Quad Pain

It sounds like your iliotibial band (ITB) is tight (very common on cyclists).
So here's a little anatomy for you: there are 2 main muscles that attach into your ITB; Gluteus Maximus and Tensor Fascia Latae (TFL)

If your riding position changes, i.e. drops are lower then being bent over will transfer more tension onto your legs, your hips and back will also rotate forward and this will increase the tension in Glute Max.

As to what the other guys have said about cleat position and Q factor, a small change to either of these will change the way the ITB pulls below the knee, so if your ITB is tight to start, then a small change like; bar height, reach or change in Q angle etc has the potential to induce quad pain.

Yeah Yeah what Skunk-hk said. I taught him everything he knows!