# Calculate the resolution in linear travel of the tape

1. Apr 22, 2007

### polyperson

Nobody replying, so I’ve reframed the question

A 24V DC motor has an optical encoder with 500 divisions which outputs the pulse frequency to an electronic counter/timer. The motor has a flat pulley of 31.827mm diameter used as a tape drive.

(a) Calculate the resolution in linear travel of the tape

(b) Determine the velocity of the tape if the motor is supplied with 24V

(c) To what accuracy can the velocity be determined?

Right (a) is simple:

Resolution = smallest distance that can be measured = linear travel of the tape per revolution divided by the number of pulses per revolution

Circumference = pi x 31.827 = 100mm

Therefore, Resolution = 100 ÷ 500 = 0.2mm per pulse

For (b) I had to use the Motor speed vs. voltage graph that we had to create as part of the experiment. I ended up with a value of 1608.56 rev/min which is 28.009 rev/s, so:

28.009 rev/sec x 100e-3m = 2.8009 m/s

But on (c) I am stuck. It's not very clear what he is asking. I think he means what is the smallest deviation from 2.8009 m/s that the encoder can measure.

Is the answer along the lines of:

If the counter/timer can't count in fractions of 1Hz (and that's merely an assumption) then surely it couldn't measure 28.009 rev/sec....so you need to find the number of rev/sec closest to 28.009 that it can measure and double it to give a tolerance band?

Last edited: Apr 22, 2007
2. Apr 22, 2007

Ping upwards