Valley Rafter with single Sprocket

This task model still needs a lot of work. However, it was a lot of work just  to draw the 3D model. So I could check the geometric lines of my drawing. There's a lot going on to draw out the Valley Sprocket Rafter. I haven't even gotten to the claws on the jack rafters, but that shouldn't be hard to draw.
















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Layover Valley Rafter Basics

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Before I get into the Hexenschnitt for the Layover Valley Rafter I needed to review the basic geometry that defines the layover valley rafter. I needed to make sure I could draw the layover valley rafter correctly in plan view (ground plan). Here's one method of a basic drawing using the layover valley rafter backing triangle to position the layover valley rafter material on the roof surface that defines the  layover valley rafter in plan view. The  layover valley rafter top bevel is easily defined by extending the  layover valley rafter backing triangle to the top of the  layover valley rafter. The other  layover valley rafter line in plan view is defined by the bottom edge of the  layover valley rafter material sitting on the  layover valley rafter backing triangle. (Roof Surface). The  layover valley rafter plan view lines at the intersection of the two roofs. I tried this method for drawing the  layover valley rafter, but this method...
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Hip Rafter Edge Bevel and Backing Angle

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In complex roof framing there are 7 main roof framing angles. Hip Rafter Backing Angle Valley Sleeper Bevel Angle Plain Titl (DP) Main Plan Angle Adjacent Plan Angle  Main Profile Rafter Slope Angle Adjacent Profile Rafter Slope Angle In this article I will discuss the hip rafter backing angle and the valley sleeper bevel angle. These two angles determine the miter angle and and saw blade bevel angles for jack rafters and purlin rafters that are plumb to the earth and for jack rafters and purlin rafters that are skewed from the eave line. A thorough knowledge of these two angles is critical in complex roof framing using geometry or trigonometry. The hip rafter edge bevel was avoided in the 12th century on some roof structures by rotating the hip rafter into the roof surface plane. However, by avoiding the hip rafter edge bevel, the carpenters-builders had to have a knowledge of the Valley Sleeper Bevel Angle. They didn't call it the Valley Sleeper Bevel Angle, but it's the same...
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Layover Valley Rafter Hexenschnitt #3

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In the book Das neue Buch vom alten Wissen der Schiftung The new book on the ancient knowledge Schiftung The new book on the ancient knowledge Roof Framing The new book on the ancient knowledge Roof Framing Geometry by Bernd Küppers I'm stuck on page 23. The geometry in the book, just doesn't return the correct miter angle for the Layover Valley Rafter Witches Cut (Hexenschnitt). I don't know if I'm drawing it incorrectly, or the BE (Bottom Edge Plane of the Layover Valley Rafter) should be drawn differently. Similar drawing at File: Kehlbohle mit Hexenschnitt.jpg There's 3 canted planes that define the Layover Valley Rafter Witches Cut Miter Angle. The main roof surface, the square tail fascia plane of the main roof and the the square tail fascia plane of the adjacent roof.  I think the problem with my geometric drawings is defining the intersection of the roof surface with the adjacent  square tail fascia plane.
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