Design of belt drive for multiple pulleys.

Maybe the title says it all. so far i have only learnt how to design belts connecting two pulleys, a driver(sitting on a motor, engine or prime mover), and a driven(sitting on a driven machine).

Now what would the design procedure be for a system involving more than one driven machinery. The best example is the I.C engine of automobiles, where the crankshaft drives the compressor, alternator, coolant pump, etc, via a belt drive.

And also the above system includes an idler pulley, whose function is to maintain belt tension. should this be treated specially.

Lets assume the data which we have is the speed and torque of prime mover and the speed of the machines.

Come on guys, no replies here ?

Not quite my country. Still, let us try. Firstly, belt drive is a friction drive. We can calculate the minimum contact area of drive pulley with the belt to transfer the maximum torque of the prime mover. From this we can arrive at the diameter of the smallest pulley that will give this area. (We have to remember that only a portion of the circumference is in contact)
From this and the RPM we get a peripheral speed of the belt. Using this we can calculate the diameters of the various other pulleys that come on this belt doing the reverse of what we did so far. That is from the torque and speed required for each load calculate the area of contact and come to a diameter of each driven pulley. Distribute these strategically adding idle pulleys as needed to ensure proper contact.

NOTE: The peripheral speed of the belt is same everywhere. Hence each load pulley has to be separately calculated.

NO great maths involved. Probably simple arithmetic and a thinking cap.