Parametric CAD slipjoint tang

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Dec 14, 2019
Messages
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The following is a step-by-step process to constrain the geometry of a slipjoint tang in CAD software. I used FreeCAD for this, but it should work similarly in other CAD packages. Full disclosure: I have never made a slipjoint and this is just an exercise in geometry that was prompted by a thread Sean Yaw posted a while ago. Since this came up again in a different thread, I thought I'd post a thread about it here. Please, let me know if you see anything wrong with it.

The first step is to create a spreadsheet with the parameters. The geometry will be constrained using the size, half-stop angle, open/closed angle and the kick length. The radius is computed by dividing the size by the square root of two.

vnyi17J.png


The first step is to draw two lines from the pivot point. Note that I am using construction mode for the moment, as the lines will not be part of the actual tang.

KffJHiI.png


The two lines now get the following constraints applied:
1. Their length is the radius
2. The angle between them is the half-stop angle
3. Their end points are on a horizontal line
The constraints result in the following geometry.

0R9CYuC.png


A third line from the pivot point is now added with the following constraints:
1. The length is the radius.
2. The angle between the new line and the second line is the half stop angle.

ZSymQAt.png


The next step is to connect the end points from the second and third line. The corner of the tang must be on this line.

XXxD1ej.png


Now, another line from the pivot is added with the following constraints:
1. The length is again the radius.
2. The angle between the first line and the new one is the opening angle

4sOjKDs.png


Again, a new line from the pivot has to be added, this time the constraints are
1. The length is the radius.
2. The angle between the line from the previous step and the new line is the half-stop angle, i.e., the angle between the new line and the first line is the half-stop angle plus the opening angle.

jmHfxe0.png


The end points of the two lines created in the previous two steps are now connected with another line.

f0GTsn9.png


Now, a point is added at the intersection of the last step and the line between the two end points (2 and 3) created earlier:

1LVZ3GA.png


This point is the corner point of the tang, and the kick can be found along the direction of the last line that was added, at the specified kick distance. In the image below, the completed tang is shown in green lines, i.e., they are not in construction mode.

nr43Qza.png


This construction method should give the correct tang geometry as long as the opening angle is less than twice the half stop angle, which should always be the case. The following three pictures illustrate how the tang and spring fit together in the three positions.

HmxdAeY.png

V5VD2oc.png

3HnChpH.png
 
Awesome. I didn't quite do mine the same way. But I am going to redo it somewhat when I remap the spring using a sub shape binder so I might get a chance to use some of your techniques, but i am going to have to read through them a few more times to get what is happening.
 
it seems like your open angle is the same as your half stop. If I change the half stop to let's say 86° will that throw off the open position of the tang? Would we not always want to have the back square and the walk up to be 90° to each other, with whatever relief is added to the inner corner? FWIW, I didn't do that as a constraint, I just assumed the backsquare and the walk up were square to each other, and the end of the tang as well. I also did a clip at an angle across the bottom of the tang (8°) to mate with the kick extent. Although I imagine, that a couple seconds on a small contact wheel will make this look much more like an arc. (That is a change I was considering adding in) As I understand the design, there are really only 2 actual points of contact in each position.
Your kick seems to be based on a length, so am I to assume changing that constraint will shift the size of the ricasso? I just did constraints on those pieces separately. ricasso length, choil length, and choil depth. I felt that gave me a little more control over the design. Perhaps even to the extent of a longer basis for something like a button lock (hopefully that wasn't too much unnecessary over-engineering.) Since I am managing the blade shape and the those are part of that calculation as well, they have been good to have. Though I guess I could have similarly used the kick length.

When I made my design, I started off just like Culver did in his book with two squares. I had to guess at the kick depth because, well he didn't share that little detail :) However, when I realized the angle was well-known I made a construction line at 8° and slid it up until it just touched the tip of the kick then used it to clip the bottom of the tang. I think going forward, It might be better with a large radius arc and some construction intersections. Since that is what most of the finished products seem to look like anyway.

It is interesting how you did a few different angles to come up with the kick angle. It is a known angle of 180 - the close angle 172 = 8° However, you are definitely making better usage of construction geometries than I am so there's that too :) Funny thing, I tend to use construction geometry temporarily, once it has allowed me to put in what I was going for, I tend to delete them. I hadn't actually considered leaving them in there. That may help moving forward. Great post.
 
You can change the angles and lengths and it will not throw off the geometry. It is fully parametric, but the sketch shows the current values, not the parameter names. I used the values from your other thread for this exercise. If you make the half stop angle smaller than half the opening angle, the tang will protrude from the spring in the closed position using this construction method, which I don't think is good. The above construction is based on the assumption that the tang and the corner of the spring are flush in the half stop position. If the half stop angle is exactly half the opening angle, the tang and spring will be flush both in the half stop and closed positions. If it is greater than half the opening angle, the corner of the tang will be inset from the corner of the spring.

I have not read Culver's book, so I can't comment much on that. It seems to me that the derivation of kick angle might have the built-in assumption that the half stop is at 90° (edit: this is wrong, see post below).

I used a B-spline, but I guess since you use a wheel anyway to shape it, an arc would be a better way to do it. Like you said, there should only be two points of contact, so what is in between does not really matter much. Like I mentioned, this was just an illustration how to constrain the geometry, so there is no relief, or even a proper blade shape...
 
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After thinking about it a bit more, the angle of the kick appears independent of the half stop angle. I am not very familiar with CAD, so I don't know if that could be used to simplify the construction. I guess the method I outlined rotates two points into the closed position to construct the line for the kick, whereas you could only rotate one point and then use an angle constraint for the direction of the line and pick an arbitrary length to fully constrain it. Both methods should give identical results.
 
Personally, and no offense but I'm not sure what your trying to accomplish here? The illustrations imo give the wrong impression of the relationship between all 3 positions of the blade with the spring for anyone who is new and trying to learn. Are you just trying to establish the best location of the pivot hole and length of the backsquare?
 
...If the half stop angle is exactly half the opening angle, the tang and spring will be flush both in the half stop and closed positions...
This observation from our discussion a while ago was a very influential conceptual development in my understanding of spring/tang fitup. I very much benefit from analysis of the type Hubert is doing here. It helps guide my intuition and actions when I actually step up to the grinder. The final fine tuning of fitup (for me) is more art/feel than math/science, but that feel is influenced by lessons learned playing around with the theoretical geometry. Everyone thinks about things in different ways, and I don't think it is the wrong path to try to dive into the angles and equations, if that is how things make sense to you. As we always like to caveat things here: "This is the process that works for me".
 
Personally, and no offense but I'm not sure what your trying to accomplish here? The illustrations imo give the wrong impression of the relationship between all 3 positions of the blade with the spring for anyone who is new and trying to learn. Are you just trying to establish the best location of the pivot hole and length of the backsquare?
No offense taken. I am trying to understand the geometry that is involved. Can you elaborate in what way the illustrations give the wrong impression between the three positions? I am not trying to establish the length of the back square, that is an input parameter. Given the length of the back square and a desired half stop and closed angle, the above procedure will determine the location of the pivot hole and the corners of the tang, as well as the line on which the kick is located (the kick is fixed through an additional distance constraint). I believe that if you require the tang to be flush in the half stop position, there is only one solution to this problem, which is found through the above procedure. If this is not the case or if there is an error in my assumptions, I would very much like to know what is wrong.

The above step-by-step procedure does somewhat obscure the simple concept behind it because of the way the constraints are established in CAD. Basically, it is just a procedure to rotate the line given by the bottom of the spring into the half stop and closed positions. The corner of the tang must be on the intersection of the two lines, and the kick must be on the line in the closed position. As a side note, this procedure also works for a spring that is not a straight line past the tang, the kick needs to be on the curve given by rotating the spring. In essence, rotating the blade counter-clockwise is the same as rotating the spring clock-wise for construction purposes.
 
No offense taken. I am trying to understand the geometry that is involved. Can you elaborate in what way the illustrations give the wrong impression between the three positions? I am not trying to establish the length of the back square, that is an input parameter. Given the length of the back square and a desired half stop and closed angle, the above procedure will determine the location of the pivot hole and the corners of the tang, as well as the line on which the kick is located (the kick is fixed through an additional distance constraint). I believe that if you require the tang to be flush in the half stop position, there is only one solution to this problem, which is found through the above procedure. If this is not the case or if there is an error in my assumptions, I would very much like to know what is wrong.

The above step-by-step procedure does somewhat obscure the simple concept behind it because of the way the constraints are established in CAD. Basically, it is just a procedure to rotate the line given by the bottom of the spring into the half stop and closed positions. The corner of the tang must be on the intersection of the two lines, and the kick must be on the line in the closed position. As a side note, this procedure also works for a spring that is not a straight line past the tang, the kick needs to be on the curve given by rotating the spring. In essence, rotating the blade counter-clockwise is the same as rotating the spring clock-wise for construction purposes.
Let me ponder how to best try to articulate a response before I get into it. I wish I could make and post a video. I hate typing. Lol
 
Ok, the following is an illustration how to do this in inkscape. I hope this is clearer since it does not use CAD constraints. We start with a drawing of a Swayback knife vaguely resembling the one by Ramon Hunt available on Chris Crawford's website.
xe48bNH.png

Note that this drawing has the added complexity that the spring is not horizontal and has a curve to it after a short straight section. The first step is to draw the length of the tang square from the corner of the spring. I used double the height of the spring for this length. I first draw a circle with a radius of 9mm around the corner of the spring. Inkscape can snap control points to path intersection, which is used in the next step to draw a line from the corner of the spring to the intersection of the circle and the spring.

BIMSkab.png

I then copy the line and paste it in place. I chose 88° for the half stop angle just to show that the angle does not have to be 90°. This will also make the spring and tang near flush in the closed position. The next step is to rotate the two red lines that are on top of each other by alpha=90°-half_stop/2=46°, one clockwise and the other counter-clockwise. After rotating the lines, the end points are moved back into their original positions.

AuCGMHF.png

The intersection of the two lines is the pivot point. By construction, the corner of the tang will be flush with the end of the spring in the half stop position. The next step is to determine the angle when closed. For this, I click once to select the blade, then again to change the controls around it to rotation mode. This also shows the rotation center of the blade in the center of the bounding box.

gJuzssL.png


The rotation center needs to be moved to the pivot point at the intersection of the two red lines. For this to work, snapping must be enabled for the rotation center, which it most likely is not by default. The picture below shows the rotation center after snapping it to the pivot point.

WSMqJSc.png


Now, I rotate the blade to determine the angle required to get the tip of the blade below the scales. For this example, the angle is 175° and is shown by the blade outlined in blue in the following picture.

sB6U552.png


Now, I select the spring and click on it again to get the rotation center to show. I move the rotation center of the spring to the pivot point just like I did with the blade in the previous step.

sobwdes.png

I then copy the spring and paste in place twice. Then, I rotate the first copy of the spring by the half stop angle (88°) in the clockwise direction, and the second copy by the closing angle (175°). The rotated copies are shown in red and blue in the picture below, respectively.

OWs3GVh.png


The second corner of the tang can be found on the intersection of the red and blue springs, and we can now move the corners of the tang and the kick to their correct locations. Since the intersection between the red and blue spring is very close to the corner control point of the blue spring, care has to be taken when moving the corner of the tang to ensure that it snaps to the intersection and not the corner point. It may help to disable snapping to control points entirely and just leave snapping to path intersections enabled.

uDFAjbd.png

I added a circle at the pivot and an arc between corner and kick so it will clear the spring. Here is the finished product.
b11bvX1.png

The following image shows an overlay of the three positions.

Bl3kSUH.png


Here is another detail view that shows the contact points a little bit better. The corner of the red tang is almost flush with the corner of the spring because the half stop angle is very close to half the closed angle.

xm47IFH.png


I hope this is a little bit clearer. The procedure with the CAD constraints in the first post does the same thing. I don't know of an easy way to rotate copies of the spring in the CAD program and constrain them, that is why I constructed the rotated versions of the spring by adding lines rotated by the half stop angle. The underlying concept is the same, though. I think if the corner of the tang and spring are required to be flush in the half stop position, there is no other solution for the remaining corner of the tang if the closed angle is given, and no other solution for the kick if the closed angle and an additional distance are given. Let me know if there is anything wrong with this method.
 
That looks really good.

A few things. The spring where the kick touches should be flat and not curved. How it is in the drawing allows the tip to drop to low and when the knife is closed the edge will smash into the spring dulling the blade.

Also on the tang, the corners are not sharp and should be radiused.
 
That looks really good.

A few things. The spring where the kick touches should be flat and not curved. How it is in the drawing allows the tip to drop to low and when the knife is closed the edge will smash into the spring dulling the blade.

Also on the tang, the corners are not sharp and should be radiused.
Thank you for the pointers. I used a drawing from Chris Crawford's website as the basis for this, and left the curved spring. It's good to know that that is something to be avoided. In the ones I've drawn from scratch, I have always used a straight spring. I think Sean Yaw Sean Yaw and Hengelo_77 Hengelo_77 have both built the pattern from Chris' website, maybe they can comment on what they did to make it come out right. I like the pattern, but I am not sure if the small tang in the original and all the material in the rear of the spring are desirable.

The post was getting a bit long and adding a radius in inkscape while keeping the geometry correct is a bit tricky. Adding a radius used to be a real pain in inkscape, but there is a path effect in newer inkscape versions that does that nicely. Using this method to round the tang makes the solution slightly incorrect if there is an arc between the corners. To radius the tang correctly in inkscape, the path effect has to be added while the lines remain straight and then the path effect has to be converted to a regular path before adding the arcs. This ensures that there remain two points in contact with the spring at the specified angles. The contact points are just slightly inset from the original locations if a small radius is used.
 
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Thank you for the pointers. I used a drawing from Chris Crawford's website as the basis for this, and left the curved spring. It's good to know that that is something to be avoided. In the ones I've drawn from scratch, I have always used a straight spring. I think Sean Yaw Sean Yaw w and Hengelo_77 Hengelo_77 have both built the pattern from Chris' website, maybe they can comment on what they did to make it come out right. I like the pattern, but I am not sure if the small tang in the original and all the material in the rear of the spring are desirable.

The post was getting a bit long and adding a radius in inkscape while keeping the geometry correct is a bit tricky. Adding a radius used to be a real pain in inkscape, but there is a path effect in newer inkscape versions that does that nicely. Using this method to round the tang makes the solution slightly incorrect if there is an arc between the corners. To radius the tang correctly in inkscape, the path effect has to be added while the lines remain straight and then the path effect has to be converted to a regular path before adding the arcs. This ensures that there remain two points in contact with the spring at the specified angles. The contact points are just slightly inset from the original locations if a small radius is used.
The swayback I made was modeled after that pattern and the GEC 47, both of which have a fairly large kick. If you make the spring/kick impact point flat all the way from the tip of the spring, your kick heigh needs to be reduced to keep the blade tip where it is in the handle. Not a problem, but then the kick is not as pronounced. If you like the visual aspect of the large kick, you need to make the blade tip sit low enough while having that large kick. The pattern does that by removing material on the spring to let the tip stay low without reducing the size of the kick. Does that make sense?

I don't add radii in mockups. I just do that when I actually build them.

Edited: For clarity, that is not the only way to make a knife with a large kick, but I suspect that is the reason the pattern has the spring carved out where the kick hits.
 
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The swayback I made was modeled after that pattern and the GEC 47, both of which have a fairly large kick. If you make the spring/kick impact point flat all the way from the tip of the spring, your kick heigh needs to be reduced to keep the blade tip where it is in the handle. Not a problem, but then the kick is not as pronounced. If you like the visual aspect of the large kick, you need to make the blade tip sit low enough while having that large kick. The pattern does that by removing material on the spring to let the tip stay low without reducing the size of the kick. Does that make sense?

I don't add radii in mockups. I just do that when I actually build them.
It makes sense, but seems contrary to Adam's suggestion to keep the bottom of the spring straight. I think in the original pattern, the blade was less tall, which would make the kick appear larger in relation to it as well.
 
It makes sense, but seems contrary to Adam's suggestion to keep the bottom of the spring straight. I think in the original pattern, the blade was less tall, which would make the kick appear larger in relation to it as well.
I would say that Adam's suggestion is my preferred way to make a spring. It is simpler to have it straight from the tip to where the kick impacts. The pattern doesn't have it that way, so when I made a swayback influenced by that pattern, my conclusion for why they had the spring that way was to keep the kick large. If you look at a GEC 47 you'll see a big kick too. It is not necessary to do that to have a large kick, but that is the only reason I could think of for the designer of the pattern to do that.
 
Wow, and so much great information all in one thread. I will say that I like how your "kick" is integrated into the shape of the tang, rather than the way I "clipped" Culver's square tang. But for now, I will keep this tang shape as I have it. I am changing how the spring inner profile is managed using a sub shape binder as I move forward. So, my next few modifications will be to simplify the design if possible (perhaps integrating the close angle from the start, and possibly coming up with a curve to do it). I will also be doing a change to probably have 2 blade bases, since I can't handle true drop point shapes to the extent that the "void" takes on a positive curve, such as in a spear, nor the concept of sheep/lamb feet and so forth.
As I simplify I am going to be trying to make my relationships more on percentage, or factors so that scaling will be much smoother. I will be reducing the number of sizes that are straight simple numbers to the least possible where others will all be either factors, or products of those numbers. This may possibly get me to a point where certain shapes are not possible to achieve, or to scale once achieved, however, I have yet to find any normal things that fit that bill. Perhaps, when I look into doing camp or SAK styles there may be blades that fit that bill, but I think I will simply not worry about the occasional one-off when such issue arises. Or, perhaps those become a "blank" where all but the final detailed shape is determined ahead of time.


As for the angles of the tang, when following Culver's book, he simply outlines a square that is 2x tall with an open ended rectangle butted up against it, the only important factor is that it is 3x tall and has the additional unmeasured kick point below .. otherwise the bottoms of it and the tang are co-linear. The pivot hole is centered in tang and his emphasis is that the points of the tang are equidistant from the center of the pivot. There is some hand-waving and a little magic and ultimately some small part of the lower corner of the tang gets eliminated, and I assume the point of the kick gets softened and voila the kick is complete... I emailed him, and wrote it off to details that really didn't matter to the book, and were easier to just work out as things progressed, so I didn't push the issue any further. After all, it is only 25 pages. One could probably take that many pages to explore the delicacy and elaborate curves of the pre-sharpened kick curve alone. After all, people have written tutorials on how to "fix" and old pocket knife whose tip no longer lies below the edge from being sharpened so many times. And they describe filing down the kick point like it is black magic. Which possibly it is, since I have never seen any reference to modifying it in any of the old literature that came with things like my Bucks and such.



Angles... I keep going off tangent here.. :) So if you are assuming a knife to close at 172° and, that has to be relative to somewhere... That relative position is 0° or 180° these numbers get messed up because sometimes start and finish are positive and negative as opposed to the whole 360°. But knife open, straight line from the spring through the spin of the knife then if you close it 172° you are presenting an 8° angle (because that is 180 - 172 and you prove it in your multiple angles that end up managing the subtraction as they cross over). That takes the tang shape from square to what is referred to as a "right trapazoid". This means 2 corners are still square and 2 edges are still parallel. The 4th edge (on the bottom in our case) will have a difference of 8° meaning 2 at 90° 1 at 98° and one at..... let's not all see the same hands.... 82°. For oversimplification this can be the whole length of the back of the tang to the end of the kick point, or any curve or intermittent shape that allows 2 points of contact with the spring. Hopefully the spring is flat the whole length of the "walk" long enough to accommodate this. If you want to have weird half stop angles (as in something other than 90°. Then the other 90° back of the tang will need to be altered into either acute or obtuse trapazoid which will shorten or lengthen the back square, though it should not affect the walk up, or the angular relationship between the back square and the walkup which for all intents and purposes is 90° (with allowance for dust on the inner angle). I think I can constrain this in such a way that it is simpler than what I have so far, and perhaps even more simple that what you did. My focus being on simplification so that manipulation of the constraints leaves much less opportunity for deformity with fewer related values to interact.

I am still thrilled with the results I have been able to achive just modifying a small number of constraints to accomplish some quite recognizable blade shapes, without changing the length. Once I change the length, there are some amazing looking shapes that I hadn't imagined appearing, especially when trying to achieve a truly elegant toothpick.

For those who haven't seen what I have come up with so far, I have a collection in a GooglePhotos album:

Collection of shapes in Google Photos
They display the co-generated inner spring profile and are in the closed position so to demonstrate the matching profile's accuracy. This will be changing as I have found a more accurate simpler way to accomplish this.

These again are all from the same design, with just 2 or 3 numbers in a spreadsheet being changed for it to generate a new image/shape with corresponding spring inner profile to go with it.

I will try some individuals:
AL9nZEVWQHnohuBik8O5HGKiVA7UpXSxSu-BYsDNwHXrsmCR7Cs0Hm58GxZo6ehia3zFzq8IXLHOKniaEXvLwgraVsnCU7bv8iYBIFRq4-hPMAwt1Od5N2C1tpRruKIRaTQgYkh9VUTw2_peW7scdJwtRu-eew=w800-h600-no

AL9nZEU_bhELVViF4zwxhN_UdFF06C89Ouhqv693SUHmxWh7VVNzsvSraYbM0AhLv77HuFh3YbtfhmaC3_8kV-iAI4H8r7dRJgCORK76Zej_BLXQeH4ftbVUa53yoo2FyF95xZSau_MgRNpfc1yCvNL2FEf2Og=w800-h600-no
AL9nZEXwzbSlr1hzRHndDXbL_n8OlTCL3XxJWAzGSTuhZ__4g63pwYw-MFPTOITuXXxCtobPGcdbb8nm3suZ2rxTTTiPLfkD5y49pH4LV-boLw4y-yGZmz4xcTQ-sjJKBWBquphzK9b2-8RGQwF0UUP6YsR6PQ=w800-h600-no
AL9nZEV9HJiiPk3dpqNOkQsSvBzueGF0NuhtS_NsVCzVnMuBO0wA9YUX9ttiKVrwhmt-rJTrxcLt7KNa0ljmW6BZqAVwZVMJCmZJOnjNFDs28GyxCnXMzlg66RJEOy8RQqynRx3sdsQRtzMMnMMl01yucWqnSw=w800-h600-no
AL9nZEXdqbIdviiiKJgHDU8u2Q98Tq323ETV6FZHMWHz4-3WAYhjudblKc5CPpfTfqZyhwYedmoegwBxgHL8kIJpE4NXI11c5K6WxRg2w7hiBEW_ZQfBi6yHEYjpvVwb8THRm96QD4WTZ4WIVNV9PuZ6Z4OQ2g=w800-h600-no
 
Wow, and so much great information all in one thread. I will say that I like how your "kick" is integrated into the shape of the tang, rather than the way I "clipped" Culver's square tang. But for now, I will keep this tang shape as I have it. I am changing how the spring inner profile is managed using a sub shape binder as I move forward. So, my next few modifications will be to simplify the design if possible (perhaps integrating the close angle from the start, and possibly coming up with a curve to do it). I will also be doing a change to probably have 2 blade bases, since I can't handle true drop point shapes to the extent that the "void" takes on a positive curve, such as in a spear, nor the concept of sheep/lamb feet and so forth.
As I simplify I am going to be trying to make my relationships more on percentage, or factors so that scaling will be much smoother. I will be reducing the number of sizes that are straight simple numbers to the least possible where others will all be either factors, or products of those numbers. This may possibly get me to a point where certain shapes are not possible to achieve, or to scale once achieved, however, I have yet to find any normal things that fit that bill. Perhaps, when I look into doing camp or SAK styles there may be blades that fit that bill, but I think I will simply not worry about the occasional one-off when such issue arises. Or, perhaps those become a "blank" where all but the final detailed shape is determined ahead of time.


As for the angles of the tang, when following Culver's book, he simply outlines a square that is 2x tall with an open ended rectangle butted up against it, the only important factor is that it is 3x tall and has the additional unmeasured kick point below .. otherwise the bottoms of it and the tang are co-linear. The pivot hole is centered in tang and his emphasis is that the points of the tang are equidistant from the center of the pivot. There is some hand-waving and a little magic and ultimately some small part of the lower corner of the tang gets eliminated, and I assume the point of the kick gets softened and voila the kick is complete... I emailed him, and wrote it off to details that really didn't matter to the book, and were easier to just work out as things progressed, so I didn't push the issue any further. After all, it is only 25 pages. One could probably take that many pages to explore the delicacy and elaborate curves of the pre-sharpened kick curve alone. After all, people have written tutorials on how to "fix" and old pocket knife whose tip no longer lies below the edge from being sharpened so many times. And they describe filing down the kick point like it is black magic. Which possibly it is, since I have never seen any reference to modifying it in any of the old literature that came with things like my Bucks and such.



Angles... I keep going off tangent here.. :) So if you are assuming a knife to close at 172° and, that has to be relative to somewhere... That relative position is 0° or 180° these numbers get messed up because sometimes start and finish are positive and negative as opposed to the whole 360°. But knife open, straight line from the spring through the spin of the knife then if you close it 172° you are presenting an 8° angle (because that is 180 - 172 and you prove it in your multiple angles that end up managing the subtraction as they cross over). That takes the tang shape from square to what is referred to as a "right trapazoid". This means 2 corners are still square and 2 edges are still parallel. The 4th edge (on the bottom in our case) will have a difference of 8° meaning 2 at 90° 1 at 98° and one at..... let's not all see the same hands.... 82°. For oversimplification this can be the whole length of the back of the tang to the end of the kick point, or any curve or intermittent shape that allows 2 points of contact with the spring. Hopefully the spring is flat the whole length of the "walk" long enough to accommodate this. If you want to have weird half stop angles (as in something other than 90°. Then the other 90° back of the tang will need to be altered into either acute or obtuse trapazoid which will shorten or lengthen the back square, though it should not affect the walk up, or the angular relationship between the back square and the walkup which for all intents and purposes is 90° (with allowance for dust on the inner angle). I think I can constrain this in such a way that it is simpler than what I have so far, and perhaps even more simple that what you did. My focus being on simplification so that manipulation of the constraints leaves much less opportunity for deformity with fewer related values to interact.

I am still thrilled with the results I have been able to achive just modifying a small number of constraints to accomplish some quite recognizable blade shapes, without changing the length. Once I change the length, there are some amazing looking shapes that I hadn't imagined appearing, especially when trying to achieve a truly elegant toothpick.

For those who haven't seen what I have come up with so far, I have a collection in a GooglePhotos album:

Collection of shapes in Google Photos
They display the co-generated inner spring profile and are in the closed position so to demonstrate the matching profile's accuracy. This will be changing as I have found a more accurate simpler way to accomplish this.

These again are all from the same design, with just 2 or 3 numbers in a spreadsheet being changed for it to generate a new image/shape with corresponding spring inner profile to go with it.

I will try some individuals:
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I think you can eliminate the "hand-waving and a little magic" with my process. I am not sure if there is a simpler way to do it, you have to find the intersection of two lines somehow. I'm very interested in what you come up with. The only reason I even tried this in CAD is the protruding tang in the pictures you posted in the other thread. I cannot imagine that will make for a smooth operation, that's why I thought it should be constrained.

DJz0MuO.png
 
4 different tang and spring shapes. These are 4 of my working templates. All 4 of these tangs are around .050" proud at the half and .15" proud closed. Round edges work smoother than square edges. Tang only makes 2 points of contact with the spring in all 3 positions. Start horseshoes and hand grenades and work your way down to zero. Even if your laser cutting your parts they still have to be handfitted. Better leave some meat to get it where you want it. That's the best I got without writing a book. :)

20220830_171446.jpg

20220830_171516.jpg
 
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