On 12/20/2022 10:36 PM, Clare Snyder wrote:

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 .
--
Snag
"You can lead a dummy to facts
but you can't make him think."

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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???

--- SoupGate-Win32 v1.05
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"Snag" wrote in message news:tnu4o6$v2io$1@dont-email.me...

On 12/20/2022 10:36 PM, Clare Snyder wrote:

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 .
Snag

-----------------

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. https://www.penntoolco.com/precise-uni-vise-grinding-fixture-202-2615/

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"Clare Snyder" wrote in message news:ko25qhdaftmpuadtopn9t9f8k8ugp49erf@4ax.com...

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???
---------------------

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

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"Snag" wrote in message news:tnu4o6$v2io$1@dont-email.me...

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

----------------------

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.
https://www.amazon.com/Screwless-Vise-Hold-Down-Clamps/dp/B01N6N7HR9

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On Tue, 20 Dec 2022 23:36:17 -0500, Clare Snyder <clare@snyder.on.ca>
wrote:

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???

Fabricate a crude sine plate that's strong enough for milling, and
clamp everything to the Bport table, which need not go off tram.

Joe Gwinn

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On Wed, 21 Dec 2022 11:40:42 -0500, Joe Gwinn <joegwinn@comcast.net>
wrote:

On Tue, 20 Dec 2022 23:36:17 -0500, Clare Snyder <clare@snyder.on.ca>
wrote:

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???

Fabricate a crude sine plate that's strong enough for milling, and
clamp everything to the Bport table, which need not go off tram.

Joe Gwinn

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".

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"Clare Snyder" wrote in message news:h6h7qhtndtu25sp806hkuquiefkmdbepj6@4ax.com...

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

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On 12/20/2022 9:36 PM, Clare Snyder wrote:

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???

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.



--
This email has been checked for viruses by AVG antivirus software.
www.avg.com

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"Bob La Londe" wrote in message news:to243s$uje$1@gioia.aioe.org...

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.
-------------------------------

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. https://www.ebay.com/itm/154747190584?chn=ps&mkevt=1&mkcid=28 https://www.mscdirect.com/browse/tnpla/06367031

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

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Jim Wilkins <muratlanne@gmail.com> wrote:

"Clare Snyder" wrote in message news:ko25qhdaftmpuadtopn9t9f8k8ugp49erf@4ax.com...

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.

[...]

---------------------

[...]

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

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 <https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities>
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.

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"James Waldby" wrote in message news:to65mv$21pug$1@dont-email.me...

Jim Wilkins <muratlanne@gmail.com> wrote:

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

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 <https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities>

------------------------

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

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On Sat, 24 Dec 2022 06:53:54 -0500, "Jim Wilkins"
<muratlanne@gmail.com> wrote:

"James Waldby" wrote in message news:to65mv$21pug$1@dont-email.me...

Jim Wilkins <muratlanne@gmail.com> wrote:

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

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 ><https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities>

------------------------

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.

Euler angles give the clue.

.<https://www.mecademic.com/en/how-is-orientation-in-space-represented-with-euler-angles>

Joe Gwinn

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"Joe Gwinn" wrote in message news:eh4fqh93tmeecg8jjl906jv0i6l20opaeo@4ax.com...

On Sat, 24 Dec 2022 06:53:54 -0500, "Jim Wilkins"
<muratlanne@gmail.com> wrote:

"James Waldby" wrote in message news:to65mv$21pug$1@dont-email.me...

Jim Wilkins <muratlanne@gmail.com> wrote:

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

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 ><https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities>

------------------------

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.

Euler angles give the clue.

.<https://www.mecademic.com/en/how-is-orientation-in-space-represented-with-euler-angles>

Joe Gwinn

-------------------------

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: https://www.leevalley.com/en-us/discover/woodworking/2020/august/compound-angled-joinery-made-easy

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.

--- SoupGate-Win32 v1.05
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On Sun, 25 Dec 2022 07:12:35 -0500, "Jim Wilkins"
<muratlanne@gmail.com> wrote:

"Joe Gwinn" wrote in message >news:eh4fqh93tmeecg8jjl906jv0i6l20opaeo@4ax.com...

On Sat, 24 Dec 2022 06:53:54 -0500, "Jim Wilkins"
<muratlanne@gmail.com> wrote:

"James Waldby" wrote in message news:to65mv$21pug$1@dont-email.me...

Jim Wilkins <muratlanne@gmail.com> wrote:

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

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 >><https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities>

------------------------

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.

Euler angles give the clue.

.<https://www.mecademic.com/en/how-is-orientation-in-space-represented-with-euler-angles>

Joe Gwinn

-------------------------

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: >.<https://www.leevalley.com/en-us/discover/woodworking/2020/august/compound-angled-joinery-made-easy>

OK if that is accurate enough.

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

.<https://www.shars.com/compound-sine-plate-6-l-x-6-w-x-3-1-8-h-0002>

Joe Gwinn

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"Joe Gwinn" wrote in message news:cbrgqh5e5c262bkfdubs9rnevgr6ibfn4f@4ax.com...

On Sun, 25 Dec 2022 07:12:35 -0500, "Jim Wilkins"
<muratlanne@gmail.com> wrote:

"Joe Gwinn" wrote in message >news:eh4fqh93tmeecg8jjl906jv0i6l20opaeo@4ax.com...

On Sat, 24 Dec 2022 06:53:54 -0500, "Jim Wilkins"
<muratlanne@gmail.com> wrote:

"James Waldby" wrote in message news:to65mv$21pug$1@dont-email.me...

Jim Wilkins <muratlanne@gmail.com> wrote:

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

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 >><https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities>

------------------------

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.

Euler angles give the clue.

.<https://www.mecademic.com/en/how-is-orientation-in-space-represented-with-euler-angles>

Joe Gwinn

-------------------------

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: >.<https://www.leevalley.com/en-us/discover/woodworking/2020/august/compound-angled-joinery-made-easy>

OK if that is accurate enough.

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

.<https://www.shars.com/compound-sine-plate-6-l-x-6-w-x-3-1-8-h-0002>

Joe Gwinn

-------------------------

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

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Jim Wilkins <muratlanne@gmail.com> wrote:

"Joe Gwinn" wrote in message news:eh4fqh93tmeecg8jjl906jv0i6l20opaeo@4ax.com...

On Sat, 24 Dec 2022 06:53:54 -0500, "Jim Wilkins"
<muratlanne@gmail.com> wrote:

"James Waldby" wrote in message news:to65mv$21pug$1@dont-email.me...

Jim Wilkins <muratlanne@gmail.com> wrote:

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

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 >><https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities>

------------------------

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.

Euler angles give the clue.

.<https://www.mecademic.com/en/how-is-orientation-in-space-represented-with-euler-angles>

...

-------------------------

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

[snip approach via:]

https://www.leevalley.com/en-us/discover/woodworking/2020/august/compound-angled-joinery-made-easy

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] <https://en.wikipedia.org/wiki/Euler_angles>
[2] <https://en.wikipedia.org/wiki/Rotation_matrix>
[3] <https://danceswithcode.net/engineeringnotes/rotations_in_3d/rotations_in_3d_part1.htm>

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.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

"James Waldby" wrote in message news:tob42h$34mqr$1@dont-email.me...

Jim Wilkins <muratlanne@gmail.com> wrote:

"Joe Gwinn" wrote in message news:eh4fqh93tmeecg8jjl906jv0i6l20opaeo@4ax.com...

On Sat, 24 Dec 2022 06:53:54 -0500, "Jim Wilkins"
<muratlanne@gmail.com> wrote:

"James Waldby" wrote in message news:to65mv$21pug$1@dont-email.me...

Jim Wilkins <muratlanne@gmail.com> wrote:

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

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 >><https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities>

------------------------

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.

Euler angles give the clue.

.<https://www.mecademic.com/en/how-is-orientation-in-space-represented-with-euler-angles>

...

-------------------------

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

[snip approach via:]

https://www.leevalley.com/en-us/discover/woodworking/2020/august/compound-angled-joinery-made-easy

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] <https://en.wikipedia.org/wiki/Euler_angles>
[2] <https://en.wikipedia.org/wiki/Rotation_matrix>
[3] <https://danceswithcode.net/engineeringnotes/rotations_in_3d/rotations_in_3d_part1.htm>

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

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Mon, 26 Dec 2022 03:22:57 -0000 (UTC), James Waldby
<j-waldby@no.no> wrote:

Jim Wilkins <muratlanne@gmail.com> wrote:

"Joe Gwinn" wrote in message
news:eh4fqh93tmeecg8jjl906jv0i6l20opaeo@4ax.com...

On Sat, 24 Dec 2022 06:53:54 -0500, "Jim Wilkins"
<muratlanne@gmail.com> wrote:

"James Waldby" wrote in message news:to65mv$21pug$1@dont-email.me...

Jim Wilkins <muratlanne@gmail.com> wrote:

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

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 >>><https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities>

------------------------

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.

Euler angles give the clue.

.<https://www.mecademic.com/en/how-is-orientation-in-space-represented-with-euler-angles>

...

-------------------------

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

[snip approach via:]

https://www.leevalley.com/en-us/discover/woodworking/2020/august/compound-angled-joinery-made-easy

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] <https://en.wikipedia.org/wiki/Euler_angles>
[2] <https://en.wikipedia.org/wiki/Rotation_matrix>
[3] <https://danceswithcode.net/engineeringnotes/rotations_in_3d/rotations_in_3d_part1.htm>

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.

Joe Gwinn

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

"Joe Gwinn" wrote in message news:ejtjqhda3rjmm5ec6iark0dmjr1sjolsul@4ax.com...
....
The full mathy way to dodge the conventions and singularities of Euler
Angles is Quaternions, used in missile guidance systems and computer
graphics.

Joe Gwinn

-------------------

Thanks. I studied the math of complex numbers as used in AC circuits,
digital signal processing and brushless motors.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Sunday, December 25, 2022 at 7:23:01 PM UTC-8, James Waldby wrote:

Jim Wilkins <murat...@gmail.com> wrote:

"Joe Gwinn" wrote in message
news:eh4fqh93tmeecg8jj...@4ax.com...

On Sat, 24 Dec 2022 06:53:54 -0500, "Jim Wilkins"
<murat...@gmail.com> wrote:

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.

Euler angles give the clue.

.<https://www.mecademic.com/en/how-is-orientation-in-space-represented-with-euler-angles>

...

-------------------------

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

[snip approach via:]

https://www.leevalley.com/en-us/discover/woodworking/2020/august/compound-angled-joinery-made-easy

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.

Yeah, for 3-D geometry I always use cartesian coordinates, vectors
for the face directions, and dot products (for the 'cos (theta)' term)
and/or cross products (to get a normal vector to a surface) to extract an angle. Some projects, like carpentry of a chimney cricket, are easy
this way. CAD is another learning curve into the future, but I've already got vector algebra skills.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)