Re: [Emc-users] EMC paper

[Jaime Dulay]

Can you please include me also in the list.

Thanks a lot!
Jim

On Sat, May 9, 2009 at 10:39 AM, Gene Heskett wrote:

> On Friday 08 May 2009, Sebastian Kuzminsky wrote:
> >sam sokolik wrote:
> >> I am also very interested.  Looks neat!
> >>
> >> sam
> >>
> >> Anders Wallin wrote:
> >>> there's a new paper out on desktop parallel kinematic machines which
> >>> uses EMC2
> >>> http://www.springerlink.com/content/j12r46v2v93g5t07/
> >>>
> >>>
> >>> I have the pdf if anyone is interested.
> >
> >The PDF is on the page Anders linked, no need to email it around:
> >
> >
>
> I'm curious, but not $34 worth curious I guess.
>
> --
> Cheers, Gene
> "There are four boxes to be used in defense of liberty:
>  soap, ballot, jury, and ammo. Please use in that order."
> -Ed Howdershelt (Author)
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>-- Shakespeare
>
>
>
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Re: [Emc-users] EMC paper

[Steve White]

Hello,

I would very much like to read it too.

Thank you,
Steve

Anders Wallin wrote:
> there's a new paper out on desktop parallel kinematic machines which 
> uses EMC2
> http://www.springerlink.com/content/j12r46v2v93g5t07/
>
>
> I have the pdf if anyone is interested.
>
> Anders
>
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>
>   


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Re: [Emc-users] EMC paper

[Jack Coats]

same here please.
IHS ... Jack


On Sat, May 9, 2009 at 11:43 AM, Steve White  wrote:

> Hello,
>
>I would very much like to read it too.
>
> Thank you,
> Steve
>
> Anders Wallin wrote:
> > there's a new paper out on desktop parallel kinematic machines which
> > uses EMC2
> > http://www.springerlink.com/content/j12r46v2v93g5t07/
> >
> >
> > I have the pdf if anyone is interested.
> >
> > Anders
> >
> >
> --
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> > production scanning environment may not be a perfect world - but thanks
> to
> > Kodak, there's a perfect scanner to get the job done! With the NEW KODAK
> i700
> > Series Scanner you'll get full speed at 300 dpi even with all image
> > processing features enabled. http://p.sf.net/sfu/kodak-com
> > ___
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> >
> >
> >
>
>
>
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[Emc-users] Gear Tooth Profile

[Kirk Wallace]

I would like to make gears, but I need to know the tooth shape in order
to make a form tool or cut an outline. This is what I came up with, if
there are any mistakes or bad assumptions, please let me know.

I referenced:
http://en.wikipedia.org/wiki/Gear 
http://en.wikipedia.org/wiki/Involute_gear 
http://en.wikipedia.org/wiki/Involute 
http://en.wikipedia.org/wiki/Rack_and_pinion 

My example gear is a 2m(module) pitch - 20mm.

A sample is on this page:
http://www.qtcgears.com/RFQ/default.asp?Page=../KHK/newgears/KHK044.html 
(Short URL) http://alturl.com/whp2 

Pitch is the tooth length, but expressed in pitch circle diameter, so a
10 tooth gear with a 20mm pitch circle = 20mm/10t = 2, but this is not
the linear tooth length. I believe the basis for involute gears is the
trapezoidal rack, so I need the linear tooth length, which should be 2
module x pi. A common pressure angle is 20 degrees. I assumed the rack
base and top are horizontally midway between the rack center line and
the 20 degree peaks, such that the X length of the rise, flats and falls
are equal. Here is my rack and pitch circle:

http://www.wallacecompany.com/machine_shop/gears/rack_and_pitch_circle.png 
(Short URL) http://alturl.com/7t8a

The first pinion tooth form guess is the complementary shape of the rack
tooth, but as the rack moves the pinion rotates and lifts, so the pinion
tooth shape needs to change to take the trapezoidal shape that matches
the rotation and lift. If I move the rack one quarter of a tooth the
pinion will rotate a proportionate angle. 
1/4t = 1.5708mm
C = pi x D = pi x 20mm = 62.832mm = 360 degrees
360deg x 1.5708mm/62.832mm = 9 degrees per 1/4t

If I move the rack shape 1/4t to the right, then rotate it 9 deg
clockwise back to the home position, the mesh point will be somewhere on
the new shape.

http://www.wallacecompany.com/machine_shop/gears/rack_and_quarter_tooth.png 
(Short URL) http://alturl.com/gd75 

If I continue the process, I'll have more mesh points.

http://www.wallacecompany.com/machine_shop/gears/rack_and_pinion_shape.png 
(Short URL) http://alturl.com/54oj 

I can then trim the lines, mirror the shape on the tooth center line,
guess at a tip and base clearance shape.

http://www.wallacecompany.com/machine_shop/gears/gear.png 
(Short URL) http://alturl.com/cqcw 

The problem is, have I made any mistakes? Is there a better, easier way?
-- 
Kirk Wallace
http://www.wallacecompany.com/machine_shop/
http://www.wallacecompany.com/E45/index.html
California, USA


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Re: [Emc-users] Gear Tooth Profile

[John Kasunich]

Kirk Wallace wrote:
> I would like to make gears, but I need to know the tooth shape in order
> to make a form tool or cut an outline. This is what I came up with, if
> there are any mistakes or bad assumptions, please let me know.
>

I'm no gear expert, but I have a few comments.  The only gears I've made
are worm gears, and I hobbed them so the tooth shape was generated
automatically.

> I referenced:
> http://en.wikipedia.org/wiki/Gear 
> http://en.wikipedia.org/wiki/Involute_gear 
> http://en.wikipedia.org/wiki/Involute 
> http://en.wikipedia.org/wiki/Rack_and_pinion 
> 
> My example gear is a 2m(module) pitch - 20mm.
> 
> A sample is on this page:
> http://www.qtcgears.com/RFQ/default.asp?Page=../KHK/newgears/KHK044.html 
> (Short URL) http://alturl.com/whp2 
> 
> Pitch is the tooth length, but expressed in pitch circle diameter, so a
> 10 tooth gear with a 20mm pitch circle = 20mm/10t = 2, but this is not
> the linear tooth length. I believe the basis for involute gears is the
> trapezoidal rack, so I need the linear tooth length, which should be 2
> module x pi. A common pressure angle is 20 degrees. I assumed the rack
> base and top are horizontally midway between the rack center line and
> the 20 degree peaks, such that the X length of the rise, flats and falls
> are equal. Here is my rack and pitch circle:

I think that assumption might not be valid.  I believe the height above
the pitch line, and the depth below the pitch line have names - addendum
and dedendum IIRC, and they are not necessarily equal to each other.  In
particular, for a pinion with a small tooth count like yours, the
dedendum is made less to avoid undercutting the teeth - the undercut
shows up in your last image.  That would result in weak teeth if the
gear was heavily stressed.

> http://www.wallacecompany.com/machine_shop/gears/rack_and_pitch_circle.png 
> (Short URL) http://alturl.com/7t8a
> 
> The first pinion tooth form guess is the complementary shape of the rack
> tooth, but as the rack moves the pinion rotates and lifts, so the pinion
> tooth shape needs to change to take the trapezoidal shape that matches
> the rotation and lift. If I move the rack one quarter of a tooth the
> pinion will rotate a proportionate angle. 
> 1/4t = 1.5708mm
> C = pi x D = pi x 20mm = 62.832mm = 360 degrees
> 360deg x 1.5708mm/62.832mm = 9 degrees per 1/4t
> 
> If I move the rack shape 1/4t to the right, then rotate it 9 deg
> clockwise back to the home position, the mesh point will be somewhere on
> the new shape.
> 
> http://www.wallacecompany.com/machine_shop/gears/rack_and_quarter_tooth.png 
> (Short URL) http://alturl.com/gd75 
> 
> If I continue the process, I'll have more mesh points.
> 
> http://www.wallacecompany.com/machine_shop/gears/rack_and_pinion_shape.png 
> (Short URL) http://alturl.com/54oj 
> 
> I can then trim the lines, mirror the shape on the tooth center line,
> guess at a tip and base clearance shape.
> 
> http://www.wallacecompany.com/machine_shop/gears/gear.png 
> (Short URL) http://alturl.com/cqcw 
> 
> The problem is, have I made any mistakes? Is there a better, easier way?

I think your derivation of the shape is correct.  There is probably a
mathematically purer way (one that doesn't involve small increments of
motion that you then blend into the form).  But I like your way better.

Note that what you did on paper is what happens in metal when you hob a
gear.  Imagine that your rack is actually one side of an acme threaded
rod.  Since the screw threads are helical, not just rings around the
rod, the "rack" teeth are inclined where they meet the gear.  So you
have to lift one end of the rod out of the paper, until the helix angle
is canceled out.

Then you cut flutes on the rod, and spin both rod and gear blank, so you
get the effect of the gear rolling along the "rack".  Finally, you
slowly feed the rod across the face of the gear.

The other approach is to buy a gear cutter with the proper form.  Note
that unlike a hob (which can be used to cut gears with any number of
teeth), a gear cutter is designed for a specific range of teeth.  I
think there is usually a set of 8 to cut everything from 12 tooth
pinions thru many tooth gears up to a rack (basically a gear with an
infinite number of teeth).

Regards,

John Kasunich



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Re: [Emc-users] Gear Tooth Profile

[Kirk Wallace]

On Sat, 2009-05-09 at 15:07 -0400, John Kasunich wrote:
> Kirk Wallace wrote:
... snip
> I assumed the rack
> > base and top are horizontally midway between the rack center line and
> > the 20 degree peaks, such that the X length of the rise, flats and falls
> > are equal. Here is my rack and pitch circle:
> 
> I think that assumption might not be valid.  I believe the height above
> the pitch line, and the depth below the pitch line have names - addendum
> and dedendum IIRC, and they are not necessarily equal to each other.  In
> particular, for a pinion with a small tooth count like yours, the
> dedendum is made less to avoid undercutting the teeth - the undercut
> shows up in your last image.  That would result in weak teeth if the
> gear was heavily stressed.

A thought I had on this, is that for different gears of the same pitch
to work together they need to have the same base rack form. Since a gear
and it's mate can be derived from the top or bottom of the base rack
form, the base form should be symmetrical. A non-symmetrical base form
could be used, but I think the gear pair will only work with its
original mate. Actually, the more I think, the rack base and top lines
don't even count, because the mesh zone is well within these limits. I
could do the derivation again with a sawtooth instead of a trapezoidal
form. I suspect the way to adjust the addendum/dedendum is with pressure
angle, but this is just a hunch at this point. I think I have enough to
make what I need, so I'm not sure how far I'll get on this issue. Some
engineers have made a life on these matters, I've only got spare time.

> > http://www.wallacecompany.com/machine_shop/gears/rack_and_pitch_circle.png 
> > (Short URL) http://alturl.com/7t8a
> > 
> > The first pinion tooth form guess is the complementary shape of the rack
... snip
> > The problem is, have I made any mistakes? Is there a better, easier way?
> 
> I think your derivation of the shape is correct.  There is probably a
> mathematically purer way (one that doesn't involve small increments of
> motion that you then blend into the form).  But I like your way better.

Wikipedia covers the involute equations, but I suspect the mesh points
are not on obvious function points.

> Note that what you did on paper is what happens in metal when you hob a
> gear.  Imagine that your rack is actually one side of an acme threaded
... snip

My one real CNC employer had an old gear hob machine. The problem was it
was easy to stand and watch it, right through your break. Another
problem was that when the guy that runs it retires, the machine gets
scrapped.

> The other approach is to buy a gear cutter with the proper form.  Note
> that unlike a hob (which can be used to cut gears with any number of
> teeth), a gear cutter is designed for a specific range of teeth.  I
> think there is usually a set of 8 to cut everything from 12 tooth
> pinions thru many tooth gears up to a rack (basically a gear with an
> infinite number of teeth).

Gear cutting tools are too expensive for me since I usually need one or
a few of each. Having a way to make any gear without special tooling
would be a big plus. One reason I am looking at a 2m - 10mm gear is that
I can use a .063" end mill to cut a thin version.
-- 
Kirk Wallace
http://www.wallacecompany.com/machine_shop/
http://www.wallacecompany.com/E45/index.html
California, USA


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Re: [Emc-users] Gear Tooth Profile

[Douglas Pollard]

Kirk Wallace wrote:
> On Sat, 2009-05-09 at 15:07 -0400, John Kasunich wrote:
>   
>> Kirk Wallace wrote:
>> 
> ... snip
>   
>> I assumed the rack
>> 
>>> base and top are horizontally midway between the rack center line and
>>> the 20 degree peaks, such that the X length of the rise, flats and falls
>>> are equal. Here is my rack and pitch circle:
>>>   
>> I think that assumption might not be valid.  I believe the height above
>> the pitch line, and the depth below the pitch line have names - addendum
>> and dedendum IIRC, and they are not necessarily equal to each other.  In
>> particular, for a pinion with a small tooth count like yours, the
>> dedendum is made less to avoid undercutting the teeth - the undercut
>> shows up in your last image.  That would result in weak teeth if the
>> gear was heavily stressed.
>> 
>
> A thought I had on this, is that for different gears of the same pitch
> to work together they need to have the same base rack form. Since a gear
> and it's mate can be derived from the top or bottom of the base rack
> form, the base form should be symmetrical. A non-symmetrical base form
> could be used, but I think the gear pair will only work with its
> original mate. Actually, the more I think, the rack base and top lines
> don't even count, because the mesh zone is well within these limits. I
> could do the derivation again with a sawtooth instead of a trapezoidal
> form. I suspect the way to adjust the addendum/dedendum is with pressure
> angle, but this is just a hunch at this point. I think I have enough to
> make what I need, so I'm not sure how far I'll get on this issue. Some
> engineers have made a life on these matters, I've only got spare time.
>
>   
>>> http://www.wallacecompany.com/machine_shop/gears/rack_and_pitch_circle.png 
>>> (Short URL) http://alturl.com/7t8a
>>>
>>> The first pinion tooth form guess is the complementary shape of the rack
>>>   
> ... snip
>   
>>> The problem is, have I made any mistakes? Is there a better, easier way?
>>>   
>> I think your derivation of the shape is correct.  There is probably a
>> mathematically purer way (one that doesn't involve small increments of
>> motion that you then blend into the form).  But I like your way better.
>> 
>
> Wikipedia covers the involute equations, but I suspect the mesh points
> are not on obvious function points.
>
>   
>> Note that what you did on paper is what happens in metal when you hob a
>> gear.  Imagine that your rack is actually one side of an acme threaded
>> 
> ... snip
>
> My one real CNC employer had an old gear hob machine. The problem was it
> was easy to stand and watch it, right through your break. Another
> problem was that when the guy that runs it retires, the machine gets
> scrapped.
>
>   
>> The other approach is to buy a gear cutter with the proper form.  Note
>> that unlike a hob (which can be used to cut gears with any number of
>> teeth), a gear cutter is designed for a specific range of teeth.  I
>> think there is usually a set of 8 to cut everything from 12 tooth
>> pinions thru many tooth gears up to a rack (basically a gear with an
>> infinite number of teeth).
>> 
>
> Gear cutting tools are too expensive for me since I usually need one or
> a few of each. Having a way to make any gear without special tooling
> would be a big plus. One reason I am looking at a 2m - 10mm gear is that
> I can use a .063" end mill to cut a thin version.
>   
It has been my understanding that the number eight cutter will cut a 
gear with 12 and 13 teeth. If you get below 12 teeth there has to be 
undercutting for the teeth to run right without chafing against each 
other.   I would think that a 10 tooth gear would need to be generated  
with a hob or a gear shaper.   There was some information on the South 
Bend lathe list where a fellow claimed that a perfect generated tooth 
for can be cut by useing a tap running on the perifery of a gear blank 
and feeding across the face. The blank is left to freewheel and be 
pulled around by the tap.  He claims it makes a perfect tooth???
   Doug

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Re: [Emc-users] Gear Tooth Profile

[Dave Caroline]

Hobbing is easy if you can measure the gear in some way easily, I use
the OD as my size reference and infeed re run to size, the nice thing
about a hobbing machine (well the one here anyway) is you can go back
to the start and still be in gear and run again. As for the use of an
endmill to create the form we had a user in IRC who posted a picture
of his day job doing just that but on a very large scale, I use a
slitting saw to do escape wheels for clocks so is an interesting
exercise in roughing out then following the form. A form tool is
easiest for plain gears but then you are limited to tooth number
ranges as JMK mentioned.

If you make a generic cgode involute program I would be interested seeing it.

Dave Caroline

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Re: [Emc-users] Gear Tooth Profile

[Kirk Wallace]

On Sat, 2009-05-09 at 22:13 +0100, Dave Caroline wrote:
> Hobbing is easy if you can measure the gear in some way easily, I use
> the OD as my size reference and infeed re run to size, the nice thing
> about a hobbing machine (well the one here anyway) is you can go back
> to the start and still be in gear and run again. As for the use of an
> endmill to create the form we had a user in IRC who posted a picture
> of his day job doing just that but on a very large scale, I use a
> slitting saw to do escape wheels for clocks so is an interesting
> exercise in roughing out then following the form. A form tool is
> easiest for plain gears but then you are limited to tooth number
> ranges as JMK mentioned.
> 
> If you make a generic cgode involute program I would be interested seeing it.
> 
> Dave Caroline

Here is the involute I believe applies to my gear.

http://www.wallacecompany.com/machine_shop/gears/involute.png 

The dots to the right on the horizontal line are spaced 9 degrees of
pitch circle apart. So when the pinion rotates 9 degrees it moves one
dot on the rack. The left side shows the same horizontal dots but
rotated around the pinion center the corresponding degrees. The yellow
lines are the distance of the corresponding 9 degree moves. The red line
is the involute of the pitch circle. It's just an XY move and a rotate
for each point.
-- 
Kirk Wallace
http://www.wallacecompany.com/machine_shop/
http://www.wallacecompany.com/E45/index.html
California, USA


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Re: [Emc-users] Gear Tooth Profile

[Kirk Wallace]

On Sat, 2009-05-09 at 17:10 -0400, Douglas Pollard wrote:
> Kirk Wallace wrote:
> > On Sat, 2009-05-09 at 15:07 -0400, John Kasunich wrote:
... snip  
> It has been my understanding that the number eight cutter will cut a 
> gear with 12 and 13 teeth. If you get below 12 teeth there has to be 
> undercutting for the teeth to run right without chafing against each 
> other.

The problem is you can't cut the base of the tooth where the required
path narrows the base, which is a problem if your setup requires you to
keep the cutter's center radial plane in line with the gear axis. 

> I would think that a 10 tooth gear would need to be generated  
> with a hob or a gear shaper.   There was some information on the South 
> Bend lathe list where a fellow claimed that a perfect generated tooth 
> for can be cut by useing a tap running on the perifery of a gear blank 
> and feeding across the face. The blank is left to freewheel and be 
> pulled around by the tap.  He claims it makes a perfect tooth???
>Doug

Well the tap has a trapezoidal shape, just like a hob cutter. After a
couple of turns of the gear, the tap and gear might self synchronize,
like a knurling tool does.
-- 
Kirk Wallace
http://www.wallacecompany.com/machine_shop/
http://www.wallacecompany.com/E45/index.html
California, USA


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Re: [Emc-users] Gear Tooth Profile

[Dave Caroline]

I have a single tooth rack form carbide cutter...I feel this should be
relatively simple to code as a generic x module x teeth 4 axis. Hand
grinding the rack form on flycutters will be easy enough and you can
run the gear pairs in after making. The cycle time to make is going to
be a bit slow though hobbing will always win there and hobbing cutters
are pretty cheap for certain sizes we just need to convince EMC about
geared spindles to match a real machine.

Dave Caroline

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Re: [Emc-users] EMC paper

[ygdan1001]

I am interested in it, too.
Thank you!
yang




在2009-05-08，"Anders Wallin"  写道：
>
>there's a new paper out on desktop parallel kinematic machines which 
>uses EMC2
>http://www.springerlink.com/content/j12r46v2v93g5t07/
>
>
>I have the pdf if anyone is interested.
>
>Anders
>
>--
>The NEW KODAK i700 Series Scanners deliver under ANY circumstances! Your
>production scanning environment may not be a perfect world - but thanks to
>Kodak, there's a perfect scanner to get the job done! With the NEW KODAK i700
>Series Scanner you'll get full speed at 300 dpi even with all image 
>processing features enabled. http://p.sf.net/sfu/kodak-com
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The NEW KODAK i700 Series Scanners deliver under ANY circumstances! Your
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Kodak, there's a perfect scanner to get the job done! With the NEW KODAK i700
Series Scanner you'll get full speed at 300 dpi even with all image 
processing features enabled. http://p.sf.net/sfu/kodak-com
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