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Crankarm is a crankarm?

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landotter

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Jan 24, 2007, 5:36:31 PM1/24/07
to
Neighbor can't find the left crank on a utility bike after they moved
to town. It's square taper, 170mm. Would this Sugino work as a
replacement:

http://tinyurl.com/2jsmw9

It looks obvious, but then there's this mention of unicycling, and
well, I start to wonder...is there unicycle threading? Unicycle
tapering? Wouldn't surprise me with all the different standards in
cycling.

Alternately, if somebody has a 170mm left crank that's doing no good in
a bucket, feel free to mail it to me. :-P

Nigel Cliffe

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Jan 24, 2007, 5:49:11 PM1/24/07
to
landotter wrote:
> Neighbor can't find the left crank on a utility bike after they moved
> to town. It's square taper, 170mm. Would this Sugino work as a
> replacement:
>
> http://tinyurl.com/2jsmw9
>
> It looks obvious, but then there's this mention of unicycling, and
> well, I start to wonder...is there unicycle threading? Unicycle
> tapering? Wouldn't surprise me with all the different standards in
> cycling.

Should work. I believe there is a slight difference in the taper between
Shimano and Campag bits, but fair chance the bike with missing crank has a
Shimano type bottom bracket.
You'll need a crank fixing nut or bolt (depending on type of bottom
bracket), and a LH pedal. I assume the neighbour lost those as well.


> Alternately, if somebody has a 170mm left crank that's doing no good
> in a bucket, feel free to mail it to me. :-P

Even if I did have one, I wouldn't be surprised to find it will cost more
than $12 to mail it from this side of the pond.

- Nigel


--
Nigel Cliffe,
Webmaster at http://www.2mm.org.uk/


Qui si parla Campagnolo

unread,
Jan 25, 2007, 8:52:49 AM1/25/07
to

John Smith

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Jan 25, 2007, 3:45:28 PM1/25/07
to
"landotter" <land...@gmail.com> wrote in message
news:1169678191.6...@l53g2000cwa.googlegroups.com...

> Neighbor can't find the left crank on a utility bike after they moved
...

> It looks obvious, but then there's this mention of unicycling, and
> well, I start to wonder...is there unicycle threading? Unicycle
> tapering? Wouldn't surprise me with all the different standards in
> cycling.
...


Just a guess here but, wouldn't one would use two "left" crank arms on a
unicycle?
One with reverse threading and one with standard threading.

Dave

A Muzi

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Jan 25, 2007, 10:00:15 PM1/25/07
to
> "landotter" <land...@gmail.com> wrote in message
> news:1169678191.6...@l53g2000cwa.googlegroups.com...
>> Neighbor can't find the left crank on a utility bike after they moved
> ...
>> It looks obvious, but then there's this mention of unicycling, and
>> well, I start to wonder...is there unicycle threading? Unicycle
>> tapering? Wouldn't surprise me with all the different standards in
>> cycling.
> ...

John Smith wrote:
> Just a guess here but, wouldn't one would use two "left" crank arms on a
> unicycle?
> One with reverse threading and one with standard threading.

Yes, that's correct.

Back to the OP - Lefts fail in high proportion to rights so replacement
lefts are readily available and cheap everywhere.
--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971

JeffWills

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Jan 26, 2007, 12:46:30 AM1/26/07
to
On Jan 25, 7:00 pm, A Muzi <a...@yellowjersey.org> wrote:
>
> Back to the OP - Lefts fail in high proportion to rights so replacement
> lefts are readily available and cheap everywhere.
> --
> Andrew Muzi www.yellowjersey.org

Unicycle arm sets are available for cheap:
http://www.bikepartsusa.com/product_info.asp?p=01%2D98134
http://www.bikepartsusa.com/product_info.asp?p=01%2D98133

Bike Parts USA has some unicycle parts, but there's probably better
sources out there.

Jeff

landotter

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Jan 26, 2007, 1:39:25 AM1/26/07
to

On Jan 25, 9:00 pm, A Muzi <a...@yellowjersey.org> wrote:
> > "landotter" <landot...@gmail.com> wrote in message


> >news:1169678191.6...@l53g2000cwa.googlegroups.com...
> >> Neighbor can't find the left crank on a utility bike after they moved
> > ...
> >> It looks obvious, but then there's this mention of unicycling, and
> >> well, I start to wonder...is there unicycle threading? Unicycle
> >> tapering? Wouldn't surprise me with all the different standards in
> >> cycling.
> > ...
> John Smith wrote:
> > Just a guess here but, wouldn't one would use two "left" crank arms on a
> > unicycle?

> > One with reverse threading and one with standard threading.Yes, that's correct.


>
> Back to the OP - Lefts fail in high proportion to rights so replacement
> lefts are readily available and cheap everywhere.

Ya, that surprised me.Never would I thought that crank failure would be
common enough to create a market for individual crank arms.

I'll check with the local Jesus People Punks first as they are pretty
hip to the scavenging thing.

Donald Gillies

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Jan 26, 2007, 3:35:03 PM1/26/07
to
A Muzi <a...@yellowjersey.org> writes:

>Back to the OP - Lefts fail in high proportion to rights so replacement
>lefts are readily available and cheap everywhere.

Fascinating. I guess it makes perfect sense, since the spider
probably reinforces the right crank arm / spindle interface, assuming
that's where the left arms fail.

I suspect that failures at the pedal eye should be the same for both
left and right cranks, is this borne out by experience, all ye
professional mechanics and shop owners ??

- Don Gillies
San Diego, CA

P.S. If the failure rates at the pedal eye are different for left
vs. right crank arms, then is it perhaps because the twisting flexion
is higher on the left sides ??

jobst....@stanfordalumni.org

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Jan 26, 2007, 4:14:18 PM1/26/07
to
A ceankarmlever is CRANK... except in bicycling where a different
regime holds the reigns.

http://www.m-w.com/dictionary/crank

Jobst Brandt

carl...@comcast.net

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Jan 26, 2007, 4:19:23 PM1/26/07
to
On 26 Jan 2007 12:35:03 -0800, gil...@cs.ubc.ca (Donald Gillies)
wrote:

Dear Don,

The left pedal's driving force goes all the way down to the bottom
bracket.

The right pedal's driving force gets sidetracked and goes through the
sprocket to the chain.

Cheers,

Carl Fogel

jobst....@stanfordalumni.org

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Jan 26, 2007, 5:58:08 PM1/26/07
to
A Muzi <a...@yellowjersey.org> writes:

>> Just a guess here but, wouldn't one would use two "left" crank arms
>> on a unicycle? One with reverse threading and one with standard
>> threading.

> Yes, that's correct.

> Back to the OP - Lefts fail in high proportion to rights so replacement
> lefts are readily available and cheap everywhere.

I wasn't aware of more left crank failures. With my many crank
failures it was about even, most breaking at the pedal eye. Of
course that stopped occurring after I modified my cranks.

http://www.chiark.greenend.org.uk/~damerell/bikes/brandt-cranks.jpg

To what do you attribute more left crank failures?

Jobst Brandt

carl...@comcast.net

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Jan 26, 2007, 6:42:25 PM1/26/07
to

Humph! After doodling a few diagrams, I don't like my half-remembered
explanation.

The force where the crank meets the bottom bracket is the same for
each side, so pushing down on the left pedal transmits the same force
to the left and right side of the bottom bracket.

The explanation for left cranks failing more often may be that the
left crank force is applied all the way out at the end of the left
pedal on an unsupported arm, while the right crank force is applied
over only half as much distance before the chain supports the arm,
steadying it.

That is, the left crank is free to wave and wallow, while the right
crank is steadied by the chain engaging the sprocket. Imagine a foot
pushing on the two pedals below

BB-------------------pedal left crank
x supported only at x

sprocket
BB-------chain-------pedal right crank
x y supported at x and y

Cheers,

Carl Fogel

Ben C

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Jan 26, 2007, 6:50:04 PM1/26/07
to
On 2007-01-26, carl...@comcast.net <carl...@comcast.net> wrote:
[snip]

>>The left pedal's driving force goes all the way down to the bottom
>>bracket.
>>
>>The right pedal's driving force gets sidetracked and goes through the
>>sprocket to the chain.
>>
>>Cheers,
>>
>>Carl Fogel
>
> Humph! After doodling a few diagrams, I don't like my half-remembered
> explanation.

I felt like I also half-remembered something like this, and I've found
the link:

http://sheldonbrown.com/brandt/installing-cranks.html

"[...] Loss of crank bolt preload is greater on left than the right
cranks, because left cranks transmit torque and bending
simultaneously while right cranks transmit these forces separately.
The left crank transmits driving torque through the spindle to the
right crank and chainwheel while the right crank drives the
chainwheel directly. Besides that, the right crank transmits torque
to the spindle only when standing on both pedals. Doing this with
the right foot forward (goofy footed) is the only time the spindle
transmits reverse torque. [...]"

David L. Johnson

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Jan 26, 2007, 6:54:10 PM1/26/07
to
On Fri, 26 Jan 2007 22:58:08 +0000, jobst.brandt wrote:

>> Back to the OP - Lefts fail in high proportion to rights so replacement
>> lefts are readily available and cheap everywhere.
>
> I wasn't aware of more left crank failures. With my many crank
> failures it was about even, most breaking at the pedal eye. Of
> course that stopped occurring after I modified my cranks.
>
> http://www.chiark.greenend.org.uk/~damerell/bikes/brandt-cranks.jpg
>
> To what do you attribute more left crank failures?

I suspect he is actually referring to the instances of ruined cranks due
to a loose fit on the spindle, which is much more common on the left side.

--

David L. Johnson

You will say Christ saith this and the apostles say this; but what canst
thou say? -- George Fox.

carl...@comcast.net

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Jan 26, 2007, 6:53:34 PM1/26/07
to

Double humph!

A further difference is that the left pedal force is applied
out-of-plane to the left side of the crank, but is tranmitted mostly
in-plane on the right side of the bottom bracket to the sprocket:

--- idle right pedal
|
|
S sprocket and chain in plane
|
|
F-------F much less twisting force on right side of BB
|
|
|
|
P-- push down on left pedal out at P

pushing down on left side
force is applied out of plane on pedal
twists left crank at bottom bracket

When the rider pushes down on the right pedal, the effect of the
out-of-plane force on that side is reduce because of the chain and
sprocket support about half-way along the crank.

CF

jobst....@stanfordalumni.org

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Jan 26, 2007, 7:38:41 PM1/26/07
to
David L. Johnson writes:

>>> Back to the OP - Lefts fail in high proportion to rights so
>>> replacement lefts are readily available and cheap everywhere.

>> I wasn't aware of more left crank failures. With my many crank
>> failures it was about even, most breaking at the pedal eye. Of
>> course that stopped occurring after I modified my cranks.

>> http://www.chiark.greenend.org.uk/~damerell/bikes/brandt-cranks.jpg

>> To what do you attribute more left crank failures?

> I suspect he is actually referring to the instances of ruined cranks
> due to a loose fit on the spindle, which is much more common on the
> left side.

I thought of that too, when I saw Carl Fogel's quote from the FAQ in
this thread. I was thinking more of crank failure from breaking off
rather than a damaged square taper.

Jobst Brandt

John Dacey

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Jan 26, 2007, 9:22:43 PM1/26/07
to
"Ego sum rex Romanus, et supra grammaticam." - Sigismund

On 26 Jan 2007 21:14:18 GMT, jobst....@stanfordalumni.org wrote:

>A ceankarmlever is CRANK... except in bicycling where a different
>regime holds the reigns.

On 27 Jan 2007 00:38:41 GMT, jobst....@stanfordalumni.org wrote:

> I was thinking more of crank failure from breaking off
>rather than a damaged square taper.

A "square taper" is oxymoronic, except apparently for the
self-selected lexicographer of rbt.
-------------------------------
John Dacey
Business Cycles, Miami, Florida
Since 1983
Our catalog of track equipment: online since 1996
Phone: 305-273-4440
http://www.businesscycles.com
-------------------------------

carl...@comcast.net

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Jan 26, 2007, 9:41:57 PM1/26/07
to

Dear Jobst & John

On the one hand, isn't my octalink tapered?

On the other hand, anyone who wants to quibble about language should:

First, proofread for "ceankarmlever" errors.

Second, learn the difference between "reigns" and "reins" (no bonus
for "rains").

Third, offer a short, clear, convenenient way to describe the
individual parts of the crank-thingy as opposed to the whole
crank-thingy assembly.

If we limit "crank" to mean just one arm, what are two cranks
connected by a bottom bracket? A meta-crank? An armed bottom-bracket?

And let's face it, "bottom-bracket" has a silly etymology.

I'll taper off now . . .

Cheers,

Carl Fogel

David L. Johnson

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Jan 26, 2007, 10:20:17 PM1/26/07
to
On Fri, 26 Jan 2007 21:22:43 -0500, John Dacey wrote:

> A "square taper" is oxymoronic, except apparently for the
> self-selected lexicographer of rbt.

Itching for a flamewar? Come on, the cross-section is square.
Technically I would call it the frustrum of a pyramid, but....

--

David L. Johnson

It is probable that television drama of high caliber and produced by
first-rate artists will materially raise the level of dramatic taste
in the nation. -- David Sarnoff, 1939

carl...@comcast.net

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Jan 26, 2007, 10:32:02 PM1/26/07
to
On Fri, 26 Jan 2007 21:20:17 -0600, "David L. Johnson"
<david....@lehigh.edu> wrote:

>On Fri, 26 Jan 2007 21:22:43 -0500, John Dacey wrote:
>
>> A "square taper" is oxymoronic, except apparently for the
>> self-selected lexicographer of rbt.
>
>Itching for a flamewar? Come on, the cross-section is square.
>Technically I would call it the frustrum of a pyramid, but....

Dear David,

Thanks for the best quibble I've seen in months!

Some consider the second "r" in your "frustrum" to be a spelling
error, but not me--I'm going to steal your point and complain heatedly
if any poster is so dead to shame as to refer to mythical "square
tapers" on this newsgroup.

Cheers,

Carl Fogel

jobst....@stanfordalumni.org

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Jan 26, 2007, 11:10:16 PM1/26/07
to
John Dacey writes:

> "Ego sum rex Romanus, et supra grammaticam." - Sigismund

>> A ceankarmlever is CRANK... except in bicycling where a different
>> regime holds the reigns.

> On 27 Jan 2007 00:38:41 GMT, jobst....@stanfordalumni.org wrote:

>> I was thinking more of crank failure from breaking off
>> rather than a damaged square taper.

> A "square taper" is oxymoronic, except apparently for the
> self-selected lexicographer of rbt.

Oh? How do you define a square shaft that is tapered toward its end.

There are conical ends which are tapered round shafts and there are
tapered splines as in ISIS.

Please explain. You cryptic comment reeks of pique.

Jobst Brandt

carl...@comcast.net

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Jan 26, 2007, 11:24:57 PM1/26/07
to

Dear Jobst,

In answering your deeply sincere question, David Johnson has lit a
beacon that shines a powerful and informative light upon the matter,
forever banishing the painfully incorrect phrase "square taper" from
RBT.

It's a frustrum. (Or frustum.)

Cheers,

Carl Fogel

jobst....@stanfordalumni.org

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Jan 26, 2007, 11:36:45 PM1/26/07
to
Carl Fogel writes:

>>> "Ego sum rex Romanus, et supra grammaticam." - Sigismund

>>>> A ceankarmlever is CRANK... except in bicycling where a different
>>>> regime holds the reigns.

>>>> I was thinking more of crank failure from breaking off


>>>> rather than a damaged square taper.

>>> A "square taper" is oxymoronic, except apparently for the
>>> self-selected lexicographer of rbt.

>>Oh? How do you define a square shaft that is tapered toward its end.

>>There are conical ends which are tapered round shafts and there are
>>tapered splines as in ISIS.

>>Please explain. You cryptic comment reeks of pique.

> In answering your deeply sincere question, David Johnson has lit a


> beacon that shines a powerful and informative light upon the matter,
> forever banishing the painfully incorrect phrase "square taper" from
> RBT.

> It's a frustrum. (Or frustum.)

From my understanding a frustum does not define the shape, it meaning
any truncated solid tapered figure, cone or hexagonal taper, if you
will.

What is it about square taper that doesn't define the shape of the
crank/spindle interface unambiguously?

Jobst Brandt

John Dacey

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Jan 26, 2007, 11:53:23 PM1/26/07
to
"Magna eloquentia, sicut flamma, materia alitur, et motibus excitatur
et urendo clarescit." - Tacitus

On Fri, 26 Jan 2007 21:20:17 -0600, "David L. Johnson"
<david....@lehigh.edu> wrote:

>On Fri, 26 Jan 2007 21:22:43 -0500, John Dacey wrote:
>
>> A "square taper" is oxymoronic, except apparently for the
>> self-selected lexicographer of rbt.
>
>Itching for a flamewar? Come on, the cross-section is square.
>Technically I would call it the frustrum of a pyramid, but....

Flamewar? - I don't think so. I content myself with simply pointing
out the inconsistency of allowing this conspicuously
self-contradictory term to go unexamined while the use of other
colloquialisms (crankarm, crankset, inter alia) from the cycling
vernacular have regularly been singled out for punishment.

I've never heard of a frustrum before, but I think it's a much better
descriptor (albeit funny-sounding). By definition, squares don't
taper.

carl...@comcast.net

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Jan 26, 2007, 11:53:03 PM1/26/07
to
On 27 Jan 2007 04:36:45 GMT, jobst....@stanfordalumni.org wrote:

>Carl Fogel writes:
>
>>>> "Ego sum rex Romanus, et supra grammaticam." - Sigismund
>
>>>>> A ceankarmlever is CRANK... except in bicycling where a different
>>>>> regime holds the reigns.
>
>>>>> I was thinking more of crank failure from breaking off
>>>>> rather than a damaged square taper.
>
>>>> A "square taper" is oxymoronic, except apparently for the
>>>> self-selected lexicographer of rbt.
>
>>>Oh? How do you define a square shaft that is tapered toward its end.
>
>>>There are conical ends which are tapered round shafts and there are
>>>tapered splines as in ISIS.
>
>>>Please explain. You cryptic comment reeks of pique.
>
>> In answering your deeply sincere question, David Johnson has lit a
>> beacon that shines a powerful and informative light upon the matter,
>> forever banishing the painfully incorrect phrase "square taper" from
>> RBT.
>
>> It's a frustrum. (Or frustum.)
>
>From my understanding a frustum does not define the shape, it meaning
>any truncated solid tapered figure, cone or hexagonal taper, if you
>will.

[snip]

Dear Jobst,

Er, why doesn't your understanding of "any truncated solid tapered
figure" include a tapering figure with a four-sided base?

It's on the left side of the back of a dollar bill.

Admittedly, most efforts to explain the truncated pyramid involve the
all-seeing eye above it, but we at RBT now know that it's actually a
hidden anti-isis, anti-octalink symbol:

http://en.wikipedia.org/wiki/Image:Eye.jpg

Who would have thought that an innocent thread about crankarms would
lead to the discovery that the masonic founding fathers secretly
favored Campagnolo bottom bracket spindle design over Shimano?

Cheers,

Carl Fogel

Tim McNamara

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Jan 27, 2007, 12:03:10 AM1/27/07
to
In article <BLacnQyDj89...@ptd.net>,

"David L. Johnson" <david....@lehigh.edu> wrote:

> On Fri, 26 Jan 2007 21:22:43 -0500, John Dacey wrote:
>
> > A "square taper" is oxymoronic, except apparently for the
> > self-selected lexicographer of rbt.
>
> Itching for a flamewar? Come on, the cross-section is square.
> Technically I would call it the frustrum of a pyramid, but....

How about an "isosceles cube?" ;-)

Clive George

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Jan 27, 2007, 12:05:15 AM1/27/07
to
"John Dacey" <jda...@businesscycles.com> wrote in message
news:tkmlr2hflh5a7ihfd...@4ax.com...

> I've never heard of a frustrum before, but I think it's a much better
> descriptor (albeit funny-sounding). By definition, squares don't
> taper.

Sort of. (Ever read Flatland?). It's a 2D term being used to describe a 3D
object - provided a square is somewhere, it's a legitimate use. The taper is
in the other dimension, therefore the combination of the two describes the
whole 3D object.

That's my theory for now, anyway :-)

cheers,
clive

landotter

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Jan 27, 2007, 12:23:44 AM1/27/07
to

On Jan 25, 9:00 pm, A Muzi <a...@yellowjersey.org> wrote:

> > "landotter" <landot...@gmail.com> wrote in message


> >news:1169678191.6...@l53g2000cwa.googlegroups.com...
> >> Neighbor can't find the left crank on a utility bike after they moved
> > ...
> >> It looks obvious, but then there's this mention of unicycling, and
> >> well, I start to wonder...is there unicycle threading? Unicycle
> >> tapering? Wouldn't surprise me with all the different standards in
> >> cycling.
> > ...
> John Smith wrote:
> > Just a guess here but, wouldn't one would use two "left" crank arms on a
> > unicycle?

> > One with reverse threading and one with standard threading.Yes, that's correct.


>
> Back to the OP - Lefts fail in high proportion to rights so replacement
> lefts are readily available and cheap everywhere.

Perhaps in the Republic of Madison, but I'm in Nashville. A call to REI
had a shakey employee take ten minutes to find a leftie in a catalog.
To REI's credit, they've got the most patient and kind staff in the
city, even if they need a little coaxing sometimes. They did piss me
off the other day--what kind of bike shop, albeit a multi sport chain,
doesn't stock toe straps?! Hrrrrmph! I may have to move to Madison for
a proper bike shop experience, or even back to Chicago so I can go to
Rapid Transit on North Ave.

I'll check if the local Jesus People Punk Rockers on Tall Bikes have a
left arm this weekend, as I've got some booty to trade. Team Murray
handlebars circa '84 anyone?

Joe Riel

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Jan 27, 2007, 1:01:43 AM1/27/07
to
carl...@comcast.net writes:

> In answering your deeply sincere question, David Johnson has lit a
> beacon that shines a powerful and informative light upon the matter,
> forever banishing the painfully incorrect phrase "square taper" from
> RBT.
>
> It's a frustrum. (Or frustum.)

Sorry, it's not a frustum. A frustum is a truncated pyramid. The
defining characteristic of a frustum is that it has two parallel
planes. The base of the taper of a bottom bracket spindle doesn't
exist (except in theory). Next you'll be telling me that this number
2 pencil with a broken lead that I'm twirling on my fingers has a
frustum on one end.

--
Joe Riel

Donald Gillies

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Jan 27, 2007, 1:26:59 AM1/27/07
to
If left cranks fail due to twisting forces being higher on these
cranks, do we only need Octlink / ISIS / flavor-of-the-month-crank
interfaces on the left, so i can keep my trusty square tapered
right-side cranks and reuse them ?? woudn't that be a hoot. Almost
as stupid-tech as ceramic ball bearings, as Qui Campagnolo likes to
say ...

I can imagine more crank squirm due to twisting on the left cranks,
causing more failures at the crank / BB interface.

A Muzi

unread,
Jan 27, 2007, 1:55:12 AM1/27/07
to
> A Muzi <a...@yellowjersey.org> writes:
>> Back to the OP - Lefts fail in high proportion to rights so replacement
>> lefts are readily available and cheap everywhere.

Donald Gillies wrote:
> Fascinating. I guess it makes perfect sense, since the spider
> probably reinforces the right crank arm / spindle interface, assuming
> that's where the left arms fail.
>
> I suspect that failures at the pedal eye should be the same for both
> left and right cranks, is this borne out by experience, all ye
> professional mechanics and shop owners ??
>
> - Don Gillies
> San Diego, CA
>
> P.S. If the failure rates at the pedal eye are different for left
> vs. right crank arms, then is it perhaps because the twisting flexion
> is higher on the left sides ??

It's the smaller amount of material around the spindle on the left I
believe. Failures are largely at the spindle on the left.

Pedal thread failures are about equal left-right but in much smaller numbers

--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971

A Muzi

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Jan 27, 2007, 2:16:59 AM1/27/07
to
op-?

>>> Just a guess here but, wouldn't one would use two "left" crank arms
>>> on a unicycle? One with reverse threading and one with standard
>>> threading.

> A Muzi <a...@yellowjersey.org> writes:
> Yes, that's correct.>
>> Back to the OP - Lefts fail in high proportion to rights so replacement
>> lefts are readily available and cheap everywhere.

jobst....@stanfordalumni.org wrote:
> I wasn't aware of more left crank failures. With my many crank
> failures it was about even, most breaking at the pedal eye. Of
> course that stopped occurring after I modified my cranks.
> http://www.chiark.greenend.org.uk/~damerell/bikes/brandt-cranks.jpg
> To what do you attribute more left crank failures?

Sloppy assembly. Insufficient torque mostly. The industry supplies all
lefts cheaply- with 'ten-pack' pricing. 170, 175; silver and black;
both with the flats inline to the crank axis and the normal diagonal. A
high volume service item for bikes under about $400.

We replace a dozen lefts to every right in service. Lefts drive through
the spindle but are less massive than rights. The taper shows a large
rounded 'star' shape after being ridden loose.

Pedal threads are a different less common failure.

Other shop owners reports?

A Muzi

unread,
Jan 27, 2007, 2:29:36 AM1/27/07
to
-snip-

> On 27 Jan 2007 00:38:41 GMT, jobst....@stanfordalumni.org wrote:
>> I was thinking more of crank failure from breaking off
>> rather than a damaged square taper.


John Dacey wrote:
> A "square taper" is oxymoronic, except apparently for the
> self-selected lexicographer of rbt.

I use that term - 'square taper'.

What do you call "normal" cranks now that we have so frentically many
variants?

A Muzi

unread,
Jan 27, 2007, 2:37:51 AM1/27/07
to
>> On Fri, 26 Jan 2007 21:22:43 -0500, John Dacey wrote:
>>> A "square taper" is oxymoronic, except apparently for the
>>> self-selected lexicographer of rbt.

> On Fri, 26 Jan 2007 21:20:17 -0600, "David L. Johnson"


>> Itching for a flamewar? Come on, the cross-section is square.
>> Technically I would call it the frustrum of a pyramid, but....

John Dacey wrote:
> Flamewar? - I don't think so. I content myself with simply pointing
> out the inconsistency of allowing this conspicuously
> self-contradictory term to go unexamined while the use of other
> colloquialisms (crankarm, crankset, inter alia) from the cycling
> vernacular have regularly been singled out for punishment.
>
> I've never heard of a frustrum before, but I think it's a much better
> descriptor (albeit funny-sounding). By definition, squares don't
> taper.

The square section of _my_ spindle does taper. Doesn't yours?

A Muzi

unread,
Jan 27, 2007, 2:38:57 AM1/27/07
to
>> On Fri, 26 Jan 2007 21:22:43 -0500, John Dacey wrote:
>>> A "square taper" is oxymoronic, except apparently for the
>>> self-selected lexicographer of rbt.

> In article <BLacnQyDj89...@ptd.net>,


>> Itching for a flamewar? Come on, the cross-section is square.

>> Technically IÂ would call it the frustrum of a pyramid, but....

Tim McNamara wrote:
> How about an "isosceles cube?" ;-)

Heh heh heh that's catchy!

Ben C

unread,
Jan 27, 2007, 3:19:59 AM1/27/07
to

I think "square taper" is OK, it's an abbreviation of "square
cross-section taper".

Square tapers are also used in 3D graphics for perspective
transformations.

carl...@comcast.net

unread,
Jan 27, 2007, 3:50:10 AM1/27/07
to

Dear Joe,

Hmmm . . .

I think that I see your analogy--the cone of the sharpened pencil
meets the pencil's hexagonal body in arcs, while the four sides ground
into the spindle meet the spindle's round body in arcs going the other
way.

But I'll gladly "stretch" a point in the "chain" of logic and theorize
the necessary planes near the hypothetical bases of any two frustra
between a rider's ankles.

So I must insist that everyone stop using "square taper" and switch to
using "frustrum" on RBT.

(Or "frustum," just to show how open-minded I am.)

I "sense" that some posters may be a little frustr-ated by my decree,
but it's just as sound as other quibbles often "cranked" out here on
RBT.

:)

Cheers,

Carl Fogel

carl...@comcast.net

unread,
Jan 27, 2007, 3:58:56 AM1/27/07
to
On Sat, 27 Jan 2007 02:19:59 -0600, Ben C <spam...@spam.eggs> wrote:

>On 2007-01-27, carl...@comcast.net <carl...@comcast.net> wrote:
>> On Fri, 26 Jan 2007 21:20:17 -0600, "David L. Johnson"
>><david....@lehigh.edu> wrote:
>>
>>>On Fri, 26 Jan 2007 21:22:43 -0500, John Dacey wrote:
>>>
>>>> A "square taper" is oxymoronic, except apparently for the
>>>> self-selected lexicographer of rbt.
>>>
>>>Itching for a flamewar? Come on, the cross-section is square.

>>>Technically I7ould call it the frustrum of a pyramid, but....


>>
>> Dear David,
>>
>> Thanks for the best quibble I've seen in months!
>>
>> Some consider the second "r" in your "frustrum" to be a spelling
>> error, but not me--I'm going to steal your point and complain heatedly
>> if any poster is so dead to shame as to refer to mythical "square
>> tapers" on this newsgroup.
>
>I think "square taper" is OK, it's an abbreviation of "square
>cross-section taper".
>
>Square tapers are also used in 3D graphics for perspective
>transformations.

Dear Ben,

I'm sorry, but that sounds like the thin end of a non-square wedge.

Next you'll be trying to get me to say that chains "stretch" instead
of "elongate due to internal wear."

Or that calling a "crank" a "crank arm" is anything but a hideous
redundancy intended to spread myth and lore.

If I give in on this point, it will only encourage you to keep posting
without providing your full name, rank, and serial number--

No, I can't listen to anonymous snipers!

Frustrum, frustrum, frustrum!

:)

Cheers,

Carl Fogel

Tim McNamara

unread,
Jan 27, 2007, 10:52:24 AM1/27/07
to
In article <12rm060...@corp.supernews.com>,
A Muzi <a...@yellowjersey.org> wrote:

Well, by definition a square is a two dimensional geometrical shape
consisting of four right angles and four equal sides. It can't taper.
;-)

John Dacey

unread,
Jan 27, 2007, 10:58:00 AM1/27/07
to
On Sat, 27 Jan 2007 01:29:36 -0600, A Muzi <a...@yellowjersey.org>
wrote:

>John Dacey wrote:
>> A "square taper" is oxymoronic,

>


>I use that term - 'square taper'.

Well I always had too, at least until now that David J has shown a
better way. Of course my slovenly ways also regularly include saying
crankset, hubset, wheelset and a few others that seem to really spall
the balls of the crank fundamentalists here. I wouldn't want you to
think me to be entirely without standards though -- I'd happily make
saying (or worse, writing) "groupos" and its 'pp' variant a capital
crime.

>What do you call "normal" cranks now that we have so frentically many
>variants?

With the developments in this thread, "frustumated" would be my
candidate, but I'll likely wait to see what the real scholars adopt
and then just follow along as I'd done previously with square taper.

-------------------------------
John Dacey
Business Cycles, Miami, Florida
Since 1983

Comprehensive catalogue of track equipment: online since 1996
http://www.businesscycles.com
-------------------------------

John Dacey

unread,
Jan 27, 2007, 1:23:27 PM1/27/07
to
On 27 Jan 2007 04:10:16 GMT, jobst....@stanfordalumni.org wrote:

>John Dacey writes:
>
>> "Ego sum rex Romanus, et supra grammaticam." - Sigismund
>
>>> A ceankarmlever is CRANK... except in bicycling where a different
>>> regime holds the reigns.
>
>> On 27 Jan 2007 00:38:41 GMT, jobst....@stanfordalumni.org wrote:
>
>>> I was thinking more of crank failure from breaking off
>>> rather than a damaged square taper.
>
>> A "square taper" is oxymoronic, except apparently for the
>> self-selected lexicographer of rbt.
>
>Oh? How do you define a square shaft that is tapered toward its end.

As I've now come to understand, it's a square based pyramidal
frustrum.

>
>There are conical ends which are tapered round shafts and there are
>tapered splines as in ISIS.

Yes, plus splined versions that don't taper at all (Shimano HollowTech
II), but if you insist on precise technical language from others for
"crank", it's inconsistent not to also see the incongruity in saying
"square taper" when you are referring to spindles with quadrilateral
tapering facets.

-------------------------------
John Dacey
Business Cycles, Miami, Florida
Since 1983

Comprehensive catalogue of track equipment: online since 1996
http://www.businesscycles.com
-------------------------------

jobst....@stanfordalumni.org

unread,
Jan 27, 2007, 1:54:34 PM1/27/07
to
Carl Fogel writes:

>>>>> "Ego sum rex Romanus, et supra grammaticam." - Sigismund

>>>>>> A ceankarmlever is CRANK... except in bicycling where a
>>>>>> different regime holds the reigns.

>>>>>> I was thinking more of crank failure from breaking off rather
>>>>>> than a damaged square taper.

>>>>> A "square taper" is oxymoronic, except apparently for the
>>>>> self-selected lexicographer of rbt.

>>>> Oh? How do you define a square shaft that is tapered toward its
>>>> end.

>>>> There are conical ends which are tapered round shafts and there
>>>> are tapered splines as in ISIS.

>>>> Please explain. You cryptic comment reeks of pique.

>>> In answering your deeply sincere question, David Johnson has lit a
>>> beacon that shines a powerful and informative light upon the
>>> matter, forever banishing the painfully incorrect phrase "square
>>> taper" from RBT.

>>> It's a frustrum. (Or frustum.)

>> From my understanding a frustum does not define the shape, it
>> meaning any truncated solid tapered figure, cone or hexagonal
>> taper, if you will.

> Er, why doesn't your understanding of "any truncated solid tapered


> figure" include a tapering figure with a four-sided base?

Yes it does but the converse is not true. Therefore, the term
"frustum" does not define what shape is truncated, only that it is.
I'm sure you are not proposing writers describing their crank spindle
begin using the term frustum.

> It's on the left side of the back of a dollar bill.

> Admittedly, most efforts to explain the truncated pyramid involve
> the all-seeing eye above it, but we at RBT now know that it's
> actually a hidden anti-isis, anti-octalink symbol:

http://en.wikipedia.org/wiki/Image:Eye.jpg

> Who would have thought that an innocent thread about crankarms would
> lead to the discovery that the masonic founding fathers secretly
> favored Campagnolo bottom bracket spindle design over Shimano?

Oh! I thought the discussion was about cranks, not "crannkarms" a
term found only in wreck.bike.

http://www.m-w.com/dictionary/crankarm
http://www.m-w.com/dictionary/crank

Jobst Brandt

jobst....@stanfordalumni.org

unread,
Jan 27, 2007, 2:03:41 PM1/27/07
to
John Dacey writes:

> "Magna eloquentia, sicut flamma, materia alitur, et motibus
> excitatur et urendo clarescit." - Tacitus

>>> A "square taper" is oxymoronic, except apparently for the
>>> self-selected lexicographer of rbt.

>> Itching for a flamewar? Come on, the cross-section is square.
>> Technically I would call it the frustrum of a pyramid, but....

> Flamewar? - I don't think so. I content myself with simply pointing
> out the inconsistency of allowing this conspicuously
> self-contradictory term to go unexamined while the use of other
> colloquialisms (crankarm, crankset, inter alia) from the cycling
> vernacular have regularly been singled out for punishment.

> I've never heard of a frustrum before, but I think it's a much better
> descriptor (albeit funny-sounding).

That's because the word is "frustum" and you should have seen it in
geometry class where it is described in most schools.

> By definition, squares don't taper.

We aren't talking about squares but the square shape of a taper.
Similarly there are round, hexagonal, triangular and square shafts that
are tapered. English has many words that in context are verbs, nouns,
adverbs and adjectives. Without that, crossword puzzles would be less
puzzling.

Jobst Brandt

jobst....@stanfordalumni.org

unread,
Jan 27, 2007, 2:24:07 PM1/27/07
to
John Dacey writes:

>>>> A ceankarmlever is CRANK... except in bicycling where a different
>>>> regime holds the reigns.

>>> On 27 Jan 2007 00:38:41 GMT, jobst....@stanfordalumni.org wrote:

>>>> I was thinking more of crank failure from breaking off
>>>> rather than a damaged square taper.

>>> A "square taper" is oxymoronic, except apparently for the
>>> self-selected lexicographer of rbt.

>> Oh? How do you define a square shaft that is tapered toward its
>> end.

> As I've now come to understand, it's a square based pyramidal
> frustrum.

>> There are conical ends which are tapered round shafts and there are
>> tapered splines as in ISIS.

> Yes, plus splined versions that don't taper at all (Shimano HollowTech
> II), but if you insist on precise technical language from others for
> "crank", it's inconsistent not to also see the incongruity in saying
> "square taper" when you are referring to spindles with quadrilateral
> tapering facets.

If you want to show off your geometric agility, you'll need to specify
what sort of quadrilateral, not just a rectangle, trapezoid, or
parallelogram, but a square (equilateral rectangle). I see you really
did skip geometry in school. I though you were just joking.

Jobst Brandt

carl...@comcast.net

unread,
Jan 27, 2007, 2:25:40 PM1/27/07
to
On 27 Jan 2007 18:54:34 GMT, jobst....@stanfordalumni.org wrote:

[snip]

>Oh! I thought the discussion was about cranks, not "crannkarms" a
>term found only in wreck.bike.
>
>http://www.m-w.com/dictionary/crankarm
>http://www.m-w.com/dictionary/crank
>
>Jobst Brandt

QED

Ben C

unread,
Jan 27, 2007, 3:45:58 PM1/27/07
to
On 2007-01-27, jobst....@stanfordalumni.org <jobst....@stanfordalumni.org> wrote:
> John Dacey writes:
[snip]

>> Yes, plus splined versions that don't taper at all (Shimano HollowTech
>> II), but if you insist on precise technical language from others for
>> "crank", it's inconsistent not to also see the incongruity in saying
>> "square taper" when you are referring to spindles with quadrilateral
>> tapering facets.
>
> If you want to show off your geometric agility, you'll need to specify
> what sort of quadrilateral, not just a rectangle, trapezoid, or
> parallelogram, but a square (equilateral rectangle).

I interpreted "quadrilateral facets" as referring to the four
trapezoidal faces of the frustrum, not to its square cross-section.

I was going to say "trapezium", but that would have been as confusing as
talking about using "paraffin" to clean chains.

http://mathworld.wolfram.com/Trapezium.html

"There are two common definitions of the trapezium. The American
definition is a quadrilateral with no parallel sides. The British
definition for a trapezium is a quadrilateral with two sides
parallel"

jobst....@stanfordalumni.org

unread,
Jan 27, 2007, 4:24:01 PM1/27/07
to
Ben C? writes:

>>> Yes, plus splined versions that don't taper at all (Shimano
>>> HollowTech II), but if you insist on precise technical language
>>> from others for "crank", it's inconsistent not to also see the
>>> incongruity in saying "square taper" when you are referring to
>>> spindles with quadrilateral tapering facets.

>> If you want to show off your geometric agility, you'll need to
>> specify what sort of quadrilateral, not just a rectangle,
>> trapezoid, or parallelogram, but a square (equilateral rectangle).

> I interpreted "quadrilateral facets" as referring to the four
> trapezoidal faces of the frustrum, not to its square cross-section.

http://www.m-w.com/dictionary/frustum

Let's not add a new piece of jargon to wreck.bike with the "frustrum".

> I was going to say "trapezium", but that would have been as
> confusing as talking about using "paraffin" to clean chains.

http://mathworld.wolfram.com/Trapezium.html

# There are two common definitions of the trapezium. The American
# definition is a quadrilateral with no parallel sides. The
# British definition for a trapezium is a quadrilateral with two
# sides parallel"

http://mathworld.wolfram.com/Trapezoid.html

# A trapezoid is a quadrilateral with two sides parallel. The
# trapezoid is equivalent to the British definition of trapezium
# (Bronshtein and Semendyayev 1977, p. 174).


I don't see how any of that bears on a square taper, which is what we
have on crank spindles. The word "square" refers to the cross section
and "taper" the reduction in that cross section toward its end. I see
this whole exercise as a smoke screen for wishy washy descriptions,
and an attempt to make describing mechanical parts an imprecise quirk
of language rather than sloppy writing.

Jobst Brandt

carl...@comcast.net

unread,
Jan 27, 2007, 4:41:06 PM1/27/07
to

Dear Ben,

Maybe we should distinguish the American from the British definition
by spelling them "trapezum" and "trapezium"?

http://www.worldwidewords.org/articles/aluminium.htm

Cheers,

H. Davy

Ben C

unread,
Jan 27, 2007, 4:43:04 PM1/27/07
to
> Ben C? writes:
[snip]

>>> If you want to show off your geometric agility, you'll need to
>>> specify what sort of quadrilateral, not just a rectangle,
>>> trapezoid, or parallelogram, but a square (equilateral rectangle).
>
>> I interpreted "quadrilateral facets" as referring to the four
>> trapezoidal faces of the frustrum, not to its square cross-section.
[snip]

> I don't see how any of that bears on a square taper, which is what we
> have on crank spindles.

The truncated pyramid shape that we're referring to with "frustum" has 6
faces altogether, a square base at each end and four trapezoidal faces
around the sides. The "quadrilateral tapering facets" I took to mean
these trapezoidal faces around the sides. That's all I was saying.

> The word "square" refers to the cross section and "taper" the
> reduction in that cross section toward its end.

I agree, I can see nothing wrong at all with the term "square taper" and
said as much in an earlier post.

It's common to characterize shapes by their cross-section-- "triangular
prism", "U-shaped drainpipe", etc.

In fact, looking at mathworld some more, we could describe the shape as
a "square prismatoid", or more strictly as a "square prismoid"

http://mathworld.wolfram.com/Prismatoid.html

Substitute "prismoid" for the more natural word "taper" and there you
have it, a square taper.

> I see this whole exercise as a smoke screen for wishy washy
> descriptions, and an attempt to make describing mechanical parts an
> imprecise quirk of language rather than sloppy writing.

I think the exercise is more just one of Carl having some fun :)

carl...@comcast.net

unread,
Jan 27, 2007, 4:57:18 PM1/27/07
to

Dear Ben,

Fie, fie, foh, frustrum!

To adapt Robertson Davies' noble motto concerning the salted-nut
traffic and his hopes for a nut-free Canada, I shall not sheathe my
sword until we have a square-taper free RBT!

Or until I read fewer "cranky" posts.

:)

Semper frustum, numquam quadra!

Cheers,

Carl Fogel

Joe Riel

unread,
Jan 27, 2007, 5:51:38 PM1/27/07
to
carl...@comcast.net writes:

> Frustrum, frustrum, frustrum!

Where'd you learn to conjugate?

Frustum, Frustati, Frustavi, Frustrated!

'Course, we don't usually conjugate nouns...

--
Joe Riel

Tim McNamara

unread,
Jan 27, 2007, 6:04:25 PM1/27/07
to
In article <87wt382...@san.rr.com>, Joe Riel <jo...@san.rr.com>
wrote:

Nouns have declensions.

carl...@comcast.net

unread,
Jan 27, 2007, 6:45:15 PM1/27/07
to

Dear Joe,

It could be similar to one of those irregularly conjugated proper
verbs derived from obscure nouns or a mish-mash of related
infinitives:

I jest, thou Joest, Jobst Jobsts.

Today I jest, yesterday I Joed, I have Jobsted.

Cheers,

Carl Fogel

A Muzi

unread,
Jan 27, 2007, 7:06:40 PM1/27/07
to
> carl...@comcast.net writes:
>> Frustrum, frustrum, frustrum!

Joe Riel wrote:
> Where'd you learn to conjugate?
> Frustum, Frustati, Frustavi, Frustrated!
> 'Course, we don't usually conjugate nouns...

We conjugate verbs, nouns get . . .declined? the declension goes:
Frustum
Frusti
Frusto
Frustum
Frustum
Frusto

plurals are left to the reader's further research -
(I can't remember them)

Joe Riel

unread,
Jan 27, 2007, 7:33:11 PM1/27/07
to
Tim McNamara <tim...@bitstream.net> writes:

Does one decline a noun?

The Latin word, frustum, means a crumb, a bit.
So a bit of a cone would be a frustum of a cone.

However, frustra, which is Carl's spelling, is
an adverb meaning "without reason" or "groundlessly".
Hmmm...

--
Joe Riel

Tim McNamara

unread,
Jan 27, 2007, 7:51:41 PM1/27/07
to
In article <87sldw2...@san.rr.com>, Joe Riel <jo...@san.rr.com>
wrote:

> Tim McNamara <tim...@bitstream.net> writes:
>
> > In article <87wt382...@san.rr.com>, Joe Riel <jo...@san.rr.com>
> > wrote:
> >
> >> carl...@comcast.net writes:
> >>
> >> > Frustrum, frustrum, frustrum!
> >>
> >> Where'd you learn to conjugate?
> >>
> >> Frustum, Frustati, Frustavi, Frustrated!
> >>
> >> 'Course, we don't usually conjugate nouns...
> >
> > Nouns have declensions.
>
> Does one decline a noun?

Yes, just as one conjugates verbs. Modern English makes very little use
of declension, unlike Old and Middle English.

http://en.wikipedia.org/wiki/Declension

By contrast, the Gaelic languages make much use of declension, on the
other hand. Gearoid O Laoi, who posts occasionally, could expound on
this better than I can as he is fluent in Gaeilge (Irish). It was when
I was trying to learn a bit of Gaeilge that I first ran across the term
and hadn't the faintest idea what they were on about.

Tim McNamara

unread,
Jan 27, 2007, 7:54:24 PM1/27/07
to
In article <12rnq44...@corp.supernews.com>,
A Muzi <a...@yellowjersey.org> wrote:

> > carl...@comcast.net writes:
> >> Frustrum, frustrum, frustrum!
>
> Joe Riel wrote:
> > Where'd you learn to conjugate?
> > Frustum, Frustati, Frustavi, Frustrated!
> > 'Course, we don't usually conjugate nouns...
>
> We conjugate verbs, nouns get . . .declined? the declension goes:
> Frustum
> Frusti
> Frusto
> Frustum
> Frustum
> Frusto

There is a Milne-ian quality to that.

Joe Riel

unread,
Jan 28, 2007, 12:08:03 AM1/28/07
to
A Muzi <a...@yellowjersey.org> writes:

>> carl...@comcast.net writes:
>>> Frustrum, frustrum, frustrum!
>
> Joe Riel wrote:
>> Where'd you learn to conjugate?
>> Frustum, Frustati, Frustavi, Frustrated!
>> 'Course, we don't usually conjugate nouns...
>
> We conjugate verbs, nouns get . . .declined? the declension goes:
> Frustum
> Frusti
> Frusto
> Frustum
> Frustum
> Frusto
>
> plurals are left to the reader's further research -
> (I can't remember them)

Frusta
Frustorum
Frustis
Frusta
Frusta
Frustis

Fortunately I have a dogeared copy of Bennett's New Latin Grammar
handy. Don't all former Latin scholars?

Popa fidem scit.
--
Joe Riel

John Thompson

unread,
Jan 28, 2007, 2:49:20 PM1/28/07
to

And as Mark Twain wrote: "I'd rather decline two drinks than one German
noun!"

--

John (jo...@os2.dhs.org)

John Dacey

unread,
Jan 28, 2007, 8:24:25 PM1/28/07
to

It's pointless to further qualify the type of quadrilateral since
spindles of this class have had, without exception that I recall,
square bases. If you can identify a model with sides of differing
lengths or angles other than 90 degrees, I'll happily revisit this.

I didn't actually skip geometry, but I confess that I cruised through.
Full investment to all those pesky formulae became difficult when,
just as in the instant case, I found that it was often easy to
adequately calculate a volume of hot air when presented with one.


-------------------------------
John Dacey
Business Cycles, Miami, Florida
Since 1983

Our catalog of track equipment: online since 1996
Phone: 305-273-4440
http://www.businesscycles.com
-------------------------------

jobst....@stanfordalumni.org

unread,
Jan 28, 2007, 11:44:49 PM1/28/07
to
John Dacey writes:

> It's pointless to further qualify the type of quadrilateral since
> spindles of this class have had, without exception that I recall,
> square bases. If you can identify a model with sides of differing
> lengths or angles other than 90 degrees, I'll happily revisit this.

> I didn't actually skip geometry, but I confess that I cruised through.
> Full investment to all those pesky formulae became difficult when,
> just as in the instant case, I found that it was often easy to
> adequately calculate a volume of hot air when presented with one.

You're dodging and weaving now. The term is used to differentiate
between Octalink, Isis tapered spline, Shimano clamped straight spline
and Campagnolo fixed spindle halves. The discussion was about whether
a square shaft could be called tapered, not that your cranks have
square tapers.

It doesn't befit a contributor to this forum to belittle education,
our president does that adequately in word and deed.

Jobst Brandt

carl...@comcast.net

unread,
Jan 29, 2007, 2:05:06 AM1/29/07
to
On 29 Jan 2007 04:44:49 GMT, jobst....@stanfordalumni.org wrote:

[snip]

> The discussion was about whether a square shaft could be called
>tapered, not that your cranks have square tapers.

[snip]

Dear Jobst,

Previously you wrote in this thread:

"Oh! I thought the discussion was about cranks, not 'crannkarms' a
term found only in wreck.bike."

http://groups.google.com/group/rec.bicycles.tech/msg/46e6d60667e79dcb

Let us know when you decide for sure what the discussion is about.

Cheers,

Carl Fogel

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