When two weavers of equal width cross at an angle, say 2θ, their area of overlap is a rhombus. If the weavers are thin enough that the engagement windows of their oblique locked crossing can be approximated as points, those four points also form a rhombus (dotted lines in diagram above) that shares the same diagonal lines as the former, but with angles slightly different—assuming the radius, r, at the bottom of the notches is not zero.
In the diagram, weavers are only indicated out to the width, 2h, where the centers of the notch radii are located. The point where the centerlines of the two weavers cross makes a natural origin for the diagram; in particular, we choose the perpendicular to the centerline at that point on our chosen weaver (the gray one) to define the line of x = 0 for our coordinates. Taking h, r, and θ as given, the geometric problem is to find the x-coordinates of the centers of the four holes (the geometry of the other weaver will be simply the mirror image of this one.)
The solution requires repeated use of trigonometric identities for geometrically similar right triangles, all having acute angles of θ and 90°-θ. Such an analysis yields these expressions for the marked dimensions indicated in the diagram:
xL = r/cosθ
xR = r/sinθ
sL = htanθ
sR = h/tanθ
The x-coordinates of the circle centers on the inner edge (upper edge in the diagram) can then be calculated from:
xL = cL - sL
xR = sR - cR
For the circle centers on the outer edge, just multiply by -1.
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