The Trikester wheelchair is simply a trike wheelchair that has been either made from scratch with DIY techniques and materials, or is the result of replacing the two front casters on a traditional "quad" wheelchair with a single trike wheel.
There are many old wheelchair frames with severely rusted caster barrels and/or destroyed casters. Their casters function so poorly that the wheelchair is not used, yet the other parts of the frame are still sound. These wheelchairs are perfect candidates for creating a Trikester wheelchair (as opposed to trashing it).
The caster barrels are used to hold a 3/8" or 1/2" bolt which then connects to the front frame which secures the trike wheel. There could be different ways to accomplish this. The photo above shows three examples.
A trike wheelchair differs from a quad wheelchair in that it has a single front caster rather than two casters. This caster sits in a more forward position than the two casters creating a longer wheelbase. The advantages of tricycles and quads have been fairly wheel established in terms of jogging strollers and wheelchair racing. That being said, most wheelchair users are unfamiliar with the advantages and disadvantages of tricycles and likely have little to no personal experience with using them.
Due to its longer front end and the physical position of the front wheel, a trike wheelchair is less suitable for tight indoor spaces. It is typically more difficult for transferring due to inference from the front wheel/frame with the wheelchair user’s feet. A trike wheelchair is also less stable during transfers. It is more likely to tip to the side if the user leans forward and also to one side. These disadvantages make a trike wheelchair less desirable than a quad for an everyday use wheelchair.
On the other hand, a trike outperforms a quad in certain types of environments. Jogging stroller and racing wheelchairs are tricycles because this configuration handles uneven surfaces better than a quad. The single front wheel tends to glide over cracks and potholes. The longer wheelbase creates more forward stability. A trike also tends to hold a straight line with less effort on beveled roads with cross-slopes. As a result, a trike is typically faster and easier to propel than a quad. Hence their popularity for jogging strollers and wheelchair racing.
Trike wheelchairs work well for rough terrain, grass/dirt/gravel paths, and both uneven and smooth pavement. But a trike wheelchair is less stable on more extreme sidehills. Therefore, many styles of rough terrain wheelchairs are quads. WCMX wheelchairs are also quads to increase side-to-side stability. Court sport wheelchairs are also typically quads for increased stability. Therefore, I think it is useful to compare a trike wheelchair in use and favorable terrain to a jogging stroller. Both mobility devices have similar performance characteristics and work best in the same types of environments.