallos and to eu lay in the mastery of symmetria, the perfect "commensurability" of all parts of the statue to one another and to the whole.
Pythagoreans also saw reality as having a pattern of oppositions. Aristotle presents the following list of Polyclitus's idea of symmetria and the pursuit of the to kallos and to eu was probably influenced by exposure to the ideas of Pythagoras of Samos ( active in the late sixth century B.C.) and of his followers. Pythagoreans were concerned with finding some underlying pattern in visual phenomenon. Their fascination with number was directly connected to this belief that in number can be found the key to physical bodies but also of abstract qualities like justice. As a demonstration of this principle, they explored musical harmony and noted how the intervals needed to produced harmonic chords on the string of a lyre were expressible in a limited group of integers ( 2:1, 3:2, 4:3,etc.). This led Pythagoras to search for these patterns in other visual phenomenon like the movements of the planets and the relationships of the stars. He believed that these underlying harmonic proportions could be found throughout nature. These patterns demonstrated the Greek conception of nature as cosmos.
Pythagoreans also saw reality as having a pattern of oppositions. Aristotle presents the following list of these binaries:
Aristotle, Metaphysics, I.5.986a22: “Members of this school [the Pythagoreans] say there are ten principles, which they arrange into two columns of cognates, thus:
limited and unlimited
odd and even
one and plurality
right and left
male and female
rest and movement
straight and curved
light and darkness
good and bad
square and oblong 

Modern scholars have seen in Polyclitus's work a similar balance of opposites. Three of these pairs are easily detected in the Dorphoros: right/left, rest/movement, and straight/curved. Scholars have noted what they call the chiastic principle in the composition of the figure of the Doryphoros. The term is derived from the Greek letter chi which is formed by two lines crossing obliquely, but the stroke descending right to left is straight while the other is, like a reversed S, curved at both ends. Thus the upper curve on the left corresponds to a mirror-image curve on the lower right and two straight halves face each other across the sinuous divide. The following illustration imposes the letter chi onto the figure of the Doryphoros:
In the figure note how the two sides of the figure are opposed with the left side as the straight side (straight arm and leg) and the right side is the bent side (bent arm and leg). These oppositions are then balanced with the contrast between active and passive parts of the body: the leg to our left is active (engaged) and is echoed across the figure with the arm supporting the spear. The leg on our right is passive (free leg) and echoed by the left arm that is relaxed or passive. The balancing of the figure is further evident in the chest turned towards our right while the head turns towards our left. The lowered left shoulder is balanced by the lowered right hip while the raised right shoulder is balanced by the raised left hip. The work can thus be seen as a harmony of the opposites much like the cosmos was seen in Pythagorean thought.
Alkmaion of Kroton (c. 500-450) writes about health of the body:
What preserves health is the equality (isonomia) of the powers -wet, dry, hot, cold, sweet, and so forth --whereas the domination (monarchia) of any one of them engenders disease; for the rule of a single contrary is destructive. The active cause of disease is excess of heat or cold, the occasion of it excess or insufficiency of nourishment, the seat of it blood, marrow, or the brain. Disease may also be engendered by external causes such as water, environment, exhaustion, torture, or the like. Health on the other hand is a proportionate (symmetron) mixture of opposites.
Note how this idea is equally applicable to health, politics, and art.

The are a number of excellent papers on Polykleitos's Canon and the idea of Symmetria in Art.
Among them are the Richard Tobin's treatise: "The Canon of Polykleitos":Tobin, Richard. “The Canon of Polykleitos”. American Journal of Archaeology 79.4 (1975): 307–321. Web... and the informative Oneonta online course: Polyclitus's Canon and the Idea of Symmetria available here: https://www.oneonta.edu/faculty/farberas/arth/ARTH209/Doyphoros.html.