Re: Need advice on mowing a slope
...Considering your statement how do you explain independent brakes (brake assisted steering) while turning? I have used them many times but never thought about them effecting the front wheels. My understanding of tractor brakes is they only brake at the rear axle.
When you step on one rear brake only, the rear axle differential allows the opposite wheel to turn and be powered by the drivetrain in a normal manner except it is turning at a higher speed due to the differential action. The drivetrain and transmission see no difference to normal non-braked operation. When you stop both rear wheels, the differential cannot work and thus the drivetrain through the transmisson and to the engine is locked. If you are driving a gear tractor with the clutch engaged, you'll stall/kill the engine unless you press on the clutch to release the engine and allow free rotation. This will happen in a 4WD tractor or a 2WD tractor.
Because the front 4WD is driven off the transmission's final drive through the transfer gearbox. It doesn't feel the effect of one rear wheel locked, but when both rears are locked and the transmission is locked, the driveshaft to the front wheels is locked and cannot rotate. Then, the front axle's differential comes into play. The front differential will stop the wheel with the least rolling friction and allow the other to turn through normal differential action. Thus, with both rears locked and the tractor in 4WD, one of the front wheels is locked so that only one front wheel is turning. If you have a front axle differential that locks up or has limited slip, then all four wheels will stop. This is the effect of 4-wheel brakes through the 4WD driveline.
On HST tractors, the secondary part of the transmission is a gear transmission. That's the part that allows you to change drive ranges (Hi-Med-Lo) or some tractors only have two ranges instead of three. In front of the gear transmission is the HST transmission. Therefore, if the gear portion is locked due to both rear wheel brakes being locked, the HST transmission will go into pressure bypass and the engine can still operate, but the torque is not transmitted to the rear transmission. The HST relief valve essentially works as a torque "fuse" to allow power to bypass the rear transmission and drivetrain.
So to summarize, you can do differential steering with the brakes on any kind of tractor because the rear differential will allow the transmission to work normally for one wheel. However, once you lock both rear wheels, the transmission is fully locked and the drivetrain will stop all the way up to the engine unless the clutch is depressed or the HST transmission goes into relief bypass.