Transfer your webcam video sream signal so it can be streamed from a different computer

If you are familiar with software like teamviewer or Logme (for remote control of a computer), you can better understand this project. Imagine you are in computer A and connect to computer B, now basically the idea is that you transmit your webcam signal from computer A to B, so you stream into several websites in computer B but using the webcam stream from computer A. Normally teamviewer or Log me in do not allow this. Now ideally i want to do this in a server, so people can connect to their computers and send the webcam signal to a server in the server they can connect to several websites that use this signal from their comuters, and the signal is split in the server so it can be used in several websites. All these websites require login credentials