What is the difference between a reversible machine and a self-locking machine?

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A reversible machine:

A non reversible machine has an efficiency less than 50%. That means the losses are more than 50%.
An example is a weight lifted by a screw jack (against gravity). There is a lot of friction around the thread, which also has to be overcome in lifting the weight. If the weight is lifted, and then we remove the driving force, it does not fall back down. It is not reversible.

If we had a much lower friction loss on the screw jack, for example using imaginary "super slick friction stop grease" so there is very little loss, the weight takes less effort to lift, and when the lifting drive is removed, the screw jack can fall back down. It is now a reversible machine. It means it doesn't need extra force (or energy) to drive it in reverse.

More mathematical description:
This simplifies things about the nature of friction to make it more easily understood.
I used figures around the 50% mark to make it simpler to grasp why 50% efficiency.

Force to lift 3kg mass against gravity, from F = ma:
1) F = 3kg * 9.81m/s/s = 29.43 newtons. The direction of the force due to the weight is down, and the lifting force is up.

2) Let additional force due to friction be 30N. This works against the movement of the weight. The direction is down because it opposes movement, so now a force of 59.43N is needed to lift the mass.

3) Remove the lifting force. The downward movement of the weight is now opposed by the friction. It leaves a net force of -0.57N. This force would mean an additional 0.57N downward force is needed for the weight to fall. Reducing the friction so it is less than the force from the weight is similar, it would fall on its own, making the machine reversible.

In practice the determination is made about the energy, which is from:
Energy_joules = force_newtons * displacement_meters
This takes into account that the opposing friction or the moving force might vary over the movement of the machine.

If a motor with a worm drive gearbox can hold the load with the power off, you know the gear losses are more than 50% for that load. Non reversible machine. You might also know there are risks because the friction can be reduced as the gears wear in, or lubrication properties change on a hot day, and also the combination may have insufficient power to lift the load on a cold day.

It becomes part of the explanation of why certain perpetual motion machines don't, related to the laws of thermodynamics but using just a mechanical explanation. Part of the Feynman lectures has a related explanation which avoids invoking friction more or less, and talks about one machine driving another using weights as the force.

Self-locking machines:

In many simple machines, if the load force Fout on the machine is high enough in relation to the input force Fin, the machine will move backwards, with the load force doing work on the input force.

So these machines can be used in either direction, with the driving force applied to either input point. For example, if the load force on a lever is high enough, the lever will move backwards, moving the input arm backwards against the input force. These are called "reversible", "non-locking" or "overhauling" machines, and the backward motion is called "overhauling". However, in some machines, if the frictional forces are high enough, no amount of load force can move it backwards, even if the input force is zero. This is called a "self-locking",

These machines can only be set in motion by a force at the input, and when the input force is removed will remain motionless, "locked" by friction at whatever position they were left.

Self-locking occurs mainly in those machines with large areas of sliding contact between moving parts: the screw, inclined plane, and wedge:

• The most common example is a screw. In most screws, applying torque to the shaft can cause it to turn, moving the shaft linearly to do work against a load, but no amount of axial load force against the shaft will cause it to turn backwards.
• In an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight.
• A wedge can be driven into a block of wood by force on the end, such as from hitting it with a sledge hammer, forcing the sides apart, but no amount of compression force from the wood walls will cause it to pop back out of the block.

A machine will be self-locking if and only if its efficiency η is below 50%:

${\displaystyle \eta \equiv {\frac {F_{out}/F_{in}}{d_{in}/d_{out}}}<0.50\,}$

Whether a machine is self-locking depends on both the friction forces (coefficient of static friction) between its parts, and the distance ratio din/dout (ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock.