Flex Connector
A flex connector is used primarily to take the stress off pumps and motors when noise absorption, vibration, or thermal growth may happen. Also if you did not engineer or install the equipment properly it can allow minor alignment to happen. Which is not the idea. The coupling is a stainless steel corrugated hose with stainless steel braid and comes in all sizes and lengths. Both ends do not have to be the same.
Flex connector connected to a pump 
Flex connected stainless steel braid 
Flex connector flange 
Inside look at stainless steel corrugated connector
FLEX CONNECTOR DATASHEETS
- Flex Connector Datasheets
- Flex Connector - Hose Length for Degree of Bend Datasheets
- Flex Connector - Hose Length for Length of Motion Datasheets
- Flex Connector - Temperature Correction Factor Datasheets
