I understand there were different types of traction catapults used in china right up to the end of the Song dynasty. As far as I know there were two main types of such catapults, the normal pao with the fixed base that was sunk into the ground and the whirlwind catapult that could be aimed in different directions. There was a variation of this that was popular during the Three Kingdoms period that was on wheels Pili Che "Thunder Cart". How prevalent was this wheeled model during the Sui, Tang, and Song dynasties? Was there a size limit with these wheeled ones?

For rope pulled machines the wheels can only be to manouver the weapon, however expreements on counterweight catapults show that having wheels allows the weapon to move foreward as the weight drops, this allows the weight to fall in a straighter line, which imparts more energy to the missile. Net result is 5-10% more power.