Cables can only transfer tension loaded forces, that is why we need two cables in order to be able to deflect into two directions: the control cables going from the cockpit to the control surfaces can be seen as a loop, as Trevor correctly identifies.
Cables also stretch, and for applying remote loads that is a disadvantage. The cable stretch is in series to all the dynamic and static behaviour of the flight controls: mounting a sloppy cable results in vague and inconsistent stick behaviour, and a feel as if the pilot is stirring in a pot of soup. The feel spring stiffness is diluted by the cable stiffness, and can never be higher. Cables must have high stiffness, so let's tension them up, let's give them a high pre-load.
However, putting a high pre-tension on the cables causes high structural forces. The cables run over pulleys, which are mounted on a bearing fastened to a structural member. One bearing. So the pulley loads the bearing with a torsional load and the cable tries to skew it, not a good situation for a cable run. It might run off the pulley and get stuck, resulting in an aircraft that cannot be controlled and a crash. Unfortunately everything in an aircraft must be light and bendy and we cannot beef up the bearing housing.
So we cannot put a very high pre-load on the cable. But a certain amount of pre-tension is beneficial:
- Cables only pull, and the cable not pulling may not be slack, otherwise it could run off as well.
- Pre-tensioned cables can provide push loads, by reducing the pre-tension it was subjected to.
An aircraft is a structure subjected to a variability of loads:
- Wing tips bend upwards during flight, bend upwards more when fuel runs out, and slam down at landing.
- As mentioned in the OP, the structure expands and contracts as a function of temperature. Thermal expansion is 23.1 µm/(m·K). A 747 is 70 m long, temperature differences of 90 °C can be reached, so the resulting stretch is 15 cm. Steel cables stretch half that amount, and the total cable run is differs 7 cm from the temperature alone.
- During flight, the elevators & tail plane put up/down loads on the fuselage as well, bending it up/downwards. Ailerons bend the wings more or less.
- During turbulence, the wings flap up and down.
- After spending 12 hours at -60 °C at cruise altitude, the fuel in the wing is very cold and only the lower wing skin is exposed to it. The upper wing skin is exposed to the sun, and upon approach gets warmed up more and more: upper skin stretches because of the heat, and the wing tip comes down by a surprising distance.
So all in all, the flight control cables must accommodate a difference in length that in a large aircraft is in order of magnitude of 10-20 cm. The control cable has a diameter of 3-5 mm. Steel elastic modulus is 200 GPa, a stretch of -0.2/70 m/m causes a tension of 500 MPa, twice that of structural steel, and a force of 4,000N (800 lb). Way too much. Yes you can increase the cable thickness with associated heaviness, but best to reduce the pre-load to the level where the non-pulling cable still has some tension.
We want some pre-tension in the cable loop, but not too much. We want it to not vary with varying length and bending, it must be always constant. And we want high differential stiffness: nice and easy springiness when not deflected, very high stiffness when deflected. What to do?
The solution is indeed in applying a spring, but not one that is attached to the aircraft structure:
- The "wheel" is not a multi-rotation unit, but two cable quadrants that deflect about 40 degrees each total.
- Springs pull them towards each other when no load is applied, when the pilot does not apply a force to the stick.
- A blocking mechanism prevents the two halves from moving relative to each other when the pilot does apply a force. A more detailed description is found in the image source above.
So while the flight controls are trimmed, the cable is tensioned nicely and accommodates varying circumstances. When forces are applied, this mechanism is partially blocked, only lightly when light forces are applied.