21st July 2006 - 01:36 PM
Because you will use a sum only, is not that important that each ball has the same mass that the others.
The main thing you should care about, is make the set of balls represents a human body. Maybe the proportion between fingers and arm, or something like that, is too much. But the body has some general proportions, relative to head`s size, and I would consider them. The mass center shouldn`t be a problem. Itīs about placing the balls symetrically, and force the position of the mass center to be approximately, where actually is. But this alone can lead to overweight on arms and legs, so there is where proportions come to play a role. Other thing you can do is take a ruler, or something graduated, and then take proportions (of mass) of the body parts of any friend. That should be faster than search in internet.
Also, the total weight must be the sum of the balls weight.
Eh...well...It`s about trying to get something similar to a human body, you have to model it, there are some constraint, but not a rule that must be followed from the beginning to the end. It would be great if you manage to get the volume ratios of differents parts, and then use it to approximate a mass distribution. But if you don`t want to do it, maybe somethings that look`s like a human is enough.
Note that you can guide yourself by volume ratios to get mass ratios if you suppose density as constant (that`s ok for what you`re doing).
To get the distances from the reference system to the human model, you can do this:
Make draws at scale (like an architect, maintain a constant ratio between your draw lenghts and areas, and the real model lenght and areas). Make draws of a frontal view, and you would need some other direction depending on how you placed the balls. Then use a rule, and get the distances, then use the scale fator.
Other method is to use a computer software, but it has to allow you to make the human model, and measure the distance from a reference system.
Other way is some analytical way. Can be pretty easy, but also would require some long calculations.
The last way I can think at this moment is that you set distance between balls, and then use some trigonometry to get diagonals an so. But take care, because force the system in this way, can produce bad models.
Then do the sum.
If you placed the axes in some symetriy axes, it`s probable that the matrix will be a diagonal one (all terms but the diagonal are null).
Good luck. Any question, only post