Awl--

Proly more inneresting to cadcamless muhfugguhs such as m'self, but mebbe
otherwise useful.

The Q is:
For a given 90 deg. V slot (eg, one V-slot in the back vise jaw), what is
the smallest rod that can be held in a V-slot (ie, too small a rod will
rattle), AND, what is largest rod that can be held by that same V slot (ie,
where the V slot walls will indeed hold the rod tangently and therefore
stable-ly, and not on the cusp of the V)?

Answer: ( d=depth of V slot; D=diam of rod )

D(small) = .829 d; D(large) = 2.828 d;
w/ the ratio of the large diameter to the small diameter being about 3.4.

Example:

Spose you want to hold a 1/8 rod horizontally in a vise jaw. You will need
to mill a V-slot no deeper than .151 deep.

Now, using the formula for D(large), the largest rod that can be stablely
held by this same V slot is max .427 diam. Or, just multiply the 1/8 rod
by the above 3.4 factor.

Probably, for 1/8 rod, you'd mill a V .135 deep, which would then limit your
large rod to about .375--still not a bad range.

Or so I think.

Now, what about iffin your V is not 90 deg? This is more of a pita, but
still do-able.

The formula becomes:
D(small) = 2d/(cos a + (sin a * tan a) + 1),

where the angle a is 90 - (included angle/2) of the V .

Or so I think.

Haven't gotten around to the D(large) for non-90 deg V's, cuz, well, my
vision is blurring and I got a bad sugar munchie attack.

Related to this is is *how high* a ball (radius = r) sits in a V-slot.
For a 90 deg V, a ball is raised by the amount .414 r .

For what it's all worth.
Iffin inyone is dyin to see the derivations, email me. Proly good SAT
practice'n'**** fer yer urchins.
----------------------------
Mr. P.V.'d
formerly Droll Troll

On Tue, 6 Dec 2005 01:32:46 -0500, "Proctologically Violated©®"
wrote:

The Q is:
For a given 90 deg. V slot (eg, one V-slot in the back vise jaw), what is
the smallest rod that can be held in a V-slot (ie, too small a rod will
rattle), AND, what is largest rod that can be held by that same V slot (ie,
where the V slot walls will indeed hold the rod tangently and therefore
stable-ly, and not on the cusp of the V)?

If I've read that correctly the max diameter would equal the
length of one leg of the V (just a tad less, actually -- that's the
limit for perfect contact with no load).

Reasoning: The Vs make a square when fully closed. The
length of one edge of the square is the same as the
diameter of an inscribed circle in the square.
Oops .. that's the smallest that can be held .. no upper limit on
the largest G.
--
Cliff

Sorta.....
If you V the back *and* the front jaw--contrary to my spec of V'ing *only*
the back jaw.

I have found that additionally V'ing the front jaw to be 1. somewhat
superfluous ito of pure holding power, 2. possibly a hindrance, as the front
jaw is loose anyway, or may even be misaligned w/ the rigid back jaw, and 3.
as you've noted, V'ing both jaws just about *doubles* the minimum size that
can be held w/ that size V slot.

Back and front V slots are, in fact, a circumscribed square around a circle,
and the problem can be solved in that manner as well.
Note, however, the diff. between using the depth of a slot and it's edge in
this calculation--altho the edge (sqrt 2 times the depth) is perhaps more
obvious geometrically, the depth is what we more easily measure in
machining--just Z.

There is indeed no upper limit on the size of the rod held, *if* you don't
care *how* it's being held!
Ie,
Past the limits I described you lose stability, because then the front
*edge* of the V is "holding" the rod, and *not* the 90 degree sides, tangent
on the circumference--in fact a condition in these calcs..
Note that as long as you are in contact w/ the sides, there is no advantage
of being deeper in the slot/using a bigger slot--the stability/holding power
is the same.
Or so I think....

And, holding larger rods on the cusp of a V slot can damage both.

Some may point out, Sheeeeit, no wonder this cadcamless muhfugguh is
slower'n'**** machining his stuff, Look at how he fritters away his goddamm
time....

Well, ackshooly, in making a super pair of jaws (w/ max. bang fer my
machining buck), I sorta needed to do this. And, in ball detent-type
scenarios and geometries, you have similar calculations.
----------------------------
Mr. P.V.'d
formerly Droll Troll
"Cliff" wrote in message
...
On Tue, 6 Dec 2005 01:32:46 -0500, "Proctologically Violated©®"
wrote:

The Q is:
For a given 90 deg. V slot (eg, one V-slot in the back vise jaw), what is
the smallest rod that can be held in a V-slot (ie, too small a rod will
rattle), AND, what is largest rod that can be held by that same V slot
(ie,
where the V slot walls will indeed hold the rod tangently and therefore
stable-ly, and not on the cusp of the V)?

If I've read that correctly the max diameter would equal the
length of one leg of the V (just a tad less, actually -- that's the
limit for perfect contact with no load).

Reasoning: The Vs make a square when fully closed. The
length of one edge of the square is the same as the
diameter of an inscribed circle in the square.
Oops .. that's the smallest that can be held .. no upper limit on
the largest G.
--
Cliff

Believe it or not, I actually wouldn't mind seeing the derivations.

Thanks,

Adam Smith
Midland, ON, Canada

"Proctologically Violated©®" wrote in message
...
Awl--

Proly more inneresting to cadcamless muhfugguhs such as m'self, but mebbe
otherwise useful.

The Q is:
For a given 90 deg. V slot (eg, one V-slot in the back vise jaw), what is
the smallest rod that can be held in a V-slot (ie, too small a rod will
rattle), AND, what is largest rod that can be held by that same V slot
(ie, where the V slot walls will indeed hold the rod tangently and
therefore stable-ly, and not on the cusp of the V)?

Answer: ( d=depth of V slot; D=diam of rod )

D(small) = .829 d; D(large) = 2.828 d;
w/ the ratio of the large diameter to the small diameter being about 3.4.

Example:

Spose you want to hold a 1/8 rod horizontally in a vise jaw. You will
need to mill a V-slot no deeper than .151 deep.

Now, using the formula for D(large), the largest rod that can be stablely
held by this same V slot is max .427 diam. Or, just multiply the 1/8 rod
by the above 3.4 factor.

Probably, for 1/8 rod, you'd mill a V .135 deep, which would then limit
your large rod to about .375--still not a bad range.

Or so I think.

Now, what about iffin your V is not 90 deg? This is more of a pita, but
still do-able.

The formula becomes:
D(small) = 2d/(cos a + (sin a * tan a) + 1),

where the angle a is 90 - (included angle/2) of the V .

Or so I think.

Haven't gotten around to the D(large) for non-90 deg V's, cuz, well, my
vision is blurring and I got a bad sugar munchie attack.

Related to this is is *how high* a ball (radius = r) sits in a V-slot.
For a 90 deg V, a ball is raised by the amount .414 r .

For what it's all worth.
Iffin inyone is dyin to see the derivations, email me. Proly good SAT
practice'n'**** fer yer urchins.
----------------------------
Mr. P.V.'d
formerly Droll Troll

Cliff wrote:
On Tue, 6 Dec 2005 01:32:46 -0500, "Proctologically Violated©®"
wrote:


The Q is:
For a given 90 deg. V slot (eg, one V-slot in the back vise jaw), what is
the smallest rod that can be held in a V-slot (ie, too small a rod will
rattle), AND, what is largest rod that can be held by that same V slot (ie,
where the V slot walls will indeed hold the rod tangently and therefore
stable-ly, and not on the cusp of the V)?


If I've read that correctly the max diameter would equal the
length of one leg of the V (just a tad less, actually -- that's the
limit for perfect contact with no load).

Reasoning: The Vs make a square when fully closed. The
length of one edge of the square is the same as the
diameter of an inscribed circle in the square.
Oops .. that's the smallest that can be held .

I think you stayed up all night, Cliff. G

For a given 90 deg. V slot (eg, ONE V-slot in the back vise jaw),
what is the smallest rod that can be held in a V-slot (ie, too small a
rod will rattle)

Slightly larger than (length of 1 "V" wall)/(square root of 2)

.. no upper limit on
the largest G.

Wrong again. BSEG

AND, what is largest rod that can be held by that same V slot (ie,
where the V slot walls will indeed hold the rod tangently and
therefore stable-ly, and NOT ON THE CUSP of the V)?


Slightly smaller than 2 times the length of 1 "V" wall.


--
Steve Walker
(remove wallet to reply)

On Wed, 07 Dec 2005 03:22:45 GMT, Steve Walker
wrote:


I think you stayed up all night, Cliff. G

I qualified it G.
--
Cliff

On Wed, 07 Dec 2005 03:22:45 GMT, Steve Walker
wrote:

. no upper limit on
the largest G.

Wrong again. BSEG

How so? Did you see a tangent condition specified?
LOL ....
--
Cliff

Proctologically Violated©® wrote:




Some may point out, Sheeeeit, no wonder this cadcamless muhfugguh is
slower'n'**** machining his stuff, Look at how he fritters away his goddamm
time....



Well, don't get a cadcam system then, cause you'll forget how to do all
that geometric mental gymnastics.
Just like the calculator has erased my memory of long division with
pencil and paper.

Fred :-)

Cliff wrote:

On Wed, 07 Dec 2005 03:22:45 GMT, Steve Walker
wrote:

. no upper limit on
the largest G.

Wrong again. BSEG

How so? Did you see a tangent condition specified?
LOL ....


Cliff:

From PV's original post: "...AND, what is largest rod that can be held
by that same V slot (ie, where the V slot walls will indeed hold the rod
tangently and therefore stable-ly, and not on the cusp of the V)?"


--
BottleBob
http://home.earthlink.net/~bottlbob