Tanren uchi is a very traditional training method to help with instilling the proper use of the whole body in cutting, but especially the hips.  
One the greatest benefits is the immediate  kinesthetic feedback one receives from the tanren through the bokken when cutting.  If a cut
is completed incorrectly, the feeling transmitted into the bokken is very different.

Traditionally, as you can see in the picture with O-Sensei above, tanren uchi wasn't done with a motorcycle tire.  Rather, saplings were
bound tightly, supported on their ends, and struck.  The saplings gauranteed that there would be some give and spring in the strike, just
as the motorcycle tire can.
At least 100 cuts a day: preferably
100 in the morning and a hundred
in the evening.
Tanren Uchi