Hi I was wondering if any bike engines would be compatible for a adults tricycle? An example of the bike I am talking about:
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Most front wheel motors will work on the trike and will install in a very similar way. There are a lot of kits on ebay, ranging in price from a couple of hundred dollars up through sensible prices to quite silly. See this question for some opinions on the cheap kits.
Most crank motors will also work and be easy enough to install. This Sunstar kit, for example. The advantage is that it uses the gearing system on the trike, so it works better than a hub motor when the trike is going very slowly. The disadvantage is that it's a pedal-assist motors, so it only works if you're pedalling.
My suggestion is that you find a local bike shop that has experience with electric bikes, ideally one that sells kits, and get them to supply and fit a kit for you. While it's possible to do the work yourself, unless you have the rights tools and experience it's very easy to make mistakes and end up with something that's unsafe, doesn't work, or is unreliable.
You can also buy ready-made electric trikes like this one. It might easily turn out to be cheaper to do that than buy a trike plus a kit if you don't already own the trike.
This bike looks similar and utilizes an engine in the front hub. You won't get as much range as you would on a bicycle, but there's lots of room for extra batteries on a tricycle. The bike in the link states it gets 30 miles on a charge, and can reach speeds of 25 mph, which is pretty impressive.