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The transfer case is bolted to the gearbox and its function is to take drive from the output of the gearbox and transfer it through 90 degrees to give rotation of the propshaft. It's a fairly simple mechanical device which consists of a crownwheel & pinion in the opposite arrangement to that of a normal rear type differential.

To get drive from the gearbox the front differential is splined both internally (for the driveshaft) as well as externally to take a drive collar. This drive collar engages with the carrier for the crownwheel in the transfer case and gives it rotational drive. The RHS driveshaft actually passes directly through the transfer case carrier and into the gearbox.

<transfer case>

If you take off the cover you can remove the crownwheel carrier revealing the pinion. As mentioned it's a pretty simple piece. In this pic you can see the outer splined section which takes the drive collar.

On the gearbox side your diff has both a set of internal splines for the driveshaft, and an external set for the drive collar.

Standard open diff centre removed from gearbox. Note the extra length and external splined section. Note this diff is from an auto box but the principle is the same. Drive collar Driveshaft placed through crownwheel carrier As it all fits when bolted together

With the transfer cases there are two types which are virtually the same. The Volvo one generally has the cover plate at 45 degrees to the centreline of the driveshaft, while the later Kuga has it at 90 degrees. They both utilize the same 41/16 crownwheel/pinion teeth count giving a transfer case ratio of 1:2.56. That means that for every one revolution of the output of the gearbox (by the drive collar and driveshaft), the propshaft will rotate 2.56 times. This is because you have the larger crownwheel driving the smaller pinion.

<Volvo TC?

<Kuga TC>

At the diff end you have exactly the same ratio of 2.56:1 only this time the propshaft rotates 2.56 times to give a wheel rotation of 1. This is because you have the smaller pinion driving the larger crownwheel. The overall ratio of the transfer case and diff must be 1:1 otherwise you risk damage to all of the drivetrain components. You cannot under or over drive either end. The other thing to understand is that the actual ratio's in the transfer case and diff are irrelevant to the gearbox gearing. The only important point is they must be EXACTLY the same. All gear ratios including the final drive ratio are done in the gearbox before the point the output is taken to the transfer case and driveshafts.