I am not fortunate enough to have a CMC, but several years ago we had a run on these “clock mats”, so we had to do these on an antique, coal burning Oval Master.
Much of my knowledge of trig and geometry has long since evaporated, so I cannot remember exactly the math that went behind this (I remember it got complicated, though) but, at least, I saved several templates.
These angles will work for any center mat as long as the horizontal and vertical diameters have a two inch difference e.g. 4 x 6, 5 x 7, 8 x 10, etc.
The placement of the small wallet sized photos (typically 1-1/2 x 2” in our area) cannot be placed on an imaginary line (the dotted line in this illustration) which also has the same two inch horizontal/vertical displacement. Rather you must adjust this horizontal diameter downward by the difference in the diameters of the wallet sizes so that the edge differences between the 12 o’clock and 3 o’clock positions are the same.
For example, if we have a 5 x 7 center photo and would ordinarily place the small wallet photos (1-1/2 x 2) on an imaginary circumference of 8 x 10, we would have to adjust this imaginary line to 7-1/2 x 10". (8 – [ 2 – 1.5 ] ) or (8 – 0.5). So this imaginary dotted line would have an oval of 7-1/2 x 10.
We’re lucky enough to have Adobe Illustrator to help us with laying out these templates on paper, but nearly any drawing program will do. We place these paper templates over the mat board and make a dimple in the center of each oval we need to cut. We generally only draw the center oval, 12 o’clock, 1 o’clock, 2 o’clock and 3 o’clock ovals, then rotate the paper template to get the 6, 7, 8 and 9 o’clock positions keeping the large central oval as an anchor point. Once that is done we flip the paper over and repeat for the 4 and 5 o’clock ovals, and rotate the paper once again to get the centers of the 10 and 11 o’clock ovals.
Depending upon my mood and ambition, I will either use trig to determine the horizontal and vertical stops for the OvalMaster, or, more likely, simply measure the horizontal and vertical placements of the dimples on the mat itself and set the Oval Master accordingly.
I also had a template for three inch differences (like for 9 x 12” and 11 x 14” center ovals), but we seldom used it since the whole mat got outrageously large.