This step describes the thought process when designing the jig. Since the construction is quite flexible, motivating some of the choices made could be useful for the modifiers. Skip to the next step if you just want to get on building the jig.
Why aluminium profile?
It is light, strong, stiff, robust, heat resistant, machinable, weldable, corrosion resistant, easily available and accurate. On the downside, it can be considered a bit expensive compared to wood or traditional metallic square profiles.
Why 1000 mm long?
For the sake of simplicity. One could manage with shorter ones and they don't all have to be equal in length. The wheelbase of regular bicycles is around 1000 mm, so with the front fork left out and the frame slightly rotated, 1000 mm is a suitable width. The height of the jig could be reduced, but we wanted to use integrated seat tubes on some of our designs and wanted to leave some room for that.
Why is the rear axle fixed and positioned like it is?
Making the bottom bracket fixed would have required space for adjustment at both ends of the jig. Fixing the rear axle saves space. In addition, attaching the profile holding the rear axle flush with the supporting (horizontal) profiles situates the centre line of the frame nicely relative to the planes of the rear drop outs.
The 250 mm position (from the bottom) for the rear axle is chosen because it allows ample room for bottom bracket height adjustment for all conventional frame geometries, but keeps the bottom bracket low for designs with long integrated seat posts.
Why an orthogonal configuration?
The seat tube and head tube do not have to be parallel to each other. The profiles can be fastened at an angle either using the same 45 GD angles or with clamps (called Cross connector) from the same supplier. See previous link to understand how the head tube angle can be made to differ from the seat tube angle. However, in most cases the orthogonal layout is sufficient and simpler to assemble because it requires no angle measurements, which can be cumbersome. Keeping everything square is far easier. It does require some calculations, but at least they are exact. The result is two coordinate systems: global and local. The global is the jig's coordinate where everything is orthogonal. The local coordinate is that of the frame, which can have tubes in any direction and the horizontal is defined by the ground when the bicycle is standing on its wheels. In the end, however, it comes down to getting the four points (head tube, seat tube, bottom bracket and rear axle) correctly positioned relative to each other. Frame geometry is traditionally thought of in the local coordinate, but the fittings can only be moved in the global coordinates. Therefore a transformation has to be made.
How is the coordinate transformation made?
The second picture shows the jig in its own (global) coordinate system. The blue triangle represents the known values of the frame (local coordinate):
BB = (Vertical) bottom bracket drop
CS = Chain stay length
Effective CS (CSeff) = Chain stay length parallel to the ground (horizontal)
ST = Seat tube angle relative to the horizontal.
The frame’s coordinate is simply rotated counter clockwise around the bottom bracket by the amount of the seat tube complementary angle. Hence, the seat tube runs vertical as do the profiles in the jig. The rear axle is fixed in the jig at a height of 250 mm from the bottom edge. We need to solve the position of the bottom bracket relative to the rear axle in the global coordinate, i.e. solve dx2, and dy1+dy2. We know the bottom bracket drop, chain stay length and seat tube angle. You might have designed your frame using the effective chain stay length to begin with, but in case you did not, it can be calculated using the Pythagorean Theorem. All equations are presented in the third picture.
The horizontal position DX of the profile holding the bottom bracket fitting can be measured using a tape measure. The vertical position DY can be measured with a calliper taking into account the radius of the fitting (Dbbfit/2). See fourth picture.
How is the center plane of the frame determined?
The slots in the 45x90 angles allow adjusting the center plane. For ease of use, we are recommending to slide the seat post and head tube fittings to one extreme of the slots. When considering the rear spacing, it becomes clear that the outermost slot of the angle has to be used. However, to avoid an unnecessarily long dummy axle the inner edge of the outer slot is best. The inner edge of the outer slot is 54 mm from the base of the angle which, together with the 8 mm diameter bolt leads to a center plane 58 mm from the aluminium profile surface. The profile with the dummy axle is hence 58+45 = 103 mm from the center plane. With a maximum rear spacing of 135 mm, this leaves 103-135/2 = 35,5 mm for the drop out thickness and nuts. One might want to move the center plane further away from the profiles if room is needed for example for a welding torch.