I have a stinker of a project - making a steering axle for a "cart" I need to fit tube for king pins at 15 degree king pin inclination and 15 degree caster. The king pin tube is 7/8" dom tube with .120 wall and it needs to fin "into" - or more accurately on the end of, either 3/4X1 solid, 3/4 X 3/4 solid, or 3/4X3/4 .120 wall welded structural steel tube. Nobody I know locally with a Bridgeport is willing to set the head off of zero because getting it back to zero is too time consuming.

One thinks he can do it with adjustabe angle vice mouinted on an angle plate - Any other suggestions???

That sounds like a solution to me ... I'm faced with a similar situation . I'm getting ready to mill the angled surfaces of a fixture to sharpen end mills . The cutter needs to be angled in 2 planes . The angle for the cutting edge and the angle so the center of the cutter is concave (I hope that's understandable) . Plus the relief angle behind the cutting edge needs to also be a compound angle . If you find a better solution , I'll be watching . Won't be cutting as we're headed out to spend time with family for Christmas . I just had a thought , mount the workpiece at an angle in a small vise that's mounted at an angle in a bigger vise . My only experience with an angle vise wasn't pleasant . They move just when you don't need it to .

That sounds like a solution to me ... I'm faced with a similar situation . I'm getting ready to mill the angled surfaces of a fixture to sharpen end mills . The cutter needs to be angled in 2 planes . The angle for the cutting edge and the angle so the center of the cutter is concave (I hope that's understandable) . Plus the relief angle behind the cutting edge needs to also be a compound angle . If you find a better solution , I'll be watching . Won't be cutting as we're headed out to spend time with family for Christmas . I just had a thought , mount the workpiece at an angle in a small vise that's mounted at an angle in a bigger vise . My only experience with an angle vise wasn't pleasant . They move just when you don't need it to . Snag

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The solution I suggested for Snag's endmill fixture amounted to empirically finding the single angle equivalent to the combination of the two angles by aligning a rod that substitutes for the end mill (or king pin) in the mill spindle and shimming and clamping the base to hold it there. When wedged under the base of my endmill fixture the shim automatically found the single resultant angle, which could be reconstructed by duplicating its location relative to the base. This would also work on a lathe faceplate by chucking the guide rod in the tailstock. Instead of setting the angles the work is fixtured while positioned at them with shims and clamps such that the sample part can be removed and replaced with the new one.

Do you have an old part to use as the model?

I have a compound angle uni-vise for the surface grinder but it isn't rigid enough for milling.

I have a stinker of a project - making a steering axle for a "cart" I need to fit tube for king pins at 15 degree king pin inclination and 15 degree caster. The king pin tube is 7/8" dom tube with .120 wall and it needs to fin "into" - or more accurately on the end of, either 3/4X1 solid, 3/4 X 3/4 solid, or 3/4X3/4 .120 wall welded structural steel tube. Nobody I know locally with a Bridgeport is willing to set the head off of zero because getting it back to zero is too time consuming.

One thinks he can do it with adjustabe angle vice mouinted on an angle plate - Any other suggestions???

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I've worked in a shop with a Bridgeport that needed new Nod gears after setting the head at angles. The head is unbalanced and very heavy. My Clausing mill is difficult to tram because tightening the clamps shifts it unpredictably.

This might be the formula for the single resultant angle. I didn't go that far in Geometry. sin (A + B) = sin A cos B + cos A sin B

I just had a thought , mount the workpiece at an angle in a small vise that's mounted at an angle in a bigger vise . My only experience with an angle vise wasn't pleasant . They move just when you don't need it to . Snag

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That's a good option if you have the right equipment. If the work has to be above the jaw tops of the large vise for clearance I'd use a "screwless" insert vise with a solid base for the smaller one, rather than crushing the bottom channel of a screw-type vise, and I'd add clamps from the tee slot set.

Found another solution Grabbed a chunk of 3/4" steel shaft, cut it to

15 degrees and cut a v in the angled face, then hit that with a grinfdtone in a die grinder. I made a jig to hold everything accurately in shape to tig it together and I will jig the ends to the right (15 degree) angle for the caster and weld the shaft into the end of the axle channel. No fancy equipment required, plenty strong, and it will look good when it's done. To make the "yoke" that fits over the end of the axle for the king pin to rotoate the spindle I'm making a 3 inch channel from 3"X 1/4 angle - which will have a 2.5" inside measurement. The kinpins will be
1/2" grade 5 bolts, the bushings are 3/8" brass pipe, machined down just a tad to press fit into the 7/8" DOM tube. The axles will be 1/2" grade 5 bolts with the heads ground to (likely) 12 degrees and welded to the yoke to give a 3? degree negative camber. Lots of cutting and trimming to make it work and make it "purdy".

Found another solution Grabbed a chunk of 3/4" steel shaft, cut it to

15 degrees and cut a v in the angled face, then hit that with a grinfdtone in a die grinder. I made a jig to hold everything accurately in shape to tig it together and I will jig the ends to the right (15 degree) angle for the caster and weld the shaft into the end of the axle channel. No fancy equipment required, plenty strong, and it will look good when it's done. To make the "yoke" that fits over the end of the axle for the king pin to rotoate the spindle I'm making a 3 inch channel from 3"X 1/4 angle - which will have a 2.5" inside measurement. The kinpins will be
1/2" grade 5 bolts, the bushings are 3/8" brass pipe, machined down just a tad to press fit into the 7/8" DOM tube. The axles will be 1/2" grade 5 bolts with the heads ground to (likely) 12 degrees and welded to the yoke to give a 3? degree negative camber. Lots of cutting and trimming to make it work and make it "purdy".

---------------------- Plywood works well for one-use welding jigs, the fires are no worse than when soldering plumbing.

I've had good results from 3/8" brass pipe bushings that I used in the bucket loader I built for my tractor. They closely matched the nominal ID of

0.493" and reamed to 0.501" easily after pressing them in. Roll-threaded bolt shanks may be a few thousandths undersize so 0.500" may work, I found the custom 0.501" reamer second-hand.

The 0.500" O-1 drill rod pivot pins that ran in them broke just outside TIG welds and needed to be annealed, which cost strength, hardness and surface finish. When I took the loader apart ~5 years later one pin was slightly bent from running the bucket into a low stone step under the snow, otherwise wear was minimal.

I looked for info on re-hardening graded bolts. The answer appears to be that it depends on what steel the maker chose, the commercial specs are for performance. 800F came up as the max for tempering. Hardware store washers vary considerably in thickness as though made from whatever was cheap and available at the time, dunno if bolts are similar. I've sorted and matched washers to use as shims to align a replacement engine shaft.

Hardware store bolt heads, shanks and threads are not concentric or axially parallel. The shanks are a few thousandths undersize though they clamp tight enough in 5C collets, not my best ones. Grade 8 is soft enough to cut with HSS lathe bits. I made threaded cup bushings and split collets to chuck by the threads and turn the ends to taper, pilot or dog points. A root diameter pilot greatly helps outdoor assembly with cold hands without dropping the nut, the tapered end aligns holes and a dog point setscrew can still be removed if the end expanded.

Drilling the pivot pins lengthwise to the center for the grease passage was tedious on my larger lathe so once started I took them to the smaller, faster one. I couldn't install the grease fittings in some of the the bushings instead because they were centered in 2" square tubing. jsw

I may not be tracking here. I have angle blocks I'll use in a vise to set an angle. If I need to set two angles I'll set the first angle with a block in an angle vise. For low precision I use the one with a protractor. For high precision I'll use the sine vise.

What I have found is often the issue is indexing the part at this point. Sometimes eyeballing is good enough. Particularly I have thought ahead and machined indexing features in previous operations. If the corner edges of the part are PERFECT and SHARP in theory you can indicate off of them, but they never are. Instead there is a theoretical edge or corner that does not actually exist. You either have a burr or a slight flat from deburring. For a couple single angles I use often I made some angle plates with a relieved internal corner, flat top section, and flat side. The flats are a precise distance engraved on the plate from that theoretical perfect corner floating in the relieved corner. The plates have magnets set in them so I can place them in the vise and indicate off of them before ever (very carefully) mounting the part. It sounds great, but the reality is it just gets me "close enough" most of the time. I don't even do any math. I just do a

2D sketch of the setup in CAD. Then I drop points or lines where I need them for the rest of my dimensions.

I may not be tracking here. I have angle blocks I'll use in a vise to set an angle. If I need to set two angles I'll set the first angle with a block in an angle vise. For low precision I use the one with a protractor. For high precision I'll use the sine vise.

What I have found is often the issue is indexing the part at this point. Sometimes eyeballing is good enough. Particularly I have thought ahead and machined indexing features in previous operations. If the corner edges of the part are PERFECT and SHARP in theory you can indicate off of them, but they never are. Instead there is a theoretical edge or corner that does not actually exist. You either have a burr or a slight flat from deburring. For a couple single angles I use often I made some angle plates with a relieved internal corner, flat top section, and flat side. The flats are a precise distance engraved on the plate from that theoretical perfect corner floating in the relieved corner. The plates have magnets set in them so I can place them in the vise and indicate off of them before ever (very carefully) mounting the part. It sounds great, but the reality is it just gets me "close enough" most of the time. I don't even do any math. I just do a

2D sketch of the setup in CAD. Then I drop points or lines where I need them for the rest of my dimensions.

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Sets like these (from Enco) have covered everything I do on the mill for my own use, though they may not answer some problems posted here.

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I loaned them to Segway when participating in a redesign of the Balance Sensor Assembly, in which the solid state "gyros" are mounted at various angles.

The main circuit board is a 3D mess of intersecting shapes, governed by the very limited space bounded by the wheel motors and battery packs, that I designed with circuit board CAD the way you mentioned, by overlaying templates and dimensioning off the intersections. It fits as if poured in there. jsw

That's the formula for the angle that's the sum of two angles about the same point, in the same plane. Eg, see the diagram at

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In the 2D case, with both angles in the same plane, A and B can be interchanged without changing the result. But if there's a rotation about one axis, followed by a rotation about a second axis, the order matters. That is, in general the result of rotating a vector about x and then y is different from that for rotating about y and then x.

I realize Clare has already cut out some parts at ok angles to weld together, but for a compound angle like Clare mentioned, a good way to figure out mill settings would be to make a CAD drawing and use Annotate-Angular to get the measure of angles to set up for.

That's the formula for the angle that's the sum of two angles about the same point, in the same plane. Eg, see the diagram at

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I hoped to prompt someone to post how to figure the resultant of two angles in orthogonal planes, such as a pyramidal cupola, gable or lathe threading bit. jsw

Thanks, you gave me what I asked for. I didn't even know the words to Google.

However I think I'll pursue this approach because it can create large rigid fixtures:

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The Uni-Vise can set compound angles but it isn't rigid enough to be safe for milling. It's fine for surface grinding custom lathe bits, recently I had to copy the groove profile on a serpentine belt pulley.

The alternative is to use Euler math to figure out the needed angle, and a sine vise bolted to the mill table to make a metal angle plate, and clamp the workpiece to that angle plate on the table for cutting the work pieces to the desired angle.

The milling equivalent is a compound sine plate on the mill table.

The alternative is to use Euler math to figure out the needed angle, and a sine vise bolted to the mill table to make a metal angle plate, and clamp the workpiece to that angle plate on the table for cutting the work pieces to the desired angle.

The milling equivalent is a compound sine plate on the mill table.

.

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Joe Gwinn

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Hopefully if I need that accuracy it will be for someone who'll pay me appropriately, or sub the job to a better equipped machinist. I don't pretend to have a commercial shop, just enough to make a repair part, special tool, test fixture or model of my ideas for engineering's approval before drawing up and bidding the job out.

At Segway I used their machine tools in preference to mine unless theirs were tied up for a long project. I do like my South Bend better than their Smithy Granite, and the rarely available CNC lathe wasn't well suited to cut-and-try modification of castings. I tended to get the jobs that required old-fashioned manual skill. jsw

I thought about mentioning Euler angles and rotation matrices ([1],[2],[3]) in my post, but didn't do so, for reasons stated fairly well in [3]: "Unfortunately, converting ... Euler angles and rotation matrices ... perennial source of confusion. The reason is not that the math is particularly complicated. The reason is there are dozens of mutually exclusive ways to define Euler angles. Different authors are likely to use different conventions, often without clearly stating the underlying assumptions. This makes it difficult to combine equations and code from more than one source." It's fairly easy to make mistakes that aren't obvious, and often it's not obvious what order to do things in. [1]

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[2]

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[3]

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Regarding using CAD dimensioning lines (like via Annotate/Angular in autocad), which I mentioned in my previous post, note that a properly drawn sheet embeds precise angles and distances (eg accuracy of 8 to

19 digits depending on system). Using snaps to get dimension values works to full accuracy, so that CAD is as accurate as calculating with Euler angles and rotation matrices, with the added advantage of an image to look at for sanity checks.

Regarding the method you mentioned in an earlier post -- "sharpening end mills", Sun, 11 Dec 2022 18:04:02 -0500, "set the end mill fixture on my mill ... raised the table to contact with the back right corner, then pushed a 1/4" thick bar into the wedge space underneath from the front (bevel) side. The bar intersects the left side 2.05" from the back and the right side 2.95" from the back" -- I think that via CAD you can get the 2.05" and 2.95" measurements more accurately than that, as follows: After drawing the fixture and drawing a plane for the table, draw another plane 1/4" up, then snap points to the intersections of that plane with the end mill fixture.

I thought about mentioning Euler angles and rotation matrices ([1],[2],[3]) in my post, but didn't do so, for reasons stated fairly well in [3]: "Unfortunately, converting ... Euler angles and rotation matrices ... perennial source of confusion. The reason is not that the math is particularly complicated. The reason is there are dozens of mutually exclusive ways to define Euler angles. Different authors are likely to use different conventions, often without clearly stating the underlying assumptions. This makes it difficult to combine equations and code from more than one source." It's fairly easy to make mistakes that aren't obvious, and often it's not obvious what order to do things in. [1]

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[2]

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[3]

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Regarding using CAD dimensioning lines (like via Annotate/Angular in autocad), which I mentioned in my previous post, note that a properly drawn sheet embeds precise angles and distances (eg accuracy of 8 to

19 digits depending on system). Using snaps to get dimension values works to full accuracy, so that CAD is as accurate as calculating with Euler angles and rotation matrices, with the added advantage of an image to look at for sanity checks.

Regarding the method you mentioned in an earlier post -- "sharpening end mills", Sun, 11 Dec 2022 18:04:02 -0500, "set the end mill fixture on my mill ... raised the table to contact with the back right corner, then pushed a 1/4" thick bar into the wedge space underneath from the front (bevel) side. The bar intersects the left side 2.05" from the back and the right side 2.95" from the back" -- I think that via CAD you can get the 2.05" and 2.95" measurements more accurately than that, as follows: After drawing the fixture and drawing a plane for the table, draw another plane 1/4" up, then snap points to the intersections of that plane with the end mill fixture.

-------------------------- I measured those with a ruler and rounded them to 2 decimal places, which I think is close enough, in fact 2" and 3" may be close enough. The endmill may have to be rotated for the grinding wheel to clear other flutes while reaching the center, which changes the angles but doesn't noticeably affect how it cuts.

I fully agree about CAD, and did just that in 2D CAD to fit circuit boards to models of external objects. I don't have 3D CAD but I learned traditional pencil and paper methods including sheetmetal transition pieces and worked as a draftsman. The engineers with Solidworks licenses made their parts on the CNC machines and left the poorly defined jobs like modifying pattern-based castings to me. . The problem here is not to determine angles to exact theoretical accuracy although knowing how has value, but to create milling setups rigid enough to not shift and accurate enough for the demands, which in this case aren't that exact, +/- a degree may not matter much. I also learned to analyze how much accuracy is really necessary, and not over-specify it.

The wedge setup I described probably wouldn't be rigid enough by itself and would need to be securely clamped down and blocked in place against rotation. jsw

Yes there are a bunch of conventions. The key is to figure out which ones are not appropriate for one's application, and to choose a single one of the acceptable conventions, and use it consistently.

The full mathy way to dodge the conventions and singularities of Euler Angles is Quaternions, used in missile guidance systems and computer graphics.

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