HENON fabien wrote:

> I know that there must be several ways to do it.
> 
> My question is simple. How would you do to make an animation of links of a
> bicyle chain running on its chainwheel and cogs, (keeping in mind that the
> each link has to be rotated, then translated to its proper place).
> 


You have to separate the chain in portion:
  - tight parts
  - slack parts
  - constrained parts
It is simpler if all your measurement use a link as the unit.

Tight parts are the simplest: it's a straight line and it transmit the 
power.
A Tight part is connected to a constrained part at each end, always.
The length of a tight part is an entire number of link.

A slack part is the hanging part which allow the length of the chain to 
be an entire number of link, as well as give it the needed elasticity.
The form of a slack part is a catenary (chainette), and you need a 
gravity vector.
You can use the slack part to adjust the offset of the link on the other 
parts as well as the number of links. (But having more than one slack 
part introduce a non-deterministic issue). No power is transmitted on a 
slack part.
A slack part is connected to a constrained part at each end, always.

Constrained parts are the parts where the chain is in contact with the 
gear (whatever the form of the gear!!!).
Assuming a circular gear with no offset (a well centered gear, the one 
you want on your classical bicycle), you can use the tangency of circles 
to fix the line of a tight part, that give you the angle from the center 
where the constrained part begin.
You then add more links around the gear until you reaches the angle of 
exit (if the next part is also tight or constrained).

The hard part of that process is the two borders of the slack part moves 
with the offset of the link (but on a bicycle worth it, you have the 
tending mechanism which allow you to get the slack part straight (and 
not the low part between the tender mechanism and the drive, but shorter 
right after the sliding-mesh gear), so it's not really difficult for a 
bicycle.


> Could it be done with an include file ?


Yes.

The simplest way is probably to generate a spline for the path, and use the existing
facility to

distribute regular point along that path (that should be fine: no link 

the slack part so as to have a perfect chain, if you have a One-speed 
children bicyle,
or previously adjust the path length with the position of the tending 
gears for a fixed length chain. (that's a little of math, but only with 
circle and straight lines, no catenary here!).
You might want to perform the distribution for each offset of an initial 
link.

At worst, your bicycle is a 'top-racing' one, with an ellipsoid drive, 
and you will have fun adjusting the tending gears according to the 
position of the drive (but again, no catenary, simple math !(ok, with an 
ellipsoid :-P)

The real headache comes when you use 'strange' gears (ellipsoid, 
irregular, heart shaped, ...) and there is no mobile gear to keep the 
parts straight...

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