I've just gotten back into karate about a month ago after a long long break, and I'm finding it hard to cope with kicks to the legs (with or without pads), especially the quads. Being a cyclist I have fairly well developed quads but even one hit through a pad can be excruciating. What can I do to condition my legs to such hits and get a bit more resistant to the pain?
My Kung Fu teachers regularly address this in sparring classes, because in contests, those kicks are a common tactic to wear down an opponent with a good cover. Most of the time, it's to risky to cover the legs (because it makes you expose more vulnerable spots) or evade the blow, so it's good if you can just take it.
We are taught to briefly tighten the muscles as much as we can at the moment of impact. Timing is essential. You want the contraction to be as short as possible. If you keep the muscles tight for too long, you lose the agility for a counter and waste energy. We practice this with one person standing in the middle and three or for others repeatedly kicking spots on that person's legs, not necessarily hard, since it's about the timing.
Shins are different, because there are no muscles on them. We sit down and slowly roll a log up and down the shins for some minutes, very regularly. The log should have some weight, so as to exert enough pressure, and, if you use one straight out of the woods, it's good if there aren't too many knobs on it, those hurt. If the log is very light, you can kneel on the log and move back and forth, using your body weight, but this might be too much pressure, at least in the beginning. This practice gradually lowers the sensitivity to pressure.
As a side note, if the shins are well prepared, and your legwork is fast enough, you can quickly pull up your knee and block a blow to the leg with your shin. This can be very effective, but you need to be fast, if you're too slow, you put your knee at risk during the upward movement. Also, as with all blocks, you want to be ready for a counter very quickly, so you want the leg back on the floor soon.