We do not have any gear motors with sprockets for #35 chain. The gear motors that we carry have sprockets for either #410 chain, or #41 / #420 chain (#41 and #420 chain are the exact same size however #420 is stronger than #41).
Most mini bike and go kart parts stores that sell sprockets for #35 chain also sell sprockets for #41 and #420 chain, and we sell a 34 tooth sprocket for #41 / #420 chain. We also have 36 tooth and 44 tooth #410 sprockets and can special order many other different sizes of #410 sprockets.
Our 24 and 36 Volt gear motors that are 450 Watts and under have sprockets for #410 bicycle chain, while our larger 36 Volt 650 Watt gear motors have sprockets for #41 and #420 chain.
For beach wagons that will not carry too much weight and will be geared for walking speed most people use a 24 Volt 350 Watt gear motor, and for beach wagons that will carry heavier loads the 36 Volt 650 Watt gear motors are typically used.
Do you know how much weight the beach wagon will need to carry, and if it will need to go up any steep hills?
These kits can be modified with different parts such as larger or smaller batteries, different throttle, etc. upon request.
Regarding us not offering advanced technical support by phone there are a couple of reasons why we can not afford to do that. The first is that we are located in an expensive area of California and likewise need to pay our technicians a high hourly rate which makes having them on phone not economically viable. The second reason, which ties into the first, is that it takes a long time to complete calls with a certain percent of our callers, sometimes upwards to a half hour. This is the reason why there is sometimes a long hold time on our phone system. We have discussed offering a technical consultation service on a pay per minute basis however that is a service which we have not decided to offer yet. We are able to offer free advanced technical support on this forum because the time we invest answering questions here becomes a publicly searchable database which is utilized over and over again to respond to everyone who has the same type of questions.
Please let us know if you have any further questions.
We currently do not carry any sprockets with a 2-7/8" bolt hole circle, we plan to carry more go kart and mini bike parts in the near future though. If you decide not to use a freewheel then a go kart sprocket with a 2-7/8 bolt hole circle for #41 and #420 chain could be machined to just under 1/8" wide in its teeth area to work with a #410 chain if using our 450 Watt and under gear motors, or could be used as it is with one of our 36 Volt 650 Watt gear motors which has a sprocket for #41 or #420 chain. The cost of the electrical parts almost doubles when going from a 24 Volt 350 Watt system to a 36 Volt 650 watt system though so it would probably be more economical to have the sprocket machined for #410 chain than to upgrade to a 36 Volt 650 Watt motor, unless you want the extra power of the larger motor.
If you want to have a freewheel then I have found a solution for that. The wheel bearing in your photo looks to be around 1-3/8" OD, and our freewheel mechanisms have a 1.375" ID, so there is no way I can see to weld a freewheel adapter onto that rim. The largest ID bore of our freewheel adapters is 1" because there needs to be a little material left on the adapter between its inside diameter bore and outside diameter threads. To install a freewheel adapter onto that wheel would require a flange to be fabricated with a 1" ID bore and 3-1/2" or larger OD that would bolt onto the wheel and the freewheel adapter would be welded onto. A metal fabrication shop could make this flange and weld the freewheel adapter onto it. This flange would basically be a huge 1" ID x 3.5" OD flat steel washer with four holes in it to mount to the wheel. It looks like it might need to be spaced away from the rim a little with washers to clear the end of the bearing. Here is a drawing of this idea.
Here is a photo of the freewheel adapter with 1" ID.
Attaching the freewheel to the sprocket is simply a matter of bolting the two parts together. We have sprockets for #410 chain that are sold with freewheels and bolts so there is no guesswork involved. Here is a photo of this part.
The freewheel in the middle of the sprocket threads onto the freewheel adapter.
It looks like this setup would place the sprocket around 1/2" further away from the wheel than it is now, however the freewheel adapter could be shortened on its back side by cutting, sanding, or machining it to make the sprocket fit closer to the rim if necessary.
Please let us know if you have any questions.
A freewheel disengages the axle or wheel from the chain sprocket when the axle or wheel rotates faster than the chain sprocket. When the chain sprocket rotates faster than the axle or wheel then the freewheel engages to transfer the power from the sprocket to the axle or wheel.
In the photos that you attached the wheel has bearings which isolate its rotation from the axle, so the axle does not rotate and is stationary, which is referred to as a dead axle. With a dead axle drivetrain the freewheel engages the wheel itself, and not the axle, so the freewheel is mounted onto the wheel instead of the axle.
In a different type of drivetrain than your beach wagon has, with a live axle, the freewheel would be mounted onto the axle and engage it when the sprocket was spinning faster than the axle.
Here is a drawing showing how freewheels work.
We sell freewheels and freewheel adapters that engage and are threaded in both clockwise and counterclockwise directions.
We do not sell any freewheel sprockets that fit our gear motors because they are not mass produced. We do sell a freewheel sprocket that fits our Currie electric scooter motors however the output shaft on these motors spins to fast for the motor to be used on a beach wagon.
If the sprocket was attached directly to the rim with bolts then that would bypass the freewheel and it would not be functional. The freewheel would only work when attached to the axle with a live axle type of drivetrain.
Please let us know if you have any questions.
Here is a drawing of the side view with the sprocket and freewheel threaded onto the adapter and flange.
It sounds like you understand my freewheel to rim adapter idea perfectly from your description.
Please do not hesitate to let us know if you have any further questions.
I can put together a kit for the project. We will just need to narrow down which parts to include with it.
If you will be installing a freewheel in the drivetrain then the beach cart would not move when the motor is in reverse. To have reverse would require the sprocket to be mounted directly to the wheel without a freewheel.
We have full length twist, half length twist, and thumb throttles that fit 7/8" OD handlebars, and a full length throttle that fits 1" OD handlebars. The throttles that fit 7/8" OD handlebars are available with battery meters, and some of them with switches that could be used for the power switch. The throttles that are compatible with a 24 Volt system are on the following pages: