Crafting war wagons for Chinese armies is tough, because (a) I don't speak Chinese, and (b) descriptions of these vehicles are tremendously rare, and (c) to the best of my understanding, there are no paintings or anything similar of these guys.  Also (d) the terms used do not translate well and are not used with the precision wargamers would like.  To make this clear, let me give an English example of military terms that are really messed up.  Wargamers talk about lances, spears, javelins, and pikes.  Those are all military terms that mean (to wargamers) different things.  The first is a long pokey thing for mounted troops, the second is a long pokey thing for foot troops in melee used mostly with one hand, the third is a long pokey thing that foot troops throw, and the fourth is a long pokey thing for foot troops in melee used mostly with two hands (and usually significantly longer than a spear).  All good, right?

Except all of those definitions are late 20th century wargamer precise.  They don't mean that to anyone else.  Archaeologists and academics are nowhere near as precise, and can use all those terms more or less interchangeably.  And all four terms were used in the 19th century and early 20th century as basically synonymous by most of the people writing about military history and usage.  And worse still, those are ENGLISH terms -- Polybius didn't write in English.  So if anyone tells you that the Carthaginian army should be allowed pikes for their foot troops, they've probably just finished reading a 19th century English author writing about military history who used that term -- but he did not mean "pike" in the wargamer idea of the weapon (if he even cared about the issue -- wargamers fixate on weapons; military historians often don't).  And worse still, he was translating from Polybius (or someone else who might have said "hasta", "dory", "sarissa", "kontos", or many other terms which don't necessarily translate to the wargamer-precise term "pike".

And with Chinese terms, it is triple as difficult.  So does the Wu Di Da Jiang Jun Che ('invinciple great general cart') mean a War Wagon (in the Triumph sense), or an Artillery, or a Plaustrella?  Or none of the above?  (portable fortifications, perhaps)

So anyway, the Ming army list has War Wagons as an option, and these were constructed to "look Chinese" and be vaguely appropriate based upon extremely limited information and some Ming woodcuts of uncertain relevance.  Hopefully better research will arise at some later point, giving us a better idea of how these things were built.