I'd like to add gears to my disabled son's pickle pashley tricycle. I have made a start by adding a 5 speed casette, but I'm stuck trying to work out how to shift the gears as there is no where to mount a derailleur and not enough vertical clearance anyway. Any suggestions for alternative gearing solutions would be appreciated.
Normally I would say "you wouldn't start from there", but since you have...
Since you've managed to add a cassette, I assume you're reasonably confident with tools. You're going to have to make a derailleur hanger that sits in the right place. If you can get a sealed bearing over the axle it'll be easier, but if not you will need to make a plain bearing that can be split to get it onto the axle. Then use that to locate a short arm that attaches to the frame and holds the hanger in the right place. I suggest starting with a scrap bike (from the tip if possible, you only need the derailleur hanger and a short length of frame, the rest can be damaged beyond recognition). One problem is that the derailleur will hang very low, with those small wheels it might not survive long in the hands of a child.
If that sounds impossibly daunting... sorry. That's why I started with "I wouldn't start from there". If you have to pay someone else to do much of the work it'll end up cheaper to buy a trike that has been built with gears from the start.
Looking from the back of the trike,you need to build the blue bit. The green bit is the bearing on the rear axle, and the really bad photo of a rear derailleur shows where that will go. The blue blob at the top is where you bolt the new part onto the frame of the existing trike.
Where I'd start from if I could?
While I'm usually reluctant to say "this brand, and only this brand" here, there really aren't any other options for readymade kids recumbents that I know of. So... The KMX kids recumbent trike (or in the UK). If you can find one and put your kid on it, see what happens. If you can get him off it without tears and screaming... maybe look at an upright trike again. If you do need to go with an upright, I'd approach Pasley and see if they can put gears on that trike, or suggest a framebuilder who can. But if you can braze or weld, building something like that will be a good start on a second career as "building stuff for my son" because from experience, you will get a better product even if you're a bit ham-fisted, and you'll definitely save money. But that assumes you have the "spare" time to do this stuff :)
But seriously, try a recumbent trike, anything that he can even vaguely fit onto will do as a first attempt. They're more stable and more robust, so as a result more fun. You might find it helps to use toe clips with heel support, or the Shimano SPD "clipless" shoes and pedals - I can't imagine riding a recumbent without them.
Also, able bodied kids ride the KMX trikes... or want to :)
But you can more reasonably get shorter ones from a scrounged bike and make an extension for one of them. Take the other one off, they just unbolt. That way if you stuff up the first attempt you can try again with the other one :)
Alternatives to adding a (possibly very low) rear derailleur:
add a hub gear instead
I'm not sure you can do this in-line with the rear axle (it would have to be joined to the hub shell), so it might need to precede the rear axle and drive a second chain.
Actually, I see Sturmey Archer make specific tricycle hub gears, but I have no idea how they're supposed to be fitted.
Edit - the TS-RF3 is described here:
This is a gearbox, not a hub and must be used in an intermediate position on the frame, with input and output chains, because the secondary sprocket attaches where the spokes would
They do make kickshift gearhubs as well, which - if suitable - would remove the need for a gear cable. Again, see Sheldon.
add a front derailleur instead
The chainguard might need modifying, but an 2-ring MTB front might work, depending on the gear range you need. You can get clamp-on front derailleurs, so it might be easier to retrofit than the RD gear hanger
add a bottom-bracket gear hub
I'm not certain anything suitable exists, but mention it for completeness. The Pinion gearbox looks much too big, which is a shame.
I found this image in an untrusted link, on a site called https://www.factorydirectbikes.com/.
It seems to show a trike with gears. Perhaps either the people at that site, or Pashley themselves might help you.
At the very least, you'll need to add a bracket to the centre frame member to hold the derailleur.
BTW, I found this by a Google image search for pickle pashley tricycle.