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DT/ST miter offset compensation

Brent,

I deleted my post after I read yours, second guessed myself and then had a bit of a freak out as I was double checking my maths.  I shouldn't have, because I think I'm correct.

My hope was to eliminate the necessity for scribe lines on this particular miter because in my case, it's too dark (I keep a light in my pocket for this task) and too difficult (I had a nasty crash last year that's left me with injuries) for me to crawl on top of my milling machine (in horizontal mode) to see if the cutter is hitting the line.

The problem is that I offset the miters of my seat tube (to the rear) and down tube (downward) so that the edge is tangent to the BB shell.  I've been using the top of DT miter length for years, but for the aforementioned reasons, I wanted a way to calculate how far to shift the X-axis of my machine from the centerline of my rotary table when I make this cut.

I came up with the formula :: ST miter offset + [DT miter offset * COS(Miter Angle °)] = x-axis change

Let's say the ST/DT interior angle is 60°, ST miter offset is 0 and DT offset is 10mm.  0 + [10(COS60)] = 5mm.  I'd have to slide my x-axis over 5mm from the rotab ctr.

if the ST/DT angle is 30°, ST offset is 0 and DT offset is 10.  0 + [10(COS30)] = 8.66mm

This makes sense because as the miter angle approaches 90° it gets the COS gets closer to 0.  At 90°, the DT miter offset has zero effect on the ST miter with 0 as the multiplier.  As the miter angle approaches 0° (if that were physically possible) the COS gets closer to 1.  At 0°, the x-axis offset would be exactly the DT miter offset because the multiplier is 1

The ST miter offset just gets added to the product of the DT miter offset and the COS of the angle because the ST is the y-axis of the machine.  Miter offset is perpendicular to that.

The drawing doesn't provide any answers, but it's a real world example of what I'm trying to get to here.

In this case it's 8 + [3(COS42.9)] = 10.198.  In order to cut this without using a scribe line, I'd have to move my x-axis 10.2mm from the center of my rotab.

I hope I've described this better than I did the first time and thanks for taking a look at it.

The image wasn't inserted.

Also, you asked me to make a user dimension...I don't think I can do that in BikeCAD in a meaningful way.  It's not a dimension that can be directly illustrated as it's not anything that relates to the frame as we view it in BikeCAD.  The best I could do, would be to show two different drawings with a different "miter to miter on top of downtube" lengths that have changed because of tube offsets and even then, you have to do the math to sort out how this affects the setup on the milling machine.

DT/ST miter compensation

Although you don't feel like you can show the dimension you need on the screen, it is possible to represent the dimension you've proposed. At this point, I'm still not sure that the dimension you need and the dimension you've proposed are one and the same.

You've proposed adding some extra length to the 8mm seat tube offset dimension. The extra length you're proposing is DT offset * COS(miter angle). If the DT offset is 3mm, you're proposing that we orient that dimension at an angle of 42.9° and obtain it's horizontal component as shown below.

If we take this value and add it to the existing 8mm seat tube offset, we get what you can see below:

I'm still struggling to see how we can justify rotating this 2.2mm dimension such that it is parallel to the 8mm seat tube offset dimension. To reiterate a point I made in my earlier response, in BikeCAD, the seat tube offset is measured perpendicular to the top section of the seat tube, not the bottom section below the bend. Meanwhile, the miter angle is measured with respect to the bottom section of the seat tube.

I see what you're saying now,

I see what you're saying now, about the offset being perpendicular to the top section.  In the "Tubing" section, when the "Curved" box is checked under the seat tube, I've been calling dimension "B" offset and calling the "offset at BB" miter offset.  I'll have to tweak my formula to get a corrected value for the X-axis shift.  Thanks for looking at it, but rather than continue to ask you to set this up as an output, I'll just stick a note on my milling machine.

New dimensions

I remain open to adding any new dimension you can dream up. It seems like you've come up with a pretty good system on your mill. However, if you're looking for another approach to complement what you're doing on the mill. You could consider using a miter template. Some builders will use the mill for the majority of cuts, but then use a miter template for the seat tube notch on the down tube, or for where the down tube or top tube might be meeting with a tapered head tube.