A circle jig and small router with a bit the shape of the profile you want. The corner triangles are likely just templates, I can't make it out in the picture, but if the center circle is continuous, then the outside square perimeter is a simple framework with the circular piece glued in That makes all the other cuts just simple edge routing on straight pieces, and the curved portions all done with a circle jig. I think you want to keep this construction very simple. Remember, if you use a circle jig, you can work on a square piece of material, then you cut the square to match the edges of the circle, then frame that in using stock with the inside edge routed with the same jig. In a sense you are just framing the square stock you've produced with the circle jig.
Not all that complex to make on closer inspection. Circular work could be in MDF or glued up panels. The outer framing is any wood you want.
You will need to fabricate the corner triangles in pieces and then attach them to the main piece.All of the curved parts can be routed from the same center, even the curved part of the 4 triangles, but the part for the triangles will then need to be cut and joined to the two straight sides of the triangles.
You really are a friendly group of woodworkers! The accrued knowledge here is as amazing as I thought it would be.
The innermost circle (green) represents a picture, while the beige/light tan circle next to it is a cardboard matboard. The matboard fits inside and behind the routed inner opening. A piece of glass lays over the matboard and picture, too, but I digress.
The triangles terminate on the outside with a straight edge, so my guess is that this indicates the line of separation between an outer frame and an inner one. To my eyes, “lobes” of the outer circle (inner frame) are cut off, making the new outside of the circle even with the straight sides of the triangles. Then, the above mentioned outer frame is prepared with the inner dimensions equal to those of the outside dimensions of the “de-lobed”, squared off circle with triangles. The profile of the triangles themselves are the same on all three sides, but the two, straight sides are cut off – truncated - before the top bead.
As Tom suggested, I am joining a separate square with a large opening to that of another, smaller square that happens to have a circular opening in it.
Is my thinking too circuitous? (just kidding… sorry for my weak humor).
Can't be done from a single piece of material (at least not properly) IMHO. The circle is a routed circle - in solid work this would be 4 pieces jointed together with something like dowels. The edges where it meets the rectangular frame are planed flat to make a good joint (often held together using a loose tenon or loose tongue which is glued in place). The outside "frame" is simply made-up from mouldings applied around the edges of a rectangular board. The circular piece is planted onto this board The beadings in the corners are worked from solid stock (this will require a circle template or maybe two for the curved sections) and then cut to fit. Be aware that when joining a straight moulding to a curved one the cut is generally curved, not straight, in order to avoid steps, and so requires careful scribing to get it just right. Not that uncommon in Victorian buildings in my experience
Thank you for the feedback, Eric, Charley, Bill, Tom and Ross. Despite being raised in a woodworking family, I'm a router neophyte. But, the adage to divide and conquer seems fitting for this project. I did not route the sample in the images that I supplied, just tried to decode the construction method in order to create multiple picture frames in its likeness. The original frames a mirror attached to a dresser that has some MDF construction. Since I can't spot seams or joints, I assumed that the frame is of MDF with filler to even out the joints present. The back of the mirror appears to be one solid piece of MDF, but was likely laminated with the front-facing assembly. The paint is hiding a lot of information.
If I understand Eric correctly, creating an heirloom piece would involve some precision joinery, and I hadn't previously considered that possibility. Such a frame would be a beautiful architectural element in a Victorian house. (btw, I'm more jealous than you can imagine that Eric has the William Morris Red House to visit in Bexleyheath. My family visited Olana in the Hudson River Valley of New York last Summer, and we loved it.)
I can see now that my assumption that the corner triangles and circle could be routed out of a single piece of flat material was incorrect. The profile of the outside of the circle doesn't match the profile of the curved section of the triangles. My bad. The joint between the separately created triangles and the outside curve of the circle seems like the most demanding joint in the whole frame.
As Charley pointed out, the curved part of the triangles will need to use the same center as the circle, even though we're talking separate pieces of wood.
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