Layover Valley Sleeper Lower Claw

Quote from
Stéphane Verboomen , Brussels Belgium, that I'm following on Facebook.

Only the study of geometry in three dimensions allows carpenters to solve difficult problems with the layout of parts or components implemented in complex joints in carpentry. It corresponds to a real intellectual process that develops the faculty of imagining the planes  and intersection of these planes in complex joints in 3D space.

It think it should be re-written to say:

Only the study of geometry in three dimensions allows carpenters to solve difficult problems with the layout of parts or components implemented in complex joints in carpentry. It corresponds to a real intellectual process that develops the faculty of imagining the canted planes  and intersection of these canted planes in complex joints in 3D space.

I started another task model from Bernd Kuppers book "The new Book on the Ancient Knowledge of Roof Framing".  The Shadow Line technique for developing the intersection of canted planes from Bernd's book , makes the intellectual process a whole lot easier. The French technique of using the Devers De Pas method could have been used, but the Shadow Line technique is 100 times easier to use and it's easier to remember.

Valley Sleeper on Nonrectangular Ground
Kehlbohle auf unwinkligen Ground

I wanted to study this task model for the geometry of the witches cut on the Layover Valley Sleeper on the Non Rectangular Ground plan. I also wanted to change the canted rafter to a canted jack rafter that intersects the layover valley sleeper to study the geometry for the lower claw on the canted jack rafter. The witches cut on the layover valley sleeper wasn't that challenging, but the geometry for the lower claw on the canted valley jack rafter was.

The task model doesn't look all that hard to draw the geometric lines that define the different cuts, but it was hard to develop all the lines for the 3 different folding roof surface planes and keep track of what line does what. I was able to develop the lines on the folding roof surface plane for the lower claw on the valley jack rafter using the Shadow line technique.

The first step was developing the layover valley sleeper footprint in ground plan. I drew the main folding roof surface plane and then drew a line parallel to the valley rafter on the main folding roof surface plane the width of my layover valley sleeper. (5 .5" on the left side of my task model and 3.5" on the right hand side of the task model.) The intersection of the main eave line and the parallel line the width of the layover valley sleeper defines one of the 4 corners of the layover valley sleeper footprint in ground plan. It also defines the corner for the edge of the layover valley sleeper in plan view. Using the Shadow line technique with the edge of the layover valley sleeper in plan view develops the fourth corner for the footprint. The other two corners of the  layover valley sleeper footprint in ground plan are developed from the  layover valley sleeper in profile.


Picture of the task model drawing, showing the development of the layover valley footprint.

 3D drawing of the task model with the canted valley jack rafter.

The lower claw on the valley jack rafter that I wanted to study.

Basic technique for developing the folding roof surface plane lines for the lower claw on the canted valley jacker on the layover valley sleper.

Drawing with all 3 folding roof surface plane lines.

3D drawing showing the folding roof surface plane lines used for the upper and lower claw lines on the canted valley jack rafter.

I need a control file to make sure the technique worked with all layover valley sleepers. So I tested the technique for developing the lower claw  on an unequal pitched roof with a rectangular ground plan. The main difference here in this drawing compared to the task model is making sure you extend the shadow line to the adjacent eave line.