Well, if you fix the input and rotate the output, you will get one figure for angular backlash, say Bo, and if you fix the output and rotate the input, you will get another figure, say Bi. For a fully back driveable box, if the overall speed ratio of the box is Ni/No, where Ni is the input speed and No the output speed, then the backlash figures are related by :
Bi/Bo = Ni/No
Which figure you are interested in depends entirely on how the gearbox is to be used. It is often easier to measure whichever of the two figures is the larger, but it all depends on the circumstances - ease of locking for example. The relationship also applies to a single non backdriveable worm-wormwheel combination.
In the case of a drive containing a worm and some other gears however, such as you have here, it may or may not be backdriveable. If it is backdriveable, the equation given above should still apply, but if it is not backdriveable, you will obviously only be able to measure the worm part of the overall backlash from the non-backdriveable side. This partial measurement, however, is quite likely to be one that you need to be particularly interested in, especially if the wormwheel is used as a positioning device. So what you were told to do was most probably correct. But the backlash on the spiral bevel may be important too, depending on the circumstances. To find that, you would have to carry out the backlash measurement on the input shaft, and then subtract out the worm backlash, taking into account the gear ratio formula given above.
