Battery build
Most all large powerchairs use a pair of 12v lead chemistry based gel or agm type batteries wired in series to create a 24v system.  This has been the norm since the 1970's.  Lead is simply unsuitable for this application for a variety of reasons.  The main three reasons are energy density, peukert effect, and lifespan.
Energy Density:  This is basically the amount of electric potential a battery can store in a given volume or weight.  You can store roughly 40 watt hours (Wh) of energy in one kilogram of a HEALTHY lead acid type battery.  Slightly less in gel types.  That's roughly 60 Wh per liter of volume.
Peukert Effect:  The change in capacity based on the rate of discharge. In short, the faster you try to pull energy from a battery, the less energy it can provide.. This is why when your car battery is "dead" and won't start, the headlights still shine bright then get more dim as you try to crank it. There may still be 300 Wh of energy left in your 800 Wh battery, but it can only provide 100 watts due to the capacity being low.  Your headlights are only drawing 1 amp (about 12 watts), which it can output.  Your starter needs 200 amps (about 2400 watts).  The energy is there, it just can't escape all at once. As a lead battery discharges the internal plates become covered in lead sulphate, which does not conduct electricity. The more the plates are covered, the less of the energy creating chemical reaction can occur.  This application consumes power in big doses, not a steady pull.  Lead batteries cannot provide the big gulps of energy once they are discharged about 40%.  Basically half or more of the stored energy is unusable.
Lifespan:  Lead is typically good for 200 to 500 charge cycles. It can vary wildly by the amount it is discharged and how it is recharged. Lead is only happy when full. It deteriorates as it generates energy from creating lead sulphate. Each time you recharge, the lead sulphate breaks off and is absorbed into the electrolyte. Some of it remains stuck on the plates along with tiny bits of lead breaking away. The deeper you discharge a lead battery the more this happens.
There are many types of lithium batteries. All are not created equal. The most common chemistry is LiCoO2, or lithium cobalt. These are found in everything from cellphones to power tools to laptops.  They have good energy density at around 190 Wh per kilogram and 550 Wh per liter.  They don't suffer from the peukert effect, can be recharged 300 to 500 times, and can be put out the energy required for this application when built large enough.  They have one huge disadvantage that completely rules them out:  Fire.  When shorted internally they generate heat proportional to their size.  A battery big enough for a powerchair could create a massive fireball if damaged.  Not good when you can't run away or it is parked in your closet.  That's why their size (capacity in Wh) is limited on airplanes. The second most common is Lipo or lithium polymer. That's what you will find in the RC cars, drones, and small jump starters for cars. They vary wildly in energy density, but some variants are over 250 Wh per kilogram and 700 Wh per liter.  They can output incredible amounts of energy for their size.  Unfortunately, they start deteriorating after 30 to 75 charge cycles and create a massive fireball when they get angry.  
The only suitable chemistry currently available to consumers is LiFePO4, or lithium iron phosphate.  You'll find these batteries in energy storage solutions, solar, and golf carts.  They are around 140 Wh per kilogram and 350 Wh per liter, depending on construction type.  They don't suffer from the peukert effect, can be recharged 3,000 times or more, and have become quite cheap as they gain popularity and patents expire.  They also do not burn when damaged or shorted internally.  They only release white smoke, smell bad, and drain a small amount of whatever liquid electrolyte the manufacturer used.  The main downside to them is the complication.  They must be kept between charge amounts to avoid damage.  Discharging them down below 2.5 volts per cell can cause damage that can sometimes not be repaired.  They also do not like to be full for more than a few hours.  They should be stored between 30 and 80% charged.  The key to building a battery pack that will outlive most breeds of cats is to assemble it from fully high quality charged cells, never discharge it below 90%, and only balance it while charging once the cells are over 3.45 volts.  

LiFePO4 batteries also have a flat discharge curve.  This means you cannot know how much energy is left in the battery based on its voltage.  This also means it is pointless to try to balance them below 3.45v per cell.  You will actually unbalance the pack if you do.  This is why off-the-shelf BMS (Battery Management Systems) that are not programmable cannot be used.  The voltage of a pack at 45% is exactly the same as a pack at 99%.  They cause far more harm than good and waste energy by moving it around from cell to cell all of the time trying to keep them balanced.

Willchair 4 Complete Assembly 2
CAD.  And no, I don't mean Cardboard Aided Design.  There's no reason not to use Computer Aided Design.  There are many CAD tools available for every budget from the usual suspects and more learning material than you could ever consume in a lifetime.
Willchair 4 Complete Assembly 1
Every part of the chair except the wiring and batter insulation was drawn and tested prior to any machining taking place.
Willchair 4 Complete Assembly 3
Every bolt, nut, washer, and switch were drawn.  Many components such as switches and relays had to be ordered first so they could be drawn and digitally test fit.
Willchair 4 Complete Assembly 4
This project would be impossible without being drawn first.  CNC machining and 3d printing need the CAD files anyway.   
Designing around all of the constraints needed made finding off-the-shelf parts difficult.  The chair must also fit in my truck so I can drive along with placement for the docking mechanism.  Things like ground clearance must be estimated due to tire pressure and suspension settings.

Most manufacturers of things like motors and gearboxes will typically provide you with a solid CAD file if you ask.  Open source IGES or STEP files are preferred.  They will rarely provide native CAD files from the design software such as Solidworks or Inventor.  Always double check them once you have the part in your hand for discrepancies before proceeding with cutting metal.  On the third chair I built I had to completely redesign and rebuild the blue parts you see below and shock mounts (not exactly like these but similar) because I made the parts based off of their supplied drawing while waiting on the custom wound motors to arrive.  The motors were 1/2" longer than the drawing.  They would not fit.  

Electronics Board Assembly 1
The basic electronic components were purchased then measured and modeled before building.  This chair has a more robust and simpler electronics system then on previous builds.  These main components shown here are the 48v to 12v converter, master/emergency disconnect, and two relays for the actuators.

Electronics Board Assembly 2
The Electronics Board was 3d printed from PETG.  The bolts thread into it then have nuts on the opposite side.  The heads of electronically hot bolts are recessed into the plastic to lessen chances of shorting.
Chassis 4
After digital installation.  The charging connector appears to be floating in space.  It is not.  It is installed in the front cover.  The visibility for it is turned off.  This lets you see how much room you have that would be hidden otherwise.

Joystick Assembly 2
This view of the joystick assembly lets you see how the belleville washers work.  
The joystick housing looks empty without the mess of wires that that there in real life.  One thing that does not match what was actually used is the front rocker switch.  The real chair uses a single pole double throw momentary switch for the master/emergency kill switch.  The two in the model are both single pole single throw latched rocker switches.  The dimensions are identical though.  

Seat 1
The seat design is a bit complicated and a little bit of a pain to build due to all of the supports.  I have built several of these though and this design has proven reliable and strong.  Proper welding techniques are REQUIRED to minimize warping and maximize strength.
It would have been much more difficult to get the angle and relationship of the swingarm mounts and caster barrels correct without CAD first.  It still took a bit of guesstimating to assure the caster barrels were straight up because it can vary with tire pressure and suspension sag settings.
This is how the taperlock hubs go together
Footrest Mount 1
Pipe The footrest assembly looks complicated but it is not.  Like the seat, I have built and used several iterations.  This one has proven reliable and strong.  Weld quality makes a big difference.
Rear Shock Upper Mount 1
The Rear Shock Mount.  The notches below the pins for the shocks are for clearance on the shock body.  
The caster forks use a pair of 3/4" id tapered roller bearings like in a truck axle.  They take a beating.  Standard roller bearings do not last.  These also have a slight amount of preload applied to help reduce caster shake at speed.  The bottom has an O ring seal to help keep water out

Follow along to the hardware build page to see how many of these parts came to life.