It’s 2281, thirty years after the nuclear war between China and the US. Our tea, lives in a fallout shelter in the remnants of Las Vegas. Our shelter relies on a nuclear generator to supply our power, but a raider strike has knocked out 48 of its steam turbine blades, rendering it inoperable. Due to the power outage, the bunker’s machine shop is out of commission. Solar panels can provide extremely low current, but not enough power to machine material. Considering the critical facilities of water retrieval and purification have been compromised, our first priority is to restore water utility operations to ensure the survival of members of the bunker, requiring us to machine piston replacements for 60 pump units.
The constraints of our situation remove the traditional types of energy (coal and steam, internal combustion, and then batteries) that instrumented the Industrial Revolutions occurring prior to the outbreak of nuclear war. However, the most ancient energy source that life has continually taken advantage of–the sun–remains in the sky. We have preserved access to a solar panel array that can provide current of magnitude great enough to turn a weighted spool in direct sun; our proximity to the desert and lack of other options makes this starting input for a system the most reasonable.
While the current can provide torque greater than the starting torque of our existing winch to physically move it, the current also never gets large enough to run the winch at cutting speeds. Our options from this point are two - from an academic perspective, we could take the extant torque in the winch and reduce its torque using a series of smaller gears, which would also have the effect of increasing the final gear’s speed to a possibly satisfactory one. Unfortunately, the torque:speed relationship is a sacrificial one–you cannot increase one side of the ratio without decreasing the other. Therefore, a tool now moving at fast enough speeds might have sacrificed the torque that would enable it to remove material from a surface. With a reduction in torque, chatter invites itself, and with a reduction in speed, jamming is possible.
The physical relationship between power is the cross product of torque with angular velocity. A certain amount of power is required to remove a thin shell of material from a surface, as is our goal with urgently milling replacement pistons from billets of aluminum. Therefore, although our solar panel can provide enough current to turn the winch, it is not able to generate enough power to do anything useful on its own.
A key dimension of power is time; the winch could theoretically create enough energy to power a cutting tool removing material for a full minute, but it might take three minutes for the winch to operate for long enough for that energy requirement to be reached. Therefore, we need to imagine a way to extract and store the energy of the winch somewhere so that we can tap into it quickly - store the energy by doing slow work with it, then expend it all in a much shorter time period, to reach the required power necessary to mill.
Of course, in the pre-war century (2100s), the answer to this scenario would be batteries. We have no such luxury. Because we have a winch, and abandoned oil wells surrounding our bunker, we have the shafts necessary to construct a gravity battery. The concept is simple; while the solar panels operate, they slowly drive the spooling up of a massive weight to ground level. When the spool needs to drive an assembly that operates with enough power to remove material (namely at dusk, since our energy source of the sun become unavailable), the gravity battery is dropped in a controlled descent, where the parameters of the descent (namely rate) dictate the power flow into our larger “factory”.
If such an above system was implemented, we can design our factory with the knowledge that we have a high power rotating shaft (with the opportunity to calculate and drop the weight to produce enough power for different assembly steps). Rotational input is the most common driver of complex mechanical systems, in the pre-raid period being sourced from non-damaged turbine or electromechanical sources, so engineers are familiar with the starting dynamics.
From the rotating spool whose angular acceleration (and thus power output) is governed by the rate of the falling weight, we propose a multi-shaft breakout gear–the variable transmission. Because certain shafts during the machining process move with different speeds, a variable transmission is a simple way to break out a shaft with one speed and torque into multiple shafts of varying speed and torques.