The problem with variable drive systems are that they tend to have a scrubbing effect, at any given speed the friction drive area is one to one in the center of contact but either over drives on one side and under drives on the other. This causes heat, power lose and premature wear. I have solved this problem using a set of cones, one inside the other. The inner cone has a conditioned surface to help grip the outer cone. The outer cone is lined on the inside with a frictional material comparable to the material on automatic clutch discs.
At low speeds the drive cone is positioned near the large end of the driven cone. This causes the drive cone to need to revolve many times to cause the driven cone to revolve once.
As the small drive cone move deeper into the large driven cone the ratio moves closer to one to one.
When the drive cone reaches its inner most position it contacts 100% around and locks the input shaft to the output shaft. So during highway travel, while it is locked up, it would be as if there were no transmission at all.
This transmission would be very easy and inexpensive to manufacture due to its simplicity. Many of the technologies used to manufacture todays transmissions could be used to mass produce this transmission.
Modern automatic transmission are very complicated and have many parts which increases the likely hood for failure. Having fewer parts makes a more dependable product.
The drawings I have attached are simplified to demonstrate only the variable mechanics. To make this unit usable in an automobile it will need a reverse idler gear and a stepper motor attached to a worm gear to control several of the variable cones in series. This is necessary to obtain the gear ratios to go from start to top speed. Even with these other parts it will still fall short of the complexity of the modern automatic transmission.

Sheet One
The large driven cone is transparent to allow the position of the drive cone to be seen. There are two constant velocity joints used. For simplicity I drew them as a ball joint. One is inside the drive cone and the other is at the far end of the larger driven cone.

Sheet Two
This is a section view showing the frictional material inside the larger drive cone. You can see in the high speed position that the shafts become one to one.

Sheet Three
While driving these are the only parts that will be turning, they will be lubricated with Automatic Transmission Fluid. The outer cone rides on an oil film between itself and the transmission case.