Multi-stage compressor and air conditioner having a linkage between the vanes of the different stages

A multi-stage compressor, comprising

• a first-stage cylinder comprising a first-stage compression cavity and a first vane disposed in the first-stage compression cavity;
• a second-stage cylinder comprising a second-stage compression cavity and a second vane disposed in the second-stage compression cavity, and a refrigerant flowing out from the first-stage compression cavity enters the second-stage compression cavity;
• a linkage structure disposed between the first vane and the second vane, so that the second vane is capable of moving with a movement of the first vane and maintaining contact with a roller in the second-stage compression cavity, wherein the linkage structure comprises a connecting rod, a first sliding groove, a first pin shaft, a second sliding groove, and a second pin shaft, the connecting rod is rotatable, tone of the first sliding groove and the first pin shaft is located on the connecting rod, the other of the first sliding groove and the first pin shaft is located on the first vane, one of the second sliding groove and the second pin shaft is located on the connecting rod, and the other of the second sliding groove and the second pin shaft is located on the second vane;
• and
• a partition plate disposed between the first-stage compression cavity and the second-stage compression cavity, wherein the connecting rod is pivotally connected with the partition plate through a third pin shaft, the first sliding groove and the second sliding groove are respectively located on two sides of the third pin shaft, the first pin shaft extends through the first sliding groove and the first vane, and the second pin shaft extends through the second sliding groove and the second vane;
• wherein the first sliding groove and the second groove are located on the connecting rod, a projection of an axis of the first pin shaft on the first vane is located at an axis of symmetry of the first vane, and/or the projection of an axis of the second pin shaft on the second vane is located at an axis of symmetry of the second vane;
• a distance H between an end of the first sliding groove adjacent to the third pin shaft and an end of the second sliding groove adjacent to the third pin shaft and a thickness h of the partition plate satisfy:
• H<h.