Hi,
I can't see any cylinder valves to control the steam . A beam engine is dual acting, steam should be controlled to enter the lower and upper chambers of the cylinder in a controlled manner and usually this is done with a steam chest on the cylinder with a sliding valve with an operating mechanism linked to the piston movement which controls the steam flow to produce smooth movement - of course there may be some 'magic mechanism' in the cylinder plinth which I am unaware of.
Also the beam will not work as shown in your drawing, as Jason says the piston rod will jam as the beam reciprocates up and down. As K2 suggests the most common solution is the Watts linkage, relatively simple and reliable.
Consider a ceramic gas burner rather than the spirit one you appear to have drawn. You should also incorporate a displacement lubricator for steam oil to lubricate the cylinder to prevent excessive wear.
The design is not too elegant aesthetically, there are a lot of engines and kits similar to this which are much more appealing.
I suggest that you do a lot more research into how steam engines, especially beam engines work.
Here are views of StuartTurner engines similar to yours, the steam valve with it's associated operating mechanism is the grey part attached to the front of the cylinder on the lower example, the brass part in front of that looks like the displacement lubricator and the Watts linkage, made up of 8 links and two side arms (called the entablature) is also shown clearly on the upper example. I think that you have some work to do.
Also a simple 'pot' boiler like the one you have shown may not produce enough steam to drive the engine, the Stuart boilers like this are of 'Babcock' design with external water tubes attached below to increase the heating area. Again I suggest research. to see more about boilers
here is an excellent series to start your researches.
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Best of luck with your project
TerryD