Andrew R Stewart 

Separate the various parts of the brake system and look at each's function. Move the lever without the cable attached. Does it move freely? Next is to pull/push the cable through the casing using your hands at each end to hold the inner cable. Does it slide freely? Next is the caliper, squeeze it together and wiggle the arms WRT the backing yoke. Do the arms move freely in only the plane of rotation to the rim or do they also slop fore and aft?


Your description usually means the caliper arms have enough slop in their pivots so as the pads contact the rim and the rim's rotation acts on the pads the arms rock with the rim a bit. This movement of the caliper arms/pads can cause sudden changes to the "power" of the system. But the condition of the cables can also have some of this effect. If a cable casing end has a casing coil not well cut/finished end it can cause a snag on the inner cable. This will make the inner cable move in bits and spirts as it's weavings snag of the casing burr. Andy.