A box of a different size

[WillAdams (William Adams (Carbide 3D))]

We draw up what we have thus far:

and then dupe the small tool and align it (well, the tip of it) at the top/inside of the joint:

and draw in a square to show the “fingers” and matching recesses of the joint:

and a matching square shows how much things need to be inset from the inside of the box:

(which is, of course, the radius of the tool)

Making this for the bottom of the box is simple since it is just an inset rectangle:

but for the sides and front/back wants open geometry — there are a number of ways to make this, but possibly the most straight-forward is to just draw some squares centered on the corners for one side and one of the pair of front/back:

and then use the midpoints and corners to draw the desired geometry:

then duplicate it and move it to an appropriate layer:

which after a bit of dimension correction nets us:

(doubled up twice when it should have been only once)

[WillAdams (William Adams (Carbide 3D))]

Next we need the geometry which allows us to clear for the top of the joinery — select all the part outlines and offset by small endmill diameter plus 10% or so:

Delete the unneeded inner element:

Then get the geometry used for the V cut down to radius depth:

and copy-paste it:

and then move all this to a new layer:

It will be necessary to close the open geometry — this is easily done by drawing in lines for the side, but the front/back with their feature for the lid demand a bit of care (and this also shows how well-suited to this the previous design was)

Draw in an oversize rectangle in register with the outline and use Trim Vectors to get to what is needed:

OK

OK

Join Vectors

dupe and align and delete open geometry:

then assign a pocket toolpath:

[WillAdams (William Adams (Carbide 3D))]

Lastly we have the actual joinery — in the past I’ve drawn in the notches/recesses and stitched them together, but in retrospect, that’s not the best approach — instead, draw the fingers and add them to a duplicate of the geometry which defines the recesses, but align them with the inside of the box:

But first, determine the width/number of fingers — dividing:

329.601/3.5 == 94.1717143

We need an odd number, so rounding down to 93 we get:

329.601/93 == 3.54409677

and we will need to make 47 protrusions and 46 recesses which is easily done with a Linear Array (albeit w/ one extra piece of geometry which will need to be deleted):

Rounding unfortunately results in a slight discrepancy:

which is most expediently dealt w/ by centering things.

We then clean up and union things:

and repeat a similar process for the other edges/joints.

[WillAdams (William Adams (Carbide 3D))]

Once everything is put in place:

it is necessary to extend the ends:

at which point toolpaths may be assigned:

toolpaths are then re-arranged to cut from top–bottom in the most efficient fashion possible:

[WillAdams (William Adams (Carbide 3D))]

Next, we add geometry to trim things all the way through and adjust the balance of things to prevent interference:

[WillAdams (William Adams (Carbide 3D))]

Lastly, the lid has to be set up — see:

Using unsupported tooling in Carbide Create: Roundover / Cove / Radius bits

Once the geometry which we wish to use is drawn up: [image] we position various V endmills relative to it: [image] and then draw the line for the contour toolpaths: [image] and create a group for the V endmill toolpaths: [image] and then assign the various V endmill toolpaths cutting to the appropriate depths: [image] until one arrives at: [image]

for how this would be done.

[WillAdams (William Adams (Carbide 3D))]

Please note that the above files will need to be tested in a piece of scrap — the last time I worked up joinery:

Bamboo Pencil Cup

when it went together for a dry fit, it required a great deal of force to get things together and then it wouldn’t come apart.

[WillAdams (William Adams (Carbide 3D))]

A further consideration is that it will also be necessary to make a fixture/jig to drill the holes for the hinge pins.

I also don’t know that rounding things helps — revisiting this using only rectangles seems a worthwhile check, and starting from the top and working down should make the toolpaths more efficient, and make things easier to visualize.

Once again, from the top…

[WillAdams (William Adams (Carbide 3D))]

Step 1:

Draw the outlines of the box parts (bottom, sides, front/back):

Step 2: draw in the geometry for the lid cutouts and round them as is appropriate and then use Trim Vectors to create the geometry for the front/back:

Step 3: draw in the lid and set its size, taking the sides into account:

(I’m pretty sure the lid in the above file doesn’t take the sides into account)

Move the lid off to the side and put it on its own layer.

[WillAdams (William Adams (Carbide 3D))]

Step 4: Draw things up in profile — the necessary dimension is how much the projecting joinery needs to be cut down so as to ensure that it will fit into the recesses — since one part will be rotated 90 degrees, there are a couple of possible options:

• cut dogbones — this removes a lot of material and increases the voids in the joint, and I worry that it creates potential points of failure
• cut the recesses up to the interior space of the box — this creates the possibility that they will show, but if lining a box, may not be an issue
• using a roundover tool on the tops
• cut the protruding joinery down lower — this actually has the advantage of leaving more material around the potentially fragile sections holding the lid in pace, so seems worth trying

Select all of the parts and inset them by that distance, and also offset them to the outside by small tool diameter plus 10%:

Then, extend the front/back parts so that they are not inset at the top, since this only needs to be done where there is joinery (using a duplicate of the front/back):

OK
OK

Join Vectors and duplicate and mirror and drag into alignment, extend the side panel interiors, draw in the geometry for the bottom and clean up and move the geometry which defines where the initial pocket will be cut to a new layer:

Set up and preview the toolpath for this layer:

[WillAdams (William Adams (Carbide 3D))]

Step 5. (or maybe 6, depends on how you’re counting)

Decide where the large V endmill will stop cutting, and draw in the geometry for the joinery. At the ends it should be workable to cut less material, but there is also the consideration of the space needed for the holes for the hinges, but it will also be desirable to draw in geometry to cut the channels for the narrow V endmill. To make things easier to work with, we will not round off the corners, leaving that to the toolpath visualization.

First, draw the channels:

Then draw in where the V endmill toolpaths will begin/end — to simplify this, just use the stock width everywhere:

Using this dimension has the advantage of making it obvious where the stock will be when rotated, so a section of the joint can be described w/ one or two rectangles:

Since the joint needs to be inset by at least the tool radius, we can effect this by just reducing the width of this rectangle by the small tool diameter:

Switching to metric allows doing math w/o mixing units:

Essentially it is necessary to reduce each half to a series of projections and matching recesses — these must:

• be large enough to reliably match the ability of the program to fit a tool into it
• be easily created and shifted about — a consistent/centered placement helps with that

One can either cut these features at a consistent width, or scale them — probably a consistent width is easier to manage, and avoids the possibility of the tool not fitting, and if it covers a region greater than necessary is easily centered:

copy-paste the rectangle, then change the dimension along the axis of the joint to be the desired width:

then halve the dimension along the other axis:

and drag it down to the lower left corner:

and set up a Linear Array which covers the entire region of the joint:

Note that we want one side to have an odd number, and the other to have an even, so it is not helpful to group the output — Delete the extra:

and select each side and group:

Select the two groups and the rectangle which defines the joinery region and use the align tool:

to center things:

(it is better to overcut and create voids, then to leave material uncut which will interfere with fit — re-working the recesses and creating “biscuits” which can be used to fill such is left as an exercise for the reader)

The joinery elements may then be Boolean Unioned with the central channel:

and this process repeated for each element of the joinery (note that for the sides meeting the front/back it will be necessary to rotate one or the other to bring them into alignment) — it is also recommended that one make everything consistent/symmetrical.

[WillAdams (William Adams (Carbide 3D))]

Eventually one arrives at:

Note that at some corners that an island is created — it is more straight-forward to leave such thus and to be careful during assembly/glue-up and to trust modern adhesives.

This geometry may then be unioned and moved to the appropriate layer for cutting:

Where one still has (or has copied over) the surrounding geometry.

Lastly, we add in geometry which defines the edges of the parts which are not involved in joinery (and check things and slightly rearrange/edit) to arrive at:

which now previews as:

[CullenS (Cullen Simpson)]

I look forward to trying this when I have time to fully consume the concepts.

[WillAdams (William Adams (Carbide 3D))]

Thanks! Looking forward to folks trying this out — I think the larger tool simplifies things sufficiently that it should be straight-forward for folks to cut.

[WillAdams (William Adams (Carbide 3D))]

Adjust the inset geometry for the initial V carving to be at diameter:

and the toolpath to match:

Adjust the open geometry for the full-depth V carving to project stock thickness from the corners:

and adjust the toolpaths to match:

(a further optimization would be to determine how low the tool can be lowered before coming into contact with the sides of the channel)

For the small V to full depth geometry, it should reduce time to only cut in-between the full-depth V passes w/ the large tool:

which all previews as expected:

[WillAdams (William Adams (Carbide 3D))]

and the box should be done:

A box of a different size_v3.c2d (212 KB)

Note that for such joinery, esp. if cut in that orientation it may be necessary to calibrate for belt stretch:

Calibrating the machines over long distances

The typical technique for machine calibration: https://my.carbide3d.com/faq/belt-stretch/ depends on precision measuring tools, and is limited by the reach of the tools in question. EDIT: It also depends on access to the MDI — if using Carbide Motion v6 it will be necessary to enable this in Settings | Options: [image] It should be possible to cut strips from a suitable blank of material, one along each axis — so we set up a square file which matches an available blank of material: [ima…

Last is the lid:

which we will do in a modified version of the previous file.

[WillAdams (William Adams (Carbide 3D))]

As opened, the file in question is ready for cutting:

as discussed at the previous link:

Using unsupported tooling in Carbide Create: Roundover / Cove / Radius bits

These are usually used in routers for decorative effects in wood: but they are potentially useful for joinery: They are also useful for rounding off parts to allow rotary motion as for a hinged lid. Unfortunately, Carbide Create does not support this endmill geometry — but using the new support for previewing a V endmill when used in a No Offset Contour toolpath, it should be possible to preview them w/ confidence by stacking a series of V endmill cuts.

roundover tooling cannot be directly previewed in the current version of Carbide Create, but can be approximated with several V endmill passes:

Modifying this file requires changing X and Y to match the dimensions of:

which brings up an interesting way to change the dimensions of a file (using this technique to change the balance of the files for the box is left as an exercise for the reader).

First, set the grid spacing to a very coarse dimension:

Then select all the elements which one wishes to adjust, including an element which is the desired dimension:

then drag it until one point is at a grid intersection:

Go into Node Edit mode:

Select one entire edge of the design which includes the point which one wants to move to the desired dimension:

begin dragging to the grid intersection:

Done

repeat for the other edge:

Done

Select any elements which need to be adjusted and align as necessary:

Note that the thickness will need to be adjusted, and the 1572 tool defined, and the fixture similarly adjusted (didn’t think to include it in the selection, mea culpa).

A box of a different size_v3 LID for 8_35mm.c2d (148 KB)

[Ed.E (Ed)]

As I follow along with this build on my computer I can’t help but being impressed on the creative nature of the joinery design. I would have never thought to use Linear Array in the box joint design. My approach would have probably been with a single element design then Duplicate and Align. Great tutorial with many lessons learned.

[WillAdams (William Adams (Carbide 3D))]

I wish I could take credit for it — a number of folks have done this sort of joinery before I finally settled upon it:

• Blind mitered finger joint boxes

• Cutting and Fitting a Blind Finger Joint - FineWoodworking

• Full Blind Finger Joints

• Overengineered box for the endmills I don't have yet

I’ve got an idea for a perfect joint, but I’m still working on the math for it — if anyone has any books on conic sections to recommend, I’d be grateful.