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Who else would like to see more wide cams on the market?
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Aug 25, 2012
Cima Margherita and Cima Tosa in the Dolomiti di B...
This is my script; it works with both Matlab and Octave. I have a more efficient version, which uses closed-form solutions for the differential equations in three of the four cases, but it's messy and efficiency doesn't matter much for this problem.

-------------------------------------------
clear, clf
% Useful constants.
crackWidth = 100;
minRadius = crackWidth / 2;
numPoints = 1000; % for plotting

% Anonymous function handles for generic spirals. All these spirals are
% described by dr/r = tan(pitch(theta)) dtheta. Pitch is a polynomial in theta.
% If the polynomial is a constant, the curve is a logarithmic spiral.

pitch = @(coeff) @(theta) polyval(coeff,theta);
spiral = @(r0,pitch,theta0) @(theta) r0*exp(arrayfun(@(x) quad(@(t) tan(pitch(t)),theta0,x),theta));

% Define curves to be plotted.
spirals(1).color = 'r'; % red
spirals(1).coeff = [14*pi/180];
spirals(1).plot = true;

spirals(2).color = 'm'; % magenta (used to be green)
spirals(2).coeff = [15*pi/180];
spirals(2).plot = true;

spirals(3).color = 'b'; % blue
spirals(3).coeff = [1/33 14.1*pi/180];
spirals(3).plot = true;

spirals(4).color = 'c'; % cyan
spirals(4).coeff = polyfit([0 pi/6 pi/4 pi/2 2*pi/3], [14.1 14.2 14.3 15 17.2]*pi/180, 4);
spirals(4).plot = true;

% Compute details for each curve.
for i=1:length(spirals)
  if spirals(i).plot
    spirals(i).pitch = pitch(spirals(i).coeff);
    % Compute the rotation required to fit the cam in the crack,
    % whose width is twice the minimum radius.
    tmpfun = spiral(1,spirals(i).pitch,0);
    spirals(i).phi = fsolve(@(theta) tmpfun(theta) - 1/cos(spirals(i).pitch(theta)), 0.1);
    spirals(i).theta0 = spirals(i).pitch(spirals(i).phi) - spirals(i).phi;
    fprintf('theta0 %s = %g degrees\n', spirals(i).color, spirals(i).theta0*180/pi);
    % Get the specific spiral.
    spirals(i).curve = spiral(minRadius,spirals(i).pitch,spirals(i).theta0);
    % Compute the final angle.
    spirals(i).finalAngle = fsolve(@(theta) spirals(i).curve(theta) .* cos(theta) + minRadius, 0.7*pi);
    fprintf('final angle %s = %g degrees\n', spirals(i).color, spirals(i).finalAngle*180/pi);
    spirals(i).maxRadius = spirals(i).curve(spirals(i).finalAngle);
    % Compute range. The factor of 2 accounts for the two opposing lobes.
    spirals(i).range = 2 * (spirals(i).maxRadius * cos(spirals(i).pitch(spirals(i).finalAngle)) - minRadius);
    fprintf('range %s = %g mm\n', spirals(i).color, spirals(i).range);
    % Percentages of range.
    spirals(i).pr = zeros(10,1);
    for j=1:10
      spirals(i).pr(j) = fsolve(@(theta) spirals(i).curve(theta) .* cos(spirals(i).pitch(theta)) ...
        - minRadius - j * spirals(i).range / 20.0, 1);
    end
  end
end

% Plot
hold on
for i=1:length(spirals)
  if spirals(i).plot
    spirals(i).t = linspace(spirals(i).theta0,spirals(i).finalAngle,numPoints);
    spirals(i).handle = polar(spirals(i).t, spirals(i).curve(spirals(i).t));
    set(spirals(i).handle,'color',spirals(i).color,'linewidth',2);
    plot([0 minRadius*cos(spirals(i).theta0)], [0 minRadius*sin(spirals(i).theta0)], ...
      spirals(i).color, 'linewidth', 2);
    plot([0 spirals(i).maxRadius*cos(spirals(i).finalAngle)], ...
      [0 spirals(i).maxRadius*sin(spirals(i).finalAngle)], ...
      spirals(i).color, 'linewidth', 2);
    plot([0 spirals(i).curve(spirals(i).pitch(spirals(i).phi))*cos(spirals(i).pitch(spirals(i).phi))], ...
      [0 spirals(i).curve(spirals(i).pitch(spirals(i).phi))*sin(spirals(i).pitch(spirals(i).phi))], ...
      spirals(i).color, 'linewidth', 1);
    for j=1:10
      plot([0 spirals(i).curve(spirals(i).pr(j))*cos(spirals(i).pr(j))], ...
        [0 spirals(i).curve(spirals(i).pr(j))*sin(spirals(i).pr(j))], ...
        spirals(i).color, 'linewidth', 1);
    end
  end
end

xlim([-52 52]);
ylim([0 82]);
line([50,50], ylim);
line([-50,-50], ylim);
axis('equal')
hold off
brenta
From Boulder, CO
Joined Feb 2, 2006
72 points
Sep 1, 2012
Crap. Had a long explanation of where this project is, and the combination of exhaustion and drooping thumbs on a laptop with touchpad lead to losing the whole thing.

Sigh.

Short version:

Thanks for posting your program Brenta. Seeing that, I'm embarrassed to post mine... Clearly I've not even stayed in a Holiday Inn Express, given how ugly my program is. But it does what I need it to do, so all is well I guess.

Key bit I was talking about is this... the equation I'm using for the curve is along the lines of: (sorry about the lack or reformatting... its hours past when I should have been in bed)

reg[\[Theta]_] = areg*Exp[Tan[\[Theta]reg]*\[Theta] + b*\[Theta]^c + d*\[Theta]^e]

where:

areg = the minimum size crack the piece can fit, taking into account single or double axle and the axle spacing

[theta]reg = the tangent angle of the curve

b = first modifier

c = first exponential modifier

d = second modifier

e = second exponential modifier

In a nutshell, it's not much different from what I heard was done with the SuperCam (with its second order modifier), but with a slight twist that allows the curve to grow within acceptable tan angles within normal rotation (like what I surmise happens with the SuperCam), and then shoot outwards in the last final bit of rotation. IIRC the formula for the plot I posted earlier was something along the lines of:

reg[\[Theta]_] = areg*Exp[Tan[14Deg]*\[Theta] +0.005*\[Theta]^2 + 0.0005*\[Theta]^6]

Sadly, after playing with this for longer that I'd like to admit I don't think there's any benefit from going this route for typical single and dual axle designs, as any gains on the tail end are easily met by simply upping the tangent angle a small amount for a regular log spiral (which leads to the usual Metolius vs BD debate). I've not looked at the implications of what happens with large amounts or rotation, so perhaps this is what lets the SuperCam do its magic. Dunno, and frankly have little interest in pursuing this train of though further unless someone chimes in with a compelling reason to do so.

So, any thoughts?




On a side note, I've been on babysitting duty the past 2 weeks, which means naptime has been spent finally reorganizing the workshop to fit the "new" lathe (1970's vintage Clausing 5900). Which in turn means I'm a big step towards having the milling machine back operational, which means this project is closer to moving forward. Which means anyone with an opinion about what they'd like better start chiming in, otherwise Killis is apparently running the show.
Aric Datesman
Joined Sep 16, 2008
145 points
Sep 2, 2012
If you are making a large cam with a large hollow axle, then you should ditch the stem completely. Spread the lobes far enough apart that you can fit your fist in the middle. This will increase the torque a bit, but an oversized axle should be able to handle it. The trigger can be a bar and curved slot through the lobes that you simple grab and squeeze. This saves weight and volume, and in my opinion, would make it easier to handle and place.

If you want to get extra range, load off the backside of one of the lobes instead of the axle. It's the same principle as the Max Cams (only one pair is offset) and Totem Cams (all lobes get an offset loading). Or do a complete spiral like the Super Cam. Or do both.
DannyUncanny
From Vancouver
Joined Aug 27, 2010
78 points
Sep 7, 2012
All Killer No Filler wrote:
I'm running nothing, I'm just up for chipping in so you can push the design envelope.


True, but you seem to be the only one chiming in, so by default you're in charge... :-)


Been cogitating on Danny's suggestion above re: MaxCam-esque design, and am going to pass on that. I've been sitting on what I think would be a solution to the MaxCam flop issue for a while now (really have to get around to cutting one of my #2's apart to try it...), but my solution won't play well with widely spaced lobes on large sizes due to side loading of the inner lobes.

Anyone have any comments re: the increasing cam angle stuff I posted above? Specifically, which would you prefer: a constant 15 deg cam angle or one that increases from 14 to 15 in the normal usable range (66% expansion) and then jumps up to ~18 deg or so for the last bit? Looks to me that there's no advantage to the increasing angle thing range-wise, but it would give relatively more holding power in the usable range.



-a.
Aric Datesman
Joined Sep 16, 2008
145 points
Sep 7, 2012
The flop issue is only because the stem and trigger were up at the offset axle. If you stick with a single axle it's fine. If you simply load a long sling off the back of two of the lobes so that they are equalized, you get very little side load (long sling = less side pull). If you still think it is too much, it would be very simple to add a spreader bar to the sling, to keep it from pulling the lobes together. DannyUncanny
From Vancouver
Joined Aug 27, 2010
78 points
Sep 7, 2012
So much for being coy about the solution... But given how long the Totems have been on the market I'm not surprised at how obvious it is now. That project has been sitting on the back burner for years, as I really don't want to cut up a cam that's on my regular rack to prove the idea works...

Anyway, I'm not sure a spreader bar on a soft good would work as you intend. I played with using roller chain to help constrain things, but didn't like that result very much either. Which brought me back to the belief that extended range cams are a dead end evolutionarily, as they're too wide on the small end and too narrow on the big end. YMMV though, and I'm more than willing to discuss this further.

-a.
Aric Datesman
Joined Sep 16, 2008
145 points
Sep 8, 2012
My input would be 15 degree constant angle and as light as possible without sacraficing too much durability.

A mechanism to hold the cam retracted would be great but possibly also a liability...
TBD
Joined Dec 27, 2001
654 points
Sep 10, 2012
...
There are some SMART folks on this thread... Locker
From Yucca Valley, CA
Joined Oct 13, 2002
2,394 points
Sep 10, 2012
Chillin' at City of Rocks
Well the real question is:

Who wishes there were more wide cracks out there????

:-)
Princess Mia
From Vail
Joined May 22, 2006
427 points
Sep 10, 2012
The route in it's entirety.
haha and the thread comes full circle. Greg G
From SLC, UT
Joined Oct 3, 2008
599 points
Sep 13, 2012
DannyUncanny wrote:
If you are making a large cam with a large hollow axle, then you should ditch the stem completely. Spread the lobes far enough apart that you can fit your fist in the middle. This will increase the torque a bit, but an oversized axle should be able to handle it. The trigger can be a bar and curved slot through the lobes that you simple grab and squeeze. This saves weight and volume, and in my opinion, would make it easier to handle and place.


Certainly a cool idea for the interface BUT

Problem with that is the length of the pull needed to retract huge lobes VS the "length" that your hand can open / squeeze. That's why the stems on larger cams are larger. Sure you could come up with mechanisms for solving that problem but that'd just add complexity and weight to the design.

Wish I could commit to buying one of whatever gets produced, but school saps all my time and $
NorCalNomad
From San Francisco
Joined Oct 6, 2011
116 points
After the 15th of this month I will be able to afford one. I'll chip in Killer boy. 175 I believe was his price.
Sep 13, 2012
Ranar wrote:
Certainly a cool idea for the interface BUT Problem with that is the length of the pull needed to retract huge lobes VS the "length" that your hand can open / squeeze. That's why the stems on larger cams are larger. Sure you could come up with mechanisms for solving that problem but that'd just add complexity and weight to the design. Wish I could commit to buying one of whatever gets produced, but school saps all my time and $


I dunno about you, but I can squeeze a hell of a lot harder with a fist than I can pull on a trigger with 2 fingers and an awkward bend in my wrist. That means a shorter pull with a higher force. I would bet even a weak person could fully retract a cam with only an inch or so of pull if they could use their full fist to squeeze the trigger.
DannyUncanny
From Vancouver
Joined Aug 27, 2010
78 points
Sep 13, 2012
DannyUncanny wrote:
I dunno about you, but I can squeeze a hell of a lot harder with a fist than I can pull on a trigger with 2 fingers and an awkward bend in my wrist. That means a shorter pull with a higher force. I would bet even a weak person could fully retract a cam with only an inch or so of pull if they could use their full fist to squeeze the trigger.


You're missing this part.

Sure you could come up with mechanisms for solving that problem but that'd just add complexity and weight to the design.
NorCalNomad
From San Francisco
Joined Oct 6, 2011
116 points
Sep 14, 2012
Having a different amount of trigger pull doesn't take any additional mechanism. With regular cams it is only a function of the location where the trigger wires attach to the lobes. With the squeeze thing I'm talking about it is a function of the curve you cut your slot at. These are all basic features that you need regardless of whether you want long trigger pull or short. DannyUncanny
From Vancouver
Joined Aug 27, 2010
78 points
Sep 15, 2012
The route in it's entirety.
Danny let's see a drawing of your design! I can sort of picture it, but am still having trouble grasping the full package. Greg G
From SLC, UT
Joined Oct 3, 2008
599 points
Sep 17, 2012
All Killer No Filler wrote:
What's the status, Oh Great One? How close are we to banging out a final design?



I thought it was mentioned a couple posts up that the thread has come full circle, like Finnegan's Wake?

Kidding aside, I don't know I've seen opinions one way or the other on the expanding cam angle thing, so that's still up in the air as far as I'm concerned (in spite of my vote against it).

Also, with the wide-mostly-used-for-TR-as-you-go I'm coming around to the MaxCam-esque design. I've got quite a few MaxCams and thinking on it more most of my issues with them are easily avoided with the push-the-gear-as-you-go-TR-the-wide approach. I mentioned there being an issue with off-axis loading earlier, but that's easily solved by me simply getting thicker material... And frankly, I'm much more excited about doing a quasi-MaxCam (with the aforementioned change to single-axle, loaded on a lever thing) than a larger BD knockoff, so I guess that's where my vote is. Simply the more I think about it, the less concern I have about larger sizes getting over-square (to steal the car engine term) and getting tippy, since they're generally not left as pro and instead pushed ahead on TR.
Aric Datesman
Joined Sep 16, 2008
145 points
Sep 17, 2012
DannyUncanny wrote:
Having a different amount of trigger pull doesn't take any additional mechanism. With regular cams it is only a function of the location where the trigger wires attach to the lobes. With the squeeze thing I'm talking about it is a function of the curve you cut your slot at. These are all basic features that you need regardless of whether you want long trigger pull or short.



I completely get where you're going with this, Danny, and strangely spent the past couple weeks pondering this very thing. Personally I think it's a dead end since I think you run into issues with getting it to handle unequal expansion and have to resort to the MaxCam 3 axle solution, the quasi-MaxCam solution mentioned upthread or a fun-but-not-practical double-axle-cam-with-only-one-axle solution I may or may not have mentioned upthread. On the off-chance I didn't mention it, the short version is that it's possible to mimic the relative lobe movement of a double axle cam in a single axle design. And not only that, once it's simplified to a single axle you can turn what had been the spacing between the axles into additional expansion range, but in the end the springs are a nightmare since it involves both rotational and linear movement. For a while I though magnets were the solution, which lead to a really-fun-but-going-nowhere-because-of-the-Splitter-Cam-patents springless design, but even that didn't get around the fact that the slot needed to make the single axle behave as a double axle compromised the strength of the lobes in flaring placements.

Anyway.... I'm voting for a single axle, loaded by a sling on the center lobes design. I had written that off for the smaller stuff I've been working on, but I've come around to the idea that big stuff is used differently.
Aric Datesman
Joined Sep 16, 2008
145 points
Sep 18, 2012
Greg G wrote:
Danny let's see a drawing of your design! I can sort of picture it, but am still having trouble grasping the full package.


Here is a quick mockup of how a squeeze trigger would work. Obviously the top bar wouldn't be floating free like that. The back face is just another spiral with a very steep curve. So you don't have any stem, you just fit your hand between the lobes and squeeze the bars together. When you let go, the bar should spring back out so it doesn't interfere with anything.

I've got some ideas about how this could work for smaller cams too.

DannyUncanny
From Vancouver
Joined Aug 27, 2010
78 points
Sep 19, 2012
Here, this is a bit more like what a cam would actually look like, still missing the full trigger mechanism though. The sling would have to be a fair bit longer I think.

The design shown here has a range of 6" to 11" using an effective min friction coeff of 0.25, (approx 14 deg cam angle). The curve of the inner lobe is calculated numerically using a stepsize of 0.01 rads based on the offset loading point. The trigger pull curve is designed for a 2.5" pull with constant torque assuming 0 friction, so it might be a bit sticky towards the top end. The cut outs I just kind of freehanded, it was probably a waste of time. Lobes are 1/4" and axle is 1/2" OD RND TUBE. I have no idea how strong any of that actually is. Space between inner lobes is 3", probably a bit tight for most hands



DannyUncanny
From Vancouver
Joined Aug 27, 2010
78 points
Sep 19, 2012
Ahhhh that makes sense now, good concept man. I wonder what would be the activation force on that guy, with the larger cams needing stronger springs. Yes I know it might seem like I'm stuck on this ergonomics thin, but that can seperate a design that works from a design that is great. NorCalNomad
From San Francisco
Joined Oct 6, 2011
116 points
Sep 19, 2012
Fun animation, Danny!

Give some thought to how that upper bar would behave when the pairs of lobes are unequal... I think the concept falls apart there, sadly.

On a side note, except for the upper bar that's pretty much what I've been leaning towards lately (with the addition of offsetting the axle, as this improves range significantly).
Aric Datesman
Joined Sep 16, 2008
145 points
Sep 19, 2012
Aric Datesman wrote:
Fun animation, Danny! Give some thought to how that upper bar would behave when the pairs of lobes are unequal... I think the concept falls apart there, sadly.

It's only a motion constraint when you are squeezing it down. If you let go, there is no force to keep the lobes, it would just go wherever they go. If the lobes are unequal the bar would be resting a bit skewed. You could have a spring or elastic push it up out of the way when you let go. Some rollers might help reduce friction.

What do you mean by offsetting the axle? For the inner lobes there, the curve is defined solely by the load point relative to the axle. There are no more degrees of freedom. Okay nm I see what you mean, starting the curve closer in yeah that could push the range more.
DannyUncanny
From Vancouver
Joined Aug 27, 2010
78 points
Sep 19, 2012
DannyUncanny wrote:
Okay nm I see what you mean, starting the curve closer in yeah that could push the range more.



Yup, moving the axle away from the center of the crack and towards the side the inner lobes contact does 2 things:
1. larger outer lobes, which means more range
2. longer lever arm on the inner lobes, which means you can use a steeper spiral, which means more range

The MaxCam takes advantage of this nicely, BTW.
Aric Datesman
Joined Sep 16, 2008
145 points
Sep 20, 2012
Grande Grotto
Just my two cents on the "MaxCam" trend. I played with the MaxCams when they were first introduced and while the concept is clever, the real world use and implementation left me cold to the design. No matter how hard I tried, they required more work/thought/care in placing then a standard cam AND the chances of a botched were seemingly much higher. The fact that you had to insert the cam and have one side of the lobes touch the rock and "Reach" over to the other side was terrible. I think the market spoke as well and that's why MaxCams became and footnote in cam evolution.

If you can't "plug and chug" a cam in desperate situations, the utility of the piece is VASTLY reduced. No one wants to be in some heinous OW and have to do anything other than push the piece in. You simply COULD NOT do that with the MaxCam.

So, for me, anything other than symmetrically deploying cams is a non-starter. It would take some SERIOUS work to convince me otherwise.

Also, while yes, these piece often can be used as a push-your-own-TR that only works for so long before you leave it behind. With wider gear, there's a MUCH greater tendency for the piece to do weird sh*t once you climb past it. Introducing less stability seems, again, a poor choice.

I'm all for thinking outside the box but beware the engineers tendency to not check in with real world users and uses. (I'm currently half way through the history of the Apollo Moon Lander and the give and take between the Engineers and Astronauts is really fascinating.) I'd seriously try and get connected with some of the better known OW players and get their input.

At the end of the day, you may just find that the best thing to make is a more refined and larger#9 C4
mattm
From TX
Joined Jun 2, 2006
1,238 points


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