This is definitely a Promethean install.
Promethean used to use a bespoke bracket which was made to fit specific projectors, they must have had a really good deal on them as they are a total pain. As Promethean no longer do installs the brackets are not actually made any more and I believe the company has gone out of business.
We have had a lot of schools who have had this issue as the direct replacement sanyo projector will not fit to the mount, however there is a plate that we have had made that will fit to the mount and allow you to fit a Sanyo XE32 directly on to it.
You could also use an in house method of attaching parts of other brackets to the mounts, that is how we used to deal with this issue.