Why can no machine ever run forever without being fed energy?

No machine can run forever without being fed energy because energy itself can't be created from nothing: it can only move from one form into another. The first law of thermodynamics is a formulation of the law of conservation of energy, and it means that in an isolated system, the total of all forms of energy stays constant no matter how it's shuffled around internally. People have sketched such machines since the Middle Ages, like Bhaskara's 12th-century wheel with weights that shift outward on one side, but none can escape that rule.

An equivalent, more practical way to say this is that perpetual motion machines of the first kind are impossible. Any time a system does work on its surroundings, it has to spend some of its own internal energy to do it, and that spent energy has to be resupplied from outside, as heat or as work, if the machine is going to keep running. There's no way around it: a machine that produces more energy than it's given, forever, would be creating energy from nothing.

This idea took shape through careful experiments. From 1842 to 1845, James Prescott Joule, who managed his family's brewery, measured what's called the mechanical equivalent of heat: how much mechanical work it takes to produce a unit of heat. In one of his setups, he generated heat by rotating a paddle inside a vat of water. In 1845 he published his results in a paper called The Mechanical Equivalent of Heat.

Joule wasn't working entirely alone in this direction: around the same time, in 1842, Julius Robert von Mayer measured a temperature rise caused by friction in paper pulp, pointing at the same underlying truth from a different angle. By 1850, Rudolf Clausius and William Rankine had both published the first full, formal statements of the law. Once that work was done, the free-running, self-sustaining machine was no longer a question of better engineering. It was ruled out by the basic bookkeeping of energy itself.