Postingan

Menampilkan postingan dari April, 2014

Roof Framing Geometry Propositions – Axioms #3

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Added a new Axiom to the Roof Framing Geometry Propositions. This one is for two rotated hip rafters for the angle on the bottom of the intersecting hip rafter. Roof Framing Geometry Proposition – Axioms # 7: A line from the intersection of the DP lines of two Hip Rafters, "a", to the hip rafter slope line "b" following the DP line, with a length equal to an arc length of the side face of the hip rafter lower claw length will determine point "c", for the angle on the bottom of the rotated hip rafter. Unfolded pattern for the head cut on the rotated hip rafter intersecting the rotated hip rafter.

Roof Framing Geometry Proposition – Axioms #2

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Using my Roof Framing Geometry Proposition – Axioms, it's like taking candy from a baby for laying out the geometry that defines the upper and lower claw angles on purlin rafters and jack rafters that tie into rotated hip rafters. Like Joe said, The Mazerolle Code has been broken. Purlin Rafter unfolded. You need 6 angles  and 2 dimensions to layout the unfolded template for the purlin rafter.  Jack Rafter Unfolded.You need 3 angles  and 1 dimension to layout the unfolded template for the jack rafter.  The roof surface angles was obtained from the drawdown method of the roof surface.

Joe Bartok's 2014 Studies

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Here's a picture of the studies for the winter of 2014 by Joe Bartok. Joe's studies include the Golden Rhombus, Golden Rhombus Parallelogram, Trèteaux Angles -- Trestle Angles -- trèteau à devers, Devers De Pas -- DP Line, trait carré -- TC, when hips collide, rotated rafters, rotated hip rafters, Warlock Cut, Warlock Rhombic, Non-Rectangular Sections, Pentahedron and Non-Rectangular Sections, Trirectangular Tetrahedron, Raccord--Origami 3D models all with upper and lower claw angles.   There's been a lot of trigonometry in Joe's studies, but there's also been a lot of geometry in his drawings leading up to his cardboard models. It was from his geometry, that he developed on his own, without looking at the French or German books, that some of my Roof Framing Geometry Proposition – Axioms were based on. The German Dachstuhlbau geometrie method or the 'Art du Trait', developed in the 13th century by the French are all based on stereotomtic principles develope

Principles Du Devers Traite A LA Sauterelle

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I was checking my Roof Framing Geometry Proposition – Axioms against Patrick Moore's Principles Du Devers Traite A LA Sauterelle drawing on this page at Historical Carpentry . My Roof Framing Geometry Proposition – Axioms work with his techniques for Devers De Pas, but mind require a rafter depth to determine some of the lines. Patrick's techniques are in theory only in that drawing, showing the principles of the art of line. No width or depth of the rafters are required for his drawing. Drawings showing the difference between the Principles Du Devers Traite A LA Sauterelle techniques and the techniques for using the Roof Framing Geometry Proposition – Axioms. Sauterelle means using a bevel square to transfer the angles from the geometric layout to the timber. Drawing showing the basic geometric layout of the roof. In this example I used a 90° eave angel with equal profile rafter slopes of 45°.  Adding the DP lines for the rotated hip rafter. Establishing the vertical plane

Warlock Rhombic

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Joe Bartok's study on 3 rotated intersecting rafters using ,  Euclidean geometry (geometry in flat space, 2D drawings that helped develop the Roof Framing Geometry Proposition – Axioms) and analytical geometry (geometry on a coordinate plane using trigonometry). _______________________________________________________________ warlock_rhombic_nr_solution.pdf warlock_rhombic_javascript_solution.pdf – find the angles and dimensions to DP lines, complete calculations with Law of Cosines – solve as for rectangular section with Compound Angle Formulas, apply bevel with Non-Rectangular Section calculator – solve angles with only the Roof Framing and Joinery Calculator _______________________________________________________________