An adjustable desk lamp can be moved to any position in its range and simply left there. There is no lever to lock, no notch to find, no screw to tighten after each adjustment. That behaviour is not a consequence of stiff joints. A joint stiff enough to hold the head by friction alone would need both hands to move. What actually holds the lamp is a balance: a spring almost exactly cancels the turning force of the head, and a small, constant friction takes care of whatever is left over.
Start with the weight. A lamp head on the end of a horizontal arm produces a turning force at the shoulder joint, and that force grows as the head is pushed farther out. Reach for a book, move the head forward, and the joint has more to resist. A fixed spring would help at one position and be wrong at every other. The lamp's spring is arranged so that its own leverage grows along with the head's leverage — as the arm swings, the spring is stretched or twisted through a geometry that makes its opposing force rise in roughly the same proportion. Across the working range, the two nearly cancel.
What the friction joint is for
Nearly is the important word. Casting tolerances, a slightly heavier shade, a different bulb: any of these leaves a small residual turning force in one direction or the other. The hinge is built with a stack of friction discs and a spring washer under a clamping screw, which applies a steady preload. Friction does not care which way the residual force points; it simply resists motion up to a certain threshold. As long as that threshold is larger than the residual, the arm stays put.
This is why the adjustment feels damped rather than notched. Push harder than the friction threshold and the arm moves smoothly; let go and it stops immediately. Deliberately overtightening the screw makes the lamp hard to move but does not make it hold better — the spring is already doing the holding, and the screw only sets the margin. Undertighten it and the residual force wins: the head begins a slow, unmistakable droop over the course of an evening.
That slow droop is the most common failure, and the diagnosis is nearly always the friction stack rather than the spring. Discs wear, the washer loses some of its preload, and the joint's threshold drifts below the residual torque. A quarter turn of the clamping screw often restores years of service. A spring that has genuinely tired would show a different symptom: the lamp would feel heavy in the hand and pull downward at every position, not just at one.
Why there are two joints
A single joint can only move the head along one arc. Extend it and the head rises and tilts, aiming the beam into the user's eyes rather than at the desk. Two linked joints let the arm fold and reach while keeping the head roughly level: one segment changes height, the other changes reach, and the head's angle is preserved by the parallelogram-like arrangement or by a small extra link. Position and direction are separated, which is the whole point of the arm.
The cable is part of the same problem. It has to cross every moving joint, so at each hinge it is given a loop or a slack turn. A cable pulled tight will be bent at exactly the same point on every adjustment, and the copper strands there work-harden and break one by one. That is the same mechanism that makes a charging cable fail just behind its plug: the strain is concentrated at the place where a stiff part meets a flexible one. Giving the cable room is cheaper than trying to make it stronger.
Even the base is doing balance work. The spring cancels the head's turning force at the joint, but it does not make the weight disappear; it redirects where the reaction goes. The whole lamp still has to keep its combined centre of mass inside the footprint of the base, which is why the base is a heavy disc rather than a light clip. Reach too far and the balance is lost no matter how well the joint holds.
Compare a folding chair, which is pushed a few degrees past its dead centre and then held by the load itself. That is a two-position device: fully open or fully folded, with nothing stable in between. The lamp arm is the opposite choice — stable everywhere in a continuous range — and it pays for that with a spring, a friction stack and a little routine maintenance. Both are honest answers to the same question of what should happen when the hand lets go.
Heat is the last constraint on the head, and it is why the head is light enough for this trick to work at all. Where an LED bulb sends its heat decides how much metal the head needs, and that mass feeds straight back into the spring calculation. A heavier head would need a stronger spring, a stiffer joint and a heavier base. The whole arm is one equation with the bulb at one end and the weight on the desk at the other.