Why can't clutches be placed between the transmission and the differential?

Is there a reason why clutches are in front of a transmission and not behind?

If there was no clutch seperating the transmission and the engine, then the gears would get grinded every time they were shifted. Or so I assume.

You are absolutely correct. The reason there is a clutch is basically to be able to shift gears, and in order to do that (on a working engine) transmission has to be disconnected from the engine. hence the placement.

What about a sequential? (Is that even the right name?) Those trannies are manual but don't use a stick or a clutch, you just pull a lever or something equavilent, to change gears. They don't use torque converters, right? If so, then how do they change gears?

Sequential is not quite the same as semi-automatic. What you are talking about is the latter. Those have very complicated electronically controlled hydrolic systems that do disengage the clutch and change gears in a matter of fractions of a second. Apart from F1 and Rally, the most successful versions are found on Ferraris and latest BMW models. Basically there still is a clutch, but it is operated automatically. I think the car might even double-clutch on downshifts. Can be wrong here. And another good thing is that with newer semi-automatic gearshift systems you don't even need to take your foot off the gas - the engine power is auomatically cut off for the split second that the gearchange takes place. As for just sequential gearboxes, if they are not semi-automatic, they still require a manual (errrm ... I mean normal - operated by foot :) ) clutch. E.g. Quaife makes sequential gearboxes that can be adapted to any car.

I don't see how the location of the clutch would effect shifting. As long as one of the shafts can spin freely, the synchros should work fine. One problem I see is the clutch would need to be much stronger, since transmissions multiply torque. Also you would still need the normal flywheel on the engine, plus another spinning disk for the clutch to grip.

And not all sequential trannies need to have the clutch disengaged to shift.

Ok, I understand now. Thanks

some differentals have clutches in them to lock both wheels together to gain traction.

Thought i would add that.