Oblique & Skewed Joints#

Oblique tenons between splayed legs and skewed crossing members

Names: cross_lap tilt heading

When to use#

• A diagonal member between two legs: a hayrake or splayed stretcher, a raked brace. Tenon each end into the leg face at the member's own slope.
• Two members crossing at an angle in one plane (the X of a hayrake, a St Andrew's cross): halve them into each other with a cross_lap.
• A compound mitre at the corner of a splayed or canted frame, when both boards are mirror images across the mitre plane.

Not covered: a skewed bridle (unsupported), crossings shallower than 15° (error), and a coped shoulder to a curved surface (the shoulder is flat on the tangent plane, standing off the curve; ADR-0027).

Syntax#

• Oblique tenon: an ordinary mortise_and_tenon. The male mark is on the member's end face; the member is placed with rot y= at its slope. The tenon runs along the member as placed, may meet the female face up to 45° off square, and the shoulder is scribed flush to that face.
• Skewed crossing: an ordinary cross_lap (or half_lap). Marks sit on the shared cheek and face each other. Each member is notched to the parallelogram the other casts on the cheek. Keep depth_ratio agreeing with the mark depth.
• Compound mitre: an ordinary miter; angle is checked as for a plain mitre.
• tilt= / heading= on a mark orient a mark that is on no stock face (a turned surface's tangent). A mark on a stock face needs neither.

Example#

project name="Hayrake" units=mm schema_version=1 {
    materials { material Oak type=hardwood }

    component LegLeft {
        stock Oak 34.0 34.0 230.0
        mark RailHigh x=34.0 y=17.0 z=-40.0 normal=pos_x
        mark RailLow  x=34.0 y=17.0 z=-190.0 normal=pos_x
    }
    component LegRight {
        stock Oak 34.0 34.0 230.0
        mark RailHigh x=0.0 y=17.0 z=-40.0 normal=neg_x
        mark RailLow  x=0.0 y=17.0 z=-190.0 normal=neg_x
    }
    component Brace {
        stock Oak 250.0 19.0 30.0
        mark Lap x=125.0 y=9.5 z=-15.0 normal=pos_y
        mark TenonStart x=0.0 y=9.5 z=-15.0 normal=neg_x
        mark TenonEnd x=250.0 y=9.5 z=-15.0 normal=pos_x
    }
    component BraceBack {
        stock Oak 250.0 19.0 30.0
        mark Lap x=125.0 y=9.5 z=-15.0 normal=neg_y
        mark TenonStart x=0.0 y=9.5 z=-15.0 normal=neg_x
        mark TenonEnd x=250.0 y=9.5 z=-15.0 normal=pos_x
    }
    joinery cross_lap name=Lap {}
    joinery mortise_and_tenon name=RailTenon {
        tenon_thickness 8.0
        tenon_width 20.0
        tenon_length 20.0
        clearance 0.0
        centering axis=z
    }

    assembly Frame {
        part LegL instance=LegLeft {
            by top_center
            pos x=17.0 y=17.0 z=0.0
        }
        part LegR instance=LegRight {
            by top_center
            pos x=251.0 y=17.0 z=0.0
        }
        part Lower instance=Brace {
            by center
            pos x=134.0 y=17.0 z=-115.0
            rot y=36.8699
        }
        part Upper instance=BraceBack {
            by center
            pos x=134.0 y=17.0 z=-115.0
            rot y=-36.8699
        }
        join joint=RailTenon male=Lower@TenonStart female=LegL@RailHigh
        join joint=RailTenon male=Lower@TenonEnd female=LegR@RailLow
        join joint=RailTenon male=Upper@TenonStart female=LegL@RailLow
        join joint=RailTenon male=Upper@TenonEnd female=LegR@RailHigh
        join joint=Lap male=Lower@Lap female=Upper@Lap
    }
}

The inside faces of the legs are 200 apart and the tenon marks 150 apart in height, so each brace is exactly 250 on its centre line and leans 36.8699° (a 3-4-5 run). Compiled: five joins synthesised, no clashes (docs/styles/models/hayrake-stretcher.kdl is the same model).

Pitfalls and diagnostics#

• faces-overlap, "shallower than the 15°": the members cross at less than 15°. Move them apart, or make the slope steeper.
• unsupported on a bridle: a skewed bridle is not laid out; use a cross_lap or half_lap.
• corner, "a compound mitre, and the boards are not mirror images": the two boards' sections on the mitre plane differ by the stated mm. Give both the same section and lean.
• Shoulder gap on a round leg: a tenon into a turned surface has a flat shoulder on the tangent plane, so it stands off the curve. Put the tenon on a flat (the square pommel).
• The tenon must lie within 45° of square to the female face, and centering axis= checks that the mark is centred on the member.
• Both lap members' marks must lie on the cheek and face each other, or the join is rejected (facing / contact).

See also#

• docs/rfc/0142-oblique-tenon-between-legs.md, docs/rfc/0144-skewed-crossing-joint.md, docs/adr/0027-oblique-and-skewed-joints.md, RFC-0022 (oriented marks).
• docs/KDL_AUTHORING.md §7 (tenons, laps, bridles and mitres) and the mark section.
• crates/ww-build/tests/oblique_skewed.rs for the measured geometry.

Names#

Every name this page declares, how the example library uses it, and the shortest real use.

cross_lap#

joinery kind; value in 3 of 116 examples (3 uses).

Shortest real use, from mid_century_slat_bench.kdl:

joinery cross_lap name=SlatLap {
    depth_ratio 0.25
    clearance glue_clearance
}

tilt#

property; property in 2 of 116 examples (6 uses).

Shortest real use, from primary_grid_lath_armchair.kdl:

mark Seat x=0.0 y="lath / 2.0" z="0.0 - dm" normal=neg_x tilt=0.01 heading=0.0

heading#

property; property in 2 of 116 examples (6 uses).

Shortest real use, from primary_grid_lath_armchair.kdl:

mark Seat x=0.0 y="lath / 2.0" z="0.0 - dm" normal=neg_x tilt=0.01 heading=0.0

Related terms#

• Cross-lap joint
• Half-lap joint