Translation the shaft encoder data

Hi all,

Have a nice day ,

I am designing a robot in real world and i want to plot everything in X,Y (Cartesian) coordinates I just want to use the encoders of wheels to determine the current position of mobile robot and its orientation depending on a specific calculation formula even if that will lead to inaccurate calculations .

Actually , I found out this formula below to compute x, y coordinates from encoder data but I still confused in some sides of this formula

I had a Rover 5 chassis form Dagu with two normal DC motors and two encoders (incremental rotary encoder) per each wheel, how could I translate the pulses of encoders or how to work out the x.y position of the robot based on the shaft encoder data.

I deduced some of values from Rover 5 chassis :

cm = conversion factor that translates encoder pulses into linear wheel displacement Dn = nominal wheel diameter (in mm)

about 20 CmCe = encoder resolution (in pulses per revolution)

Encoder resolution: 1000 state changes per 3 wheel rotationsn = gear ratio of the reduction gear between the motor (where the encoder is attached) and the drive wheel.

Gearbox ratio: 86.8:1In Rover 5 chassis there are 4 small wires with female headers. RED is +5V for the encoder , BLACK is 0V (ground) , WHITE is signal A , YELLOW is signal B . The impotent wires in each encoder are signal A and signal B ,so

How to get values of NL , NR in the formula above from signal A & signal B ?

Is the value of NL is the direct value from wire signal A or signal B ? the same question for NR .

Thanks a lot