Kbio,
This is a great explanation of how the Maudslay reversing gear operates and you should be commended for doing it.
Having said that there is one tiny mistake in your very first post where you stated: -
'the two shafts rotate in the same direction'
Assuming you mean the crankshaft and the eccentric shaft...This is not true with a 4 gear arrangement... they would actually rotate in opposite directions.
Apart from that tiny error the remainder of the article is excellent and very well explained, so very well done.
Advancing the topic a little further... your article, as written, only relates to steam engines with simple line-on-line slide, or piston, valves where there is no steam lap or lead involved.
For engines that have valves with steam lap and/or lead then the eccentric would lead the crank by more than the 90degrees, stated in your article, in the direction of crank rotation and this could be as much as 120degrees... possibly more.
In such an engine, and many small model engines do have such valves, the Maudslay gear would need to move the eccentric shaft much more than the 180degrees described in your article.
It would need to move the eccentric shaft by 240degrees or more... i.e, 2 x the eccentric lead.
This can make the selection of the gears required, and/or shaft spacing, somewhat more complex especially where space might be restricted, however, the same basic principle discussed in your article would apply and use of the mathematical formulae provided in your attachment can easily solve such issues.
I only mention this since there may well be members of the forum who are, perhaps, considering converting their engines to Maudslay reversing gear, but would run in to problems if their engine had valves with steam lap.
Just thought it worth mentioning this and it is not intended as any form of criticism on your most excellent article.
My very best regards.
Sandy. (ex ACS Engineering).