Biceps

This one is an attempt to write a mathematical function which looks like the biceps muscle. I have plotted the biceps in both relaxed and contracted state. Below, I will walk you through the process of how to go about constructing such a function (But will not mention the actual functions of course). Firstly make a spiral. In the  figure, you can observe the spine of the spiral which is red in color. The parametric equations are given below.

x = r Cos[a t] ; y = r Sin[a t] ; z = t ;           a is a constant which controls the frequency of the turns; r is the radius;

Muscle Fiber - Spiral

You should now make a spindle out of it. The spindle is made by controlling the radius along the spiral’s length. Also you should bend it’s spine. That is shown below.

Muscle Fiber Bent Spine

In the next step, make several of such things and rotate them around an axis. You will now get a biceps model. (A 3-D Image might have given a better view but that cannot be done here)

Wire-frame Models:

1. Relaxed State

Muscle Fiber Relaxed

2. Contracted State

Muscle Fiber Contracted

After testing using wire-framed models, I have plotted the surface. They are shown below.

Surface Models:

1. Relaxed State

Muscle Fibre Surface Relaxed

2. Contracted State

 

Muscle Fibre Surface Contracted

A diagram of the contracted and relaxed biceps muscle can be seen here

When I make models of other muscles, I will certainly post them.

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