Could one build a device which accepts an led, then regardless of led , the arduino begins to ramp up voltage measuring the current draw, the outcome is the forward voltage drop.
In my head i see the arduino incrementing voltage until we hit the knee of the diode as current starts to really flow, the arduino detects the knee and stops the led from burning out, then it spits out the safe forward voltage, along with optimal resistor value to drive the led...
I did something like this on a bread board to test the current-voltage relationship of some LEDs.
It's fairly simple. I made a little schematic
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R1 and C1 are configured as a low pass filter, smoothing the PWM output from the arduino. The higher values of R1 and C1, the less voltage ripple in the output, but the slower reaction to change in putput. I suggest you use a timer1 or timer2 pwm output and set the frequency to 31 kHz. See the pwm cheat sheet page. The high frequency means you can use fairly small filtering components and still have small voltage ripple but fast reaction time.
Q1 is a NPN transistor, configured as emitter follower. The output at the emitter will be approx the base voltage minus 0.6 V.
R2 is a shunt resistor used to monitor the current.
Now you just insert an LED or other 2 lead electronic component you want to analyze and slowly ramp up the PWM while monitoring the current and voltage at out1 and out2. When you hit some current limit you stop, or alternativley you write an algorithm to detect the knee.