Let's try to make this more clear...
Let's assume that the satellite is not transmitting circularly polarized (CP), which is true of nearly all. So your goal is to enable you to avoid fades as the satellite rotates and the linear polarization changes direction.
As have been mentioned here there are two choices: A CP antenna or switching from horizontal to vertical. In both cases with Yagis, you need a vertical and a horizontal set of elements. CP has the advantage that you don't have to switch--it works regardless of the direction of the incoming linear polarization and requires no relay, nor relay coil power. (Some people, including one of my best ham friends, swear by the ability to switch the CP antenna from right hand to left hand circular. I am not one of those when working linear satellites :-) ) To make a CP antenna, many have described the required coax length and impedance. I have not seen this said, but I believe that the crossed elements of the yagi also have to be a specific distance apart and at different distances, the coax length will need to be different. (I'm no expert here...I just bought an LEO Pack).
The other choice is to have a coax relay that will switch from horizontal to vertical polarity. The advantage is that it is simpler...the cable lengths and locations of the elements are less "fussy". The disadvantage is the opposite of the above: You have to manually switch back and forth to find the best polarity and you need power in some form out at the antenna to drive the relay coil.
I hope this helps. There are obviously two different ideas going on in this thread, so I wanted to try to sort them out.