I'm wondering exactly how many different kinds of helmets were worn by pikemen. The traditional "pikeman's pot," similar to a cabasset (what, precisely is the difference?) is probably the best known. Most pikemen's armours seem to be associated with these types of helmets. I've also seen many drawings of pikemen wearing morions. How common was it for them to wear a combed morion rather than a comb-less helmet?

Furthermore, I've seen (I'll try to find them and post them here) illustrations of pikemen wearing burgonets. Usually the German-style mid to late 1500s style burgonet, the kind with a high, arched peak (brim), comb, and wide cheek pieces. Did they actually wear these kind of helmets or is this just a case of artistic license?

How common was it for pikemen to wear gauntlets? Would higher ranking men have them even if the rank and file did not?

Finally, in one of my books there is a photo of an English pikeman's armour with full pauldrons, rerebraces (with fully articulated inner elbows), vambraces and gauntlets, and a close burgonet with a Savoyard style helmet. It looks like a hybrid of a typical cuirassier's armour with a pikeman's tassets and breastplate. Part of me suspects the armour is made up from pieces from two different suits, but it is all decorated in the same way and looks very proportional.

Would a very wealthy senior pike officer have ever worn complete upper body protection like this?

In which period?

As for gauntlets, it depends. Gauntlets were sometimes worn, and sometimes supposed to be worn, but not always. By the looks of it, not often. I read something about this recently in my commuting reading:

From F. M. Kelly, The Corslet and the Burgonet, The Burlington Magazine for Connoisseurs, Vol. 36, No. 206 (May, 1920), pp. 218- 219+222-224+227:

"From these we gather that corslet in I6th century military usage means strictly the complete defensive equipment of an infantry man: i.e., of picked fighting men such as pikemen, halbardiers, and certain officers and N.C.O.'s, but in particular of the first-named. With the increasing weight of heavy "proof" armour the soldier indeed was only too apt to take any occasion of reducing this to a minimum, nay, more, there seem to have been authorities quite ready to meet him half-way, much to the scandal of old-fashioned precisians like Hawkins, Robert Barret and Sir John Smythe. What the latter and their school held to be the proper equipment for the pike is clear, viz., gorget, breast, back, pouldrons, vambraces, taces and headpiece. This last is mostly described as a burgonet; but on this point see below. Smythe would include gauntlets, but it would seem as though for some time these had been in nowise regarded as a sine qua non."

And from the relevant footnotes:

Barret: op. cit. says of the ensign, " He shall alwaies go gallant and well armed with a faire Corslet, Burgonet .... which are his proper arming .... ". That there was an inferior class of pikemen much more imperfectly armed " with- out any corslet, or, at the most, the bare cuyrats only and morion " appears from the same treatise, though the true, first-class pikeman should have "gorget, Morion, tasses, pouldrons, vambraces and gauntlets .... whatever opinion other men may hold to the contrary, supposing a bare payre of Cuyrats onely sufficient ". Note how Barret, a precisian in language, says " morion ", which class of helmet was fast both superseding the burgonet and usurping its name. So identified was the pikeman with the corslet that throughout the latter part of the i6th and much of the i7th centuries we find in English and French pikeman, pike, corsleteer, corslet used regularly as synonymous :-" 200 pikes ", the same number of corslets ", " a corslet or pikeman ", " three score corsleteers ". See Minshon, Sherwood, Barret, in fact almost any contemporary author, French or English ".

Hawkins' stricture on the Englishman's hatred for the encumbrance of armour and his preference for a pot of wine is well known. We have seen Barret's protest against the mere " pair of cuirats " as sufficient. Smythe would not even spare the pikeman his gauntlets, although " certaine of our captains " overseas were content with headpiece, gorget back and breast.

Not only are gauntlets not postulated by most writers, but an edict (4 and 5 Philip and Mary) quoted by Meyrick states, " The want of a gantlet or gantlets shall not be reckoned a deficiency for a corcelet ".

It depends on the period and region in question, but the dynamic that commanders often wanted more armor than soldiers preferred to wear - and princes could afford! - goes back to Fourquevaux's 1548 treatise if not earlier. Fourquevaux wanted three-quarters harness plus mail hose for most of his pikers and he specified helmets with sights almost closed.

Also note that Smythe, writing in the 1590s, claimed it was Spanish and Italian practice for pikers to wear gauntlets. As an aside, I think its overly simplistic to describe Smythe as a traditionalist and English nationalist. He certainly was both of those, but his appeals to the old bow and bill came along citations of Spanish and especially Turkish military practice. His ideal cavalry force departed significantly from English custom and took inspiration from Turkish and Eastern European cavalry as well as from Western European history (for the mounted crossbowers).