gifCompound Mitres

Edge Type Struts

If a strut end has been projected onto the hub intersection plane, then it is necessary to know the bevel and/or mitre angle for the saw. If the strut end has both a bevel and mitre angle, then a “compound mitre” cut is required.

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Pivot Angles of Saw

The standard mitre power saw has two pivots of rotation - one for the bevel and one for the mitre:

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Bevel Angle

The bevel is a cut through the depth of the strut.

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The dotted lines represent the disc of the saw, shown edge on. When the angle is acute, the bevel angle is 90°-alpha. When the angle is obtuse, the bevel angle is beta-90°. The bevel angle is rarely obtuse, and when this occurs, you will be warned in the Log. In either case, Geodesica gives the Delta angle to set on the saw, so no calculation is required.

NOTE: The diagram shows a cut on the LEFT end of a strut; when cutting on the RIGHT end of a strut, the Obtuse and Acute directions are reversed, so the saw swings in the opposite directions.

Mitre Angle

The mitre is a cut through the width of the strut.

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The dotted lines represent the disc of the saw, shown edge on. When the angle is obtuse, the mitre angle is 180°-beta. The mitre angle is rarely obtuse, and when this occurs, you will be warned in the Log. In either case, Geodesica gives the Delta angle to set on the saw, so no calculation is required.

Analyse Strut

Swith to the ANALYSE tab and choose the Strut select tool. Click on a strut. The cutting angles for compound mitres are displayed in the log window. As an example, here is the log output for a strut of a seed Icosahedron with hub intersection ON and the strut ends projected to the bottom discs of the Cylindrical hubs (not shown):

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<----------------------------------------------------->
TsQEIcosahedron
  Primal_S_A

 STRUT
  Scale Factor = 10.000000000
         Units = Feet and Inches
   Using Strut Length: center line of strut.
  Strut Label: ?
  Strut   QE_ID: 11
          UN_ID: 4775
          Length =  9.880584565 Feet or 118.567014780 Inches.
    Org   QE_ID: 3
          UN_ID: 4623
    Dest  QE_ID: 2
          UN_ID: 4617
     Left face QE_ID: 1
               UN_ID: 4611
    Right face QE_ID: 3
               UN_ID: 4647

  Dihedral Orbit Info for Strut QE_ID: 11
                                UN_ID: 4775
  Circumflex = NO.
  Dihedral = 138.18968510
           = 138° 11' 22.8663752"

     Theta = 69.09484255
           = 069° 05' 41.4331876"

     Sigma = 20.90515745
           = 020° 54' 18.5668124"

      Beta = 110.90515745
           = 110° 54' 18.5668124"


  Cutting info for Strut QE_ID: 11
                         UN_ID: 4775

  Compound angles at ORG:
    Org Bevel is OBTUSE.
    Org Bevel Alpha = 148.28252559
                    = 148° 16' 57.0921187"

    Org Bevel Delta = 58.28252559
                    = 058° 16' 57.0921187"

    Org Mitre Alpha = 90.00000000
                    = 090° 00' 0.0000000"

    Org Mitre Delta = 0.00000000
                    = 000° 00' 0.0000000"

  Compound angles at DEST:
   Dest Bevel is OBTUSE.
   Dest Bevel Alpha = 148.28252559
                    = 148° 16' 57.0921187"

   Dest Bevel Delta = 58.28252559
                    = 058° 16' 57.0921187"

   Dest Mitre Alpha = 90.00000000
                    = 090° 00' 0.0000000"

   Dest Mitre Delta = 0.00000000
                    = 000° 00' 0.0000000"
<----------------------------------------------------->

The Dihedral Orbit angles Theta, Sigma and Beta are explained on this page.