Hi,
I have run into a bit of a problem that i hope you can help me with.
I am building a controller that can change the speed/direction of a cassette deck very dynamically. As in very fast direction changes and speed changes.
My original plan was to use the capstan, please see the link below if unfamiliar with the cassette deck mechanism.
http://www.cse.iitk.ac.in/~amit/cour.../contents.html
I thought this would be the best solution. But the mechanism is a combination of clutches, springs, and spools to keep the tension in the tape and speed constant, so a capstan that has a changing speed and direction will not work, it will eat the tape or the clutch will disengage, losing accuracy in following the input signal.
i thought about making the spool rotate at the same speed as the capstan, but this will not work either, as the radius of the tape on the spools changes, so this will snap the tape eventually and i also need to be able to have fixed speed playback when needed.
So now i have decided to scrap the capstan completely and use two stepper motors in the spools (which comes with its own set of problems!) to control tape speed through the head. So this brings me to my mathematical problem that i cant resolve.
I will have a tempo lock function, which will require the tape to pass through the head at constant rate. Due to the fact that the reels will be controlling the speed, the motors will need to increase/decrease speed at a rate which is proportional to the increase/decrease in radius of the tape on the reel.
I have tried to work this out, but my problem is that nothing remains constant. Even the rate of the increase in radius of the tape on the reel decreases the more tape that is on the reel! (i think)
So to pose the question directly:
What is the rate of change a motor on the take up spool would have to maintain to ensure tape speed remains constant over the playback head.
I am aware that this probably isnt a simple linear value, but more likely to be the function of a curve (which means it will be unworkable probably). I may find another way to do it, but now that i have tried to work it out the question has been bothering me. Perhaps i am misunderstanding something and over complicating the problem.
P.S. I wasnt sure whether to post this here or in the maths section.[/url]
EDIT: I will supply numbers when i get the chance, such as radius of reels, thickness of tape etc