I agree with John that it is some form of radial valve-gear, if not Marshall then perhaps the similar Bremme. These are related to Hackworth but use swinging-links in place of a sliding die-block. Some marine-engines also used Joy gear with swinging-links rather than long slotted expansion-links.
Can you assemble it more fully and obtain clearer photos? The one showing the reverser side is upside down and I had to turn it right-way up in 'Photo-editor'; to try to understand it better.
The link dangling from the bell-crank looks as if it is actuated by a pin on the connecting-rod, but I could not determine that. There seem to be two slotted links in that tray of parts, that may be expansion-links – straight so Hackworth?
As Jeff says, the locomotive does have a certain LBSC look to it, and more 'Tich' than its slightly bigger sister 'Juliet'. If I remember rightly 'Tich' design uses Walschaerts or Baker valve-gear (also radial but more complicated) but I am sure it does not have that confection of links below the reverser-stand.
I am inclined to think you have acquired what would have been serviceable if its builder had not tried to modify it. The cosmetic detail of the reverser-stand shape re-inforces that, even before we question what all those links do.
So what might be wrong? Without knowing exactly what valve-gear we have here, I can only offer some pointers:
Lack of symmetry in the motion geometry – so unequal valve openings. On Hackworth and related gear, the die-link being ahead of or behind its proper position relative to the driving-axle can give that problem. I think I am right that with this gear, if the valve-spindle and piston-rod are parallel the engine centre-lines plot a rectangle in mid-gear.
Note that this gear is affected badly by incorrect axle-springing distorting the motion geometry.
Incorrect link dimensions somewhere.
Incorrect valve or port dimensions. I know from personal experience that with Hackworth gear at least, over-long valve laps grossly exaggerate the die-link angle necessary to gain any port opening at all. The related gears would probably show corresponding misbehaviour. In our case we traced it to an error on the drawing; a "first edition". I think without actually knowing, that the designer corrected it very rapidly as other builders of the same loco told me they'd had no difficulties with it.
If too long travel of course, the valve would hit the end of the valve-chest before opening the opposite-end port properly.
If the engine was built to a published, popular design, wrong dimensions are most likely a builder's error although it is not unknown for published drawings to contain mistakes. If a freelance or as some of us think, a heavily-modified, machine the errors could well be in the design.
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I hope you won't mind me passing on some tips regarding photographing technical subjects like these, that I have found in my own workshop:
I don't know if you took your photos with a 'phone, but apart from my having no choice anyway I prefer to use a camera on a tripod or other rigid stand so I can align it properly and obviate shake.
It does not need to be a high-grade specialist camera for moderately-sized subjects such as that loco. A simple digital "snap-shot" instrument should cope with it.
Ensure the subject is not so close it is below the camera's focussing range.
Use the shutter-timer (most have this) so you are not touching the camera when it takes the picture.
Use better lighting too – slightly diffuse day-light outdoors is best.
And experiment to obtain the best results and delete the poor ones.