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Parametrics In The Human Anatomy






The human arm, in function, and as one of the many parts of the human body, expresses the ultimate parametric relationship between its components (muscle and bone). Through each of the arm's parts, we can fined a carefully established relationship to help in its functionality - in this case, motion. Furthermore, The arm presented is in an abstracted manner, transformed from its organic form into a geometrically based construct. The aim of  using the geometry in this study, will help in analyzing the overall relationship of the components, in addition, to the forces of compression and tension on and within the muscles while they are motorizing the arm.

One of the challenges in constructing a digital 'human arm' based on pure mathematical relationships, is the fact that, the human arm includes no exact measurements. There are variations in the bone structure, so the average or the standard, almost does not exist. On the other hand, the structure itself is based on proportions (e.g. golden section). So, to construct the model, a number of steps must proceed the analysis of muscular motion. 

To further understand the process, an overall image of the arm is presented below (image 1). It shows four main components: the Humerus (upper part the arm), the Radius and Ulna (lower part of the arm), the Hand (including the wrist and fingers), and the muscles (on both the upper bone and lower bones of the arm).


Image 1

Constructing the arm, after viewing the main components of the arm (Image 1 above), the first step that follows is the Humerus (upper part of the arm). In  image 2 below, it shows how the basic geometrical form of the construction of the arm - the circle. Each circle is related to another in a mathematical relationship to help maintain the proportions of each single detail of that bone  figure and the other parts of the arm. 


Image 2


Image 3

After constructing the upper part of the bone structure, then the geometrical element is used to construct the guiding lines for the lower parts of the arm (Radius and Ulna) in image 4 below. 


Image 4


Image 5

After the completion of the upper parts of the arm, the following step is to construct the Hand (wrist and fingers). Image 6 below. 


Image 6


Image 7

All the main parts of the arm are at this stage complete. The following is adding muscles to the bone structure, image 8 below. 


Image 8

The muscles added to the bone structure are the main element that will help in explaining the parametric conception depicted in the Sketch. Each muscle is connected from one end of the bone to the other. The muscles will stretch based on the motion of the activity the arm is performing. This change in the muscles will highlight the tension and compression within them to explore the different  shapes based on their parametric relationship. 

First the hand in still motion (image 9 below), will show an equal size of both muscles attached to the lower part of the arm. Image 10, will show the second phase of the ulteration, the upper muscle in compression (pulling the hand upwards) while the lower muscle in tension (because it is being pulled with the hand upwards). Image 11, shows the hand being pulled downwards inverting the entire process of the muscular shape.  


Image 9: Shows the hand in still motion, but in the second (image 9.1), it shows the constraints used to establish the connection between the different parts of the arm while in motion. 


Image 9.1


Image 10: shows the compression in the upper part of the hand and the tension in the lower part of the arm while pulling the hand upwards. 


Image 11: The process is inverted in this image, it shows the lower muscle in compression. 


Image 12: is a test of functionality, is the arm capable of moving the hand 90 degrees - which is impossible to be performed naturally. The image shows a distortion of the muscle, which proves the functionality of the arm in  connection between simulation and reality.   

The animated motion of the arm below (hand movement), shows the muscle behavior to the tension and compression forces as explained above.


As for the following images (13 and 14), they explore the same method  but for the upper part of the arm while pulling the lower part of the arm - the hand is fixed in this motion. 


   Image 13: Below, shows the compression in the muscle facing the lower arm when lifted, and tension in the muscle on the other side.    


Image 14: shows the compression in the outwards muscle while the lower arm is pushed down - the invert process of what is shown in image 13 above.

The animated motion of the arm below (lower arm lifted), shows the muscle behavior to the tension and compression forces as explained above. 


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