using a predefined pot for example you get 10kohm potentiometer and you want it to control the duty cycle from 0 to 100% you need it to vary from 1/3vcc to 2/3vcc... but for example if you wanted it to go from 25% to 95% how to know what resistors to use? simple... ohms law...

lets take the first example... if you get a 10kohm resistor is easy to see that if you add another two 10kohm resistors in either side it connecting to the vcc will already vary from 1/3 to 2/3 of vcc...

but why is that? well resistors in series share the same current... so basically what i´msaying is that finding the voltage variation you desire you simply calculate the current and from the current and anyother voltage you want you calculate for the resistors....

lets use an easy value for example if vcc is 5v 1/3 of 5v is 1,666v 1,666v/by 10kohm = 166microamps;;; (100% range)

if i wanted to vary from 25% to 95% ex than i need to recalculate the voltage variance i need

now for example i want in my circuit that it goes from 2v up to 3,33 volts to go from 25% to 100% since i work with vcc 5v

to find the 25% i subtracted the min voltage for 0% duty from the voltage for half vcc where is 50% duty cycle... than divided the result by two and than sum with 1/3 vcc again... if vcc is 5v 25% will be than for 555 timer 2.008v

so i actually now wants to vary 1,33v instead of 1/3 of vcc so 133micro amps

hope it helps...

another thing is to calculate the frequency of the 555 use the formula f=0,7185/R*C you can calculate the factor if you measure the frequency to get the best aproximation for your chip or board.. sometimes it vary a little... factor=F*R*C