... just curious. What sort of angular resolution do you require?
If you can abide by 5° increments, attach a one inch diameter rope to the end of the arm, and then place contrasting marking tape at appropriate intervals, using a protractor to establish corresponding angles. The marking tape could be detected by a photo diode/LED arrangement, and then connected to a simple counter. The marked rope is routed through a freewheeling pulley, positioned in the vicinity of the winch to allow its movement ... as the arm rotated.
As the arm rotates from zero to its final position, the counter would register each time a marker passed by the photo-pick-up device.
The 1.5 meter arm length would allow something like two meters of length that would require markers ... of some sort.:
S = θ *R = (∏/2) * R = 1.57 * 1.5 m = 2.35 m
It may be possible to place markers on the rope at intervals corresponding to 1° of rotation, if you require a higher resolution.
The one drawback of this scheme is that you will have to have a means of signalling the digital counter as to whether you are raising or lowering the arm. If you are raising the arm, the count should increment ... if lowering it should decrement.
The benefit of this scheme is that the counting output signal is the input to a simple two digit counter with an appropriated readout. A μ-processor is not required. True ... some innovation would be required in marking the measure rope, and designing a reliable, long-lasting mark reader.
... reviewing the original problem description, it sounds like you could attach the length of marked rope to the arm at the same point as the winch cable. When the lift cable is released, the marker rope would just swing free. ... If the winch cable could be marked at the appropriate increments, you might be able to use that instead of a separate rope.
... Can you provide any other useful information about the mechanism, or its purpose? The constraining assumption made in this suggestion is that the winch attachment point is at the extreme end of the arm, not at its rotational axis.