Based on my previous thread : RVM installed by Ruby not working? where i had installed RVM using the root user, I then had to entirely remove the RVM install and now i am in
If you first installed RVM as root and then uninstalled it. And now you are trying to install it as a non sudo user and you're getting the following error:
mkdir: cannot create directory `/usr/local/rvm': Permission denied
Make sure that you have logged out of the root session before trying to install under the user.