Re: What is the real name of a Hag's Tooth Plane?
Derek Cohen (in Perth, Australia)
A Hag's (or Old Woman's) Tooth plane is the predecessor to the router plane, but it is not quite the same. Abreviated to OWT for political reason 

This is the classic OWT. It is made with a plough ("plow" in non-English speaking countries) plane blade, and not the more familiar L-shaped blade found on modern router planes made by Stanley, Record, Veritas and Lie Nielsen.
The OWT is an example of how a workman might re-use existing tool parts. I imagine that the blades given to Barry were plough plane blades. If so, these require a different design to a wooden router plane, such as the ones I have built, as shown in the link provided by William.
This is one I made for a Wood Central auction ...

This uses the Veritas blades.
Note that the angle of the L-shaped blade allows the foot to cant forward to create a relief angle below. It would stop cutting if parallel to the surface of the wood.
For those wishing to sharpen a current router plane blade, I developed a technique which will ensure the sharpest of edges. Maintainng the edge is really easy. The article is here: http://www.inthewoodshop.com/WoodworkTechniques/SharpeningRouterPlaneBlades.html
Vic Tesolin recently made a video of the method:
https://m.youtube.com/watch?v=cuNu-GlgH88
Regards from Perth
Derek