"Rust", a short story by Joseph E. Kelleam, also the answer to the old question Short story about robots wearing out and 'dying'; first published in Astounding Science Fiction, October 1939, available at the Internet Archive. It has appeared in a few anthologies; I'm going to guess that you read it 40 years ago in The Great Science Fiction Stories Volume 1, 1939, an anthology edited by Isaac Asimov and Martin H. Greenberg.
The story is about 2 war robots who have survived a war that wiped out humanity world-wide.
"L-1716," whispered X-120, "do you think there are any men left in the world?"
"I don't think so. Remember, the Great War was general, not local. We were carried to all parts of the earth, even to the smallest islands. The robots' rebellion came everywhere at almost the same time. There were some of us who were equipped with radios. They died first, long ago, but they talked with nearly every part of the world." Suddenly he wearied of speech. "But why worry now. It is spring. Men made us for killing men. That was their crime. Can we help it if they made us too well?"
I have a mental image of a roughly spherical body with 3 short legs underneath and 2 long arms, terminating in long claws, at opposite points on the midline. The limbs were segmented, like flexible tubing.
He and his companions were highly developed robots, the last ever to be made by the Earthmen. X-120 consisted of a globe of metal, eight feet in diameter, mounted upon four many-jointed legs. At the top of this globe was a protuberance like a kaiser's helmet which caught and stored his power from the rays of the sun.
From the "face" of the globe two ghostly quartz eyes bulged. The globe was divided by a heavy band of metal at its middle, and from this band, at each side, extended a long arm ending in a powerful claw. The claw was like the pincers of a lobster and had been built to shear through metal. Four long cables, which served as auxiliary arms, were drawn up like springs against the body.
One of the robots is more thoughtful than the other and realises that if they can't find a way to repair themselves they will eventually run down. It tries to construct a smaller robot with hand-like manipulators instead of the claws they were built with for killing.
X-120 stood in the broken street, and the sunlight made a shimmering over his rust-dappled sides.
"This is where we have failed," he mused as he looked at his clawlike arms. "We have tried to make robots like ourselves. Men did not make us for life; they fashioned us for death." He waved his huge lobster claw in the air. "What was this made for? Was it made for the shaping of other robots? Was it made to fashion anything? Blades like that were made for slaughter—nothing else."
"Even so," whined the crippled robot, "I have nearly succeeded. With help I can win."
"And have we ever refused to help?" snapped L-1716. "You are getting old, G-3a. All winter you have worked in that little dark room, never allowing us to enter."
There was a metallic cackle in G-3a's voice. "But I have nearly won. They said I wouldn't, but I have nearly won. I need help. One more operation. If it succeeds, the robots may yet rebuild the world."
Reluctantly, X-120 followed the two back into the shadowy ruins. It was dark in there; but their round, glassy eyes had been made for both day and night.
"See," squeaked old G-3a, as he pointed to a metal skeleton upon the floor. "I have remade a robot from parts that I took from the scrap heap. It is perfect, all but the brain. Still, I believe this will work." He motioned to a gleaming object upon a littered table. It was a huge copper sphere with two black squares in a tarlike substance set into it. At the pole opposite from these squares was a protuberance no larger than a man's fist.
"That," said G-3a thoughtfully,"is the only perfect brain I could find." You see, I am not trying to create something; I am merely rebuilding.
** Making the critical linkage, its claw accidentally causes a short circuit, slagging the brain and destroying the robot.**
Clumsily he lifted the copper sphere and its cluster of wires from the table. He worked slowly and carefully. One by one the huge claws crimped the tiny wires together. The job was nearly finished. Then the great pincers, hovering so carefully above the last wire, came into contact with another. There was a flash as the power short-circuited. X-120 reeled back. The copper sphere melted and ran before their eyes.
In the final scene, the 2 robots are trudging through snow, one of them trailing its no-longer-functional arms. Its arms snag on an unseen rock and it falls. It doesn't get up, and the other walks on.
The elusive spring had changed into a more furtive summer. The two robots were coming back to their hall on an afternoon which had been beautiful and quiet. L-1716 moved more slowly now. His broken cables trailed behind him, making a rustling sound in the dried leaves that had fallen.
Two of the cables had become entangled. Unnoticed, they caught in the branches of a fallen tree. Suddenly L-1716 was whirled about. He sagged to his knees. X-120 removed the cables from the tree. But L-1716 did not get up. "A wrench," he said brokenly; "something is wrong."
A thin tendril of smoke curled up from his side. Slowly he crumpled. From within him came a whirring sound that ended in a sharp snap. Tiny flames burst through his metal sides. L-1716 fell forward.
And X-120 stood over him and begged, "Please, old friend, don't leave me now." It was the first time that the onlooking hills had seen any emotion in centuries.
[. . . .]
And the snow fell, slowly and silently, until only a white mound showed where X-120 had been.