Depends on the age of your machine. Earlier "New Royal" machines were made by Free, though with a different design than other Free machines, and under more names than New Royal.
for later machines, "New Royal" was a badge and used by a few companies on their machines.
Older New Royal machines have a rectangular needle plate and the serial number is stamped on the base behind teh pillar. Only way to determine Model is visually.
http://www.quiltingboard.com/vintage...n-t263469.html
Here is a thread for a machine that turned out to be an older style New Royal. There are some pictures and links that may be helpful to determine what you have - BTW - I've also seen later Free made machines with the badge "New Royal" on them, but they are made from the Free design, not the New Royal design,