double hung pivot shoe

This looks like our 15-192. Note that the Simonton version of this shoe has a slightly different metal cam, so I'd swap your old one with the one in the new shoe to ensure pivot bar compatibility. Let me know if you have further questions. 

If you're referring to the shoe in the upper right corner of the picture showing pivot shoes on this page here, that is indeed the 15-192. Your shoe is damaged, but it's otherwise clearly the same design. This shoe does connect to coil balances, which are springs in the window jamb that regulate the movement of the window. If those parts are undamaged, you can just replace the pivot shoe. See the video below for more details.