One of the problems with worm drives is that they tend to be a little inefficient, which limits their maximum power because they heat up. This often prevents them from being backdriven. This is due to the sliding friction between the worm and the worm wheel, which becomes a bigger problem for larger reduction ratios because of the smaller leads.
Suppose you have an “inverse planetary roller screw”, a planetary roller screw where a cage of screws revolves around a central screw but is not free to move relative to the central screw, but instead of driving longitudinal displacement of an outer “nut”, it drives the rotation of a worm wheel. This eliminates sliding friction, and when the planetary screws are of the opposite handedness from the sun screw, also amounts to a differential gear drive, permitting very high reduction ratios. This worm wheel can also have much lower backlash than the traditional sliding-contact type.
The screws can to some extent be “throated”, with the planets being hourglass-shaped in order to maintain contact with the wheel around some of its circumference instead of just a point, requiring the sun to bulge out into a cocklebur shape to compensate. This variation of radius reintroduces some sliding friction due to the varying radii, but I think it will still be much less than an ordinary worm drive, particularly if the worm is large compared to the worm wheel. The worm wheel can likewise be throated to maintain contact with the planets through more than a single point in their travel.
To maintain large areas of continuous contact it is desirable for the planets to be very small compared to their orbit size so that there can be very many of them, but this eliminates the possibility of extreme reduction ratios through the roller-screw mechanism itself. Extreme throating of the worm wheel, with each of its teeth encompassing a near-semicircle of the planets, might nevertheless allow such large ratios.
Another variant that would reduce the variability of contact from five or six rollers is to split the cage into two or more sections, each of which has separately rotating rollers, which are staggered. For example, one half of the cage might have roller screws around the center screw at 0°, 60°, 120°, 180°, 240°, and 300°, while the other half has them at 30°, 90°, 150°, 210°, 270°, and 330°. These roller screws would be half as long as they would be otherwise, so this doesn’t increase the total amount of area of contact, but it does potentially distribute it better, producing smaller distortions.
The unbalanced forces on the shaft from pressing against the worm wheel can be balanced on the shaft in different ways. An additional identical worm wheel on the other side is one possibility; the shaft can held in heavy bearings on one or both sides of the worm drive; or the “top lands” or “threadform truncations” or “crests” on the tops of the planetary screw threads can roll against a simple cylinder on the opposite side from the worm wheel, or an hourglass shape if the planets are throated.
Similarly, the radial side load on the worm wheel can be balanced by placing one or two other worms on the other side. If only balancing the radial force is desired, these additional worms can either be idlers or driven synchronously, but they can also serve as additional driven elements, either for sensing or to provide mechanical power.
Another way to use these differential roller screws is in place of a micrometer screw, whether to measure the sizes or angles of things or to actuate to precise distances or angles with very low backlash, though of course you need to minimize thermal distortion and possibly compensate for it before you get too far.