i believe that a dogbox is a gearbox with straight cut gears, not helical like a normal gearbox...they are used for racing
Actually, the "dog" in dogbox does not refer to the gears at all, but the the shifting mechanism. You can have a dogbox without straight cut gears. And you you can have a straight cut gearbox with synchronizers.
Production car gearboxes have helical cut gears to keep them quiet. The constant mesh and thrust of the helical cut design keeps the gears quiet but they generally not as strong as straight cut gears and do not transmit torque as efficiently. Straight cut teeth are ususally bigger but there is backlash and the teeth knocking together produce the distinctive gear whine. Gear profile has a lot to do with how much noise there is, some straight cut gearsets are not that noisy at all.
Production gearboxes also use synchronizers to provide smooth, quiet shifting. The synchro's job is to "grab" the gear when you are shifting and match it to the same speed as the driven shaft to provide a smooth silent shift with no grinding. This happens as you move the lever into the gate for that particular gear.
The trouble with synchros is they slow down the shifting process and they have little teeth which aren't so strong compared to the mysterious "dogs". The engaging teeth on the gears are equally small so you could potentially strip all the little synchro engaging teeth (you can also call them dog teeth) off the gear and have no more drive in that gear even though all the gear teeth are in perfect condition!
A dogshift box does without the synchronizers. Instead you have 6 or 8 big dog "teeth" on the gear. On the shift slider you may have a corresponding number of "slots" that the dogs fit into. The are other designs as well. When you shift since there is no synchro to make the gear speeds match you have to match revs with a blip of the throttle for a smooth shift. But that's not necessarily accurate, really, because you can crash it right in. That's why they are also known as "crashboxes". The clutch is not required when shifting. When accelerating a quick, partial lift of the throttle will do. When downshifting a blip of the throttle to match revs will ensure a smooth shift. A dogbox will shift as fast as you can move the gear lever! No waiting for synchros. When you try to shift slowly is when you are most likely to grind a dogbox! When driving around on the street I will usually use the clutch but in competition the clutch is only for starts. One advantage is being able to downshift in a corner without the clutch while left foot braking.
Also, the dog mechanisms don't take up as much room as synchros so a wider gear can be fitted.
The dogs will allow you to slam through the gears without using the clutch. One thing of note that I don't think has been mentioned, however, is that just like synchros the dogs do wear. The less you intentionally abuse the tranny the longer they will last. Dog 'boxes are merely stronger, not invincible.
that the only think i can say..correct me if im wrong...anyone can add..