Articulation

[Mac]

It's just a quick post today, but I hope it addresses an important point.

Our two dimensional models have only addressed what happens at one plane in a three dimensional thing. This has been the plane which forms the horizon or high point in a side view or elevation.

On the right, I show a cross section through one of those lames that might make up a knee or elbow voider. It is as if cutting through the limb. That section is more or less a semicircle. The line "A" represents the saggital section which we have been using in out models. On the left is the usual two dimensional model at that plane. I have also randomly chosen two additional planes marked "B" and "C" and cast parallel lines for all three of them over to the two dimensional model on the left.

The important thing is that when we draw the arcs described by the motion of all three points, the motion between the primary and secondary locks is essentially the same when taken as an angle. By extension, this can be done for any plane, or any point along out articulated joint. This presumes that the pivots are more or less coaxial. In practice one always has to make small adjustments near the pivots, but I plan to say more on that later.



Within limits this all holds true for things who's section is not semicircular. In the upper example below, I have drawn a cross section through a typical mitten gauntlet lame. Like the example of the voider, I have shown the typical two dimensional model on the left. The highest point is marked "A", and the "shoulders" of the lame are marked "B". Even though the section is very different than the that of the voider, the same relationship holds for points plotted on the model. That is to say, what works in the middle will work at the shoulders, and by extension, everywhere in between.

In the lower example, I have shown a gauntlet with a zig-zag section of the sort we sometimes see. The two high points are marked "A". The corners and the central "valley" fall at about the same height and are marked "B". The two outer valleys are marked "C". Like our previous examples, all of these points will trace out approximately the same angle between the primary and secondary locks when modeled in two dimensions.



The take away here is that the two dimensional model works for armor of various sections, and even for complex sections.

Mac

[sirfelix]

I was going to do that yesterday, but I noticed that this set does not have a cuff template. I've just searched the likely places and haven't found it. I'll post a set for the larger size in a bit. They won't just go on the scanner bed, and I need set up the camera and a background.

Mac
[/quote]

thank you, in your own time, but thank you! i will be patiently waiting!

[Indianer]

The second set has been used many times, and is part of one of my standard "sportified" hourglass gauntlets.



Mac

Hi Mac, thank You for sharing. Could You provide a few basic working steps in proper order? A rough outline is all?
Greetings, Indi

[Mac]

The second set has been used many times, and is part of one of my standard "sportified" hourglass gauntlets.



Mac

Hi Mac, thank You for sharing. Could You provide a few basic working steps in proper order? A rough outline is all?
Greetings, Indi

I cheat. I turned up a set of punch-press dies to rough out the lames. This is why my templates specify all the lines.

One pair makes the ridges, another makes the valleys. A third pair refines the "corner" ridges. From there I only need to dress them up a bit around the pivots and close up a few gaps. Albert Collins does them the right way. I need to try that some time.

Mac

[Mac]

Earlier, I showed that we can model a gauntlet mitten, starting with a "generating" arc or circle.



Today, lets imagine the we take two of those "number one" lames and set them in opposite directions on the circle. Now let's connect them with a sort of double ended "lame zero".



It should be easy to see how one of the lames can be re-imagined as a metacarpal lame, while keeping the underlapping part the same. Lame "zero" is not a knuckle plate. This assembly is represented with both articulations at their primary lock.



If we go to straighten the assembly, we find a point where the underlaps seem to strike one another and prevent further motion. This is not what happens in practice, though. While the underlaps might strike one another sometimes, there is always a tendency for one or the other of them to get to the conflicted space first. The other one ends up sliding into the space above. The lower two figures show both of the possibilities. In either case the assembly will straighten out more or less fully.



The idea of the underlapps sliding past one another seems a great affront to the modern mind, but we need to get over that. It happens smoothly and cleanly, and almost never betrays itself with a little bump before the lames decide which way they are going to lie. This bizarre and unlikely magic occurs under every knuckle plate. We will also see later that it's not uncommon in articulated elbows.

Mac

[wcallen]

As an example of lames crossing each other under the knuckle plate:

This case is a lot more aggressive than Mac's drawing. The hand is on the right, fingers on the left. You can see the thumb hinge on the bottom.
In this case, when the hand moves back past the position a hand can actually reach the first lame on one side actually underlaps the second lame on the other.

Wade

[Mac]

Thank you, Wade!

Mac

[Mac]

Today we are going to start by taking a step back. Earlier I told you that in the simplest type of articulation there was a relationship between the amount of "throw" (measured as an angle) and two variables; the height and the distance of the pivot forward of the articular edge at the horizon.

These two diagrams should look familiar.





I have recently understood a way to quantify that relationship, and I would like to present that before going forward.

It turns out that in any articulation of this sort one can predict the total throw between the primary and secondary locks by knowing the angle between the pivot location and a perpendicular from the horizon of the articular edge of the overlapping plate. In the diagram, points "A", "B", and "C" are all on a line which is 10° from that perpendicular. The figures A, B, and C show models based on those locations. In all cases, the total throw is 20°. That is twice the angle.



To show that this relationship still holds at other angles, this diagram shows three pivot locations based on a 20° angle from the perpendicular. They all throw about 40°.



With that out of the way, let's do something interesting. As I have alluded to in the earlier posts, we can change anything about the plate which is not actually part of the articulation. You will recall that we turned the "mutable" areas into sabaton toe caps gauntlet metacarpals, etc.

Let's start with something like example "B" in the above diagram. In the central figure, we will take the mutable part of the plate and bend it down sharply at 40°. In the lower figure we take the overlapping plate of the resulting model and return it to the secondary lock position.



If we take the underlapping material of that model, lengthen it a bit, and let it be curved down, we can get a bit more throw out of the articulation. In this case another 20°. This gives us a total of 60° of throw between the primary and secondary lock positions.



We are not quite done with it yet, though. So long as the underlapping edge does not strike the inside of the overlapping plate we are free to make the horizon of that plate be at an angle. In this case, we can effectively get another 15° before we have any internal interference. The lower figure shows how we can make the other end of this lame be the underlapping part of the next articulation.



We can now imagine string a couple of these articulations together to make a boxy sort of gauntlet. In this case I show two lames like a manifer, but one could add a third one to cover the finger tips. That would give us a thing like we see in some locking gauntlets.



It is possible to "soften" the angular nature of this articulation and sort of "melt into" the organic shape of a 15thC Italian gauntlet. It all still functions the same way, but it has a vastly different aesthetic.



Next time, I hope to show some shallower versions of these articulations, like might be used in articulated thumbs and fingers.
Mac

[Mac]

Just a quick note today.

I'm sure that many of you are wondering when I will address knees and elbows. The short answer is that I'm working up to it.

A longer and more honest answer is that I'm still trying to understand them. Knees and elbows have a lot more variables than the things I have been describing so far. I hope to be able to quantify those variables and present them logically. This whole series has been and will continue to be a learning experience for me. I've been taking things that I intuitively understand and attempting to derive their geometric underpinnings so that I can present them in terms of first principles.


I typically design knees and elbows one lame at a time, and from the center out. It's a process of trial and error based on an understanding what the typical shapes are and what the end results must be. There seems to be no one right answer, but rather a sea of possibilities dotted with islands of workable solutions.

Late last night I had a different idea. Taking the approach I used with the gauntlet mittens and the Gothic gauntlet back, I made a quick sketch based on what a knee assembly should look like at full flexion. Just to mix it up a bit, I sketched in one lame between the cuisse and the cop, and two lames between the demigreave and cop. This is, of course, a common construction for 15thC Italianate knees.



This morning, I made up the usual light table overlays to see how it worked and was surprised to find that all the articulations functioned within specifications. I expected to have to move some pivots at the very least, but I didn't have to. When extended to (or just shy of) the secondary locks, the assembly looked like this.



The only things that needed attention were some of the edges. This sketch shows them corrected.



Flexing the assembly back to the primary locks now looks like this.



So... is this some sort of an intellectual breakthrough, or just a fluke? I don't know yet. It all depends on what I find when I start with different design parameters. I need to spend a few days (or weeks) messing with this idea and trying to distill out the important points. Perhaps this has given me a new framework for understanding and explaining a complex problem. Or maybe I just got lucky. In either case, it's back to the drawing board and the light table.

Mac

[Indianer]

Mac, thou wouldst not happen to have a pttern for these mittens, would thee?

[jdr1066]

This thread is so exciting, I have started about three new projects...

[Mac]

A big part of this thread is attempting to quantify the things I have an intuitive understanding of. This involves a lot of test sketches to try to see the effects of different variables. Most of those sketches just pile up somewhere in the corner of the room while I decide what it the best way to put the results forward. Today, I thought I'd just post some of those tests to show something about the process.

The shape of a knee or elbow cop is central both literally and figuratively in determining how the joint will function. There are really three variables that matter. They are....
-- the "height" of the cop as measured from the pivots to the articular edge of the mid-saggital plane, labeled "H" in the diagram
-- the distance between the pivots, labeled "W" in the diagram
-- the angle formed by lines drawn from the pivots to the articular edge, labeled θ (theta) in the diagram



Note that the lower figure in the diagram is functionally identical to the upper one.

It's important to understand that articulated joints will scale. We can blow them up or reduce them on a photocopier or any other way. As long as the proportions are maintained they will function identically.

My gut feeling was that the most important variable was the functional angle of the cop. To test this, I made up a series of sketches with different angles. I treated all of them as identically as I could within the context of the test. All of the diagrams show a two lame articulation. The width of the lames was approximately the maximum that would not overlap in the middle. The "cannons" (cuisse and demigreave) were presumed to be more or less cylindrical, and not to have any compound curvature in the articulation. The "straight" position is shown just short of the secondary locks, so as to allow a bit of hyperextension. The flexed position is shown at the primary locks. I have measured the resulting angle two ways; against the center line, and against a perpendicular to that center line.

Let me stress that these are not the only way to make this articulation. They are probably not even the best way. They are just what I chose to do to test the effect of different functional angles of the cop.


Here is the series, from 30° to 70°.











The results are not at all surprising. The greater the cop angle, the greater the angle the articulation will move through.

To look at a different variable, I made up two additional series where I kept the angle the same and varied the the distance between pivots (W).

Here is a series for 50°









Again, there are no big surprises here. Increasing the spacing between pivots (W) increases the amount of possible movement in the joint, but only slightly. The difference is about using a wider lame.

This brings us to several questions...
--how much motion is necessary?
--how much motion is desirable?
--how much motion did real armor have?
--what angles do real cops have?
--what are the effects of using different numbers of lames?
--how do I design a joint to do what I want?

There are probably other questions as well, and I hope to address them all eventually. For now, though, let's have a look at some some pictures of historical armor and see what we can learn.

Unfortunately, it's not easy to find pictures of knee armor at full flexion, so we have to rely on a rather small sample size. What we do see is a range of values.

On the stingy end of things we have armor that barely gets past a right angle. This first one is not quite fully flexed, so I have drawn lines where I expect it to end up when taken all the way to the primary locks. It seems to give an included angle of 83°



This is what people in biometry or in physical therapy would measure as 97° because they measure flexion from the straight leg, rather than the included angle.



This one has a rather more generous range of motion, with an included angle of 67°. The physical therapist would call this 113°.



In this photo, we have a very similar angle to the previous. The important thing here is that it's clear that this approximately where the back of the greave will run into the back of the cuisse. In a very real sense, this is all the motion that is required of the knee articulation. Anything beyond that is a wast. In fact, it's more than just a waste because additional flexion comes at the cost of greater intrusion of the lames into the inside of the armor. I plan to demonstrate that in a subsequent post.



This takes us to the question of what angle authentic knee cops use. I have measured the angles in the three examples above, but unfortunately these measurements come with a serious caveat. The angle that the camera "sees" is very sensitive to it position relative to the cop.

To show this, I have photographed a knee cop from three different heights and two different distances.

In this first pic the camera is about 18" (about 50cm) away, and at a level where the pivot holes of both sides would line up. The angle measures 52°



When I move the camera up a bit but retain the same distance from the cop, the angle now measures 42°. Either of these views might be considered to be "nice clean side views".



When we move the camera just a bit higher (but maintain the same distance) the apparent angle now becomes 39°.



On the other hand, by backing up to about 6 feet (1.8 meters) away and employing the telephoto lens so that the subject takes up a similar amount of the frame, the angle measures a rather surprising 68° This is taken at a level where the pivot holes line up.



This bit of cardboard has been cut to fit the inside of that cop, and the locations of the pivot are accurate.



When I measure it with my digital angle gizmo, we can see that the last photo is accurate within the limits of our measurements.



What does this last demonstration show us? In a nutshell, it shows that when we try to measure the angle from a photo, it will almost certainly give us a smaller angle than what is really there. Unless the photo have been taken from well back and very square and perpendicular to the cop, the real angle will be significantly greater than what we measure from the picture.

So... what angles are used on historic knee cops? I don't know, but I hope to pursue this further and see If I can come to a better answer.

Mac

[Sean M]

Sounds like something to explore with Wade or Dr. Toby or another friendly curator!

There is a school of thought that leg harness is particularly dependent upon biological sex (ie. rules of thumb which work for almost all men work for few women). That might be fun for someone with a lot of customers to explore.

[wcallen]

I don't have all that many knees. They are annoyingly hard to find.
I do have:
https://www.european-armour.com/A-200.html
https://www.european-armour.com/A-162.html
https://www.european-armour.com/A-169.html
My other knees are part of knee length tassets and they are often not designed to work completely since they (usually) aren't worn with greaves.
Also annoyingly, most of the images seem to center on the center of the piece, not the cop, so they are somewhat distorted.

Wade

[wcallen]

This is probably my best existing picture:

It gives a pretty good impression of the cop.

Wade

[Mac]

I don't have all that many knees. They are annoyingly hard to find.
I do have:
https://www.european-armour.com/A-200.html
https://www.european-armour.com/A-162.html
https://www.european-armour.com/A-169.html
My other knees are part of knee length tassets and they are often not designed to work completely since they (usually) aren't worn with greaves.
Also annoyingly, most of the images seem to center on the center of the piece, not the cop, so they are somewhat distorted.

Wade

Can I get you to take a couple of pics when you get a chance?

The most useful ones would be taken from a couple of yards away, with the legs straight and then flexed as far as they are willing to go.


Thanks!
Mac

[wcallen]

Mac,

I'll get some in the next few days. Stay tuned.

Wade

[Mac]

Mac,

I'll get some in the next few days. Stay tuned.

Wade

Excellent! Thank you!

Mac

[Mac]

I've edited out a post here. Somehow I had managed to quote myself and repost while trying to edit the May 8 post.

Mac

[Andeerz]

I am at work at the moment, but, for what it is worth, I tried to take a stab at this. I fired up Blender and opened a photogrammetric model of the Parade Armor of King Eric XIV of Sweden I got from Sketchfab (here is a video on how the model was made!). I looked at the knee cops as straight on as I could from the side with my really crappy Blender skills and set the camera to orthographic view, which should completely eliminate any distortion due to distance from the camera. The attached screenshot (sorry... I don't currently have access to a proper image hosting service) shows the model plus the angle I used to measure the angle. I could maybe spend more time on this after work to see if I can get a more accurate measurement, but I got an angle of 80.4 degrees.

[Sean M]

I wonder if we could do something with the images on the Wallace Collection Iron Key? Dr. Toby would know about how far the camera was away from the armour.

[Mac]

I am at work at the moment, but, for what it is worth, I tried to take a stab at this. I fired up Blender and opened a photogrammetric model of the Parade Armor of King Eric XIV of Sweden I got from Sketchfab (here is a video on how the model was made!). I looked at the knee cops as straight on as I could from the side with my really crappy Blender skills and set the camera to orthographic view, which should completely eliminate any distortion due to distance from the camera. The attached screenshot (sorry... I don't currently have access to a proper image hosting service) shows the model plus the angle I used to measure the angle. I could maybe spend more time on this after work to see if I can get a more accurate measurement, but I got an angle of 80.4 degrees.

I have pulled down that render and put it in my album so I can post it here.



I posted in response to this earlier today. I had misinterpreted the presence of the other knee and cuisse as part of the one in the foreground. It was a bit like one of those optical illusions where the brain latches onto an interpretation and won't let go. I had suggested that there was some sort of twist in the render. A couple hours later I returned to the image and it suddenly made sense. In my panic and embarrassment, I deleted the post.

I hope I can take a lesson away from this. If something seem oddly wrong, I should let it sit for a while and see it it doesn't make more sense on subsequent viewing. Perhaps that will keep me from looking like a fool.

Mac

[Mac]

Today, I'd like to show a series of models based on a two lame articulation of a 60° knee cop. I'm keeping everything the same, but changing the width of the underlapping part of the lame.

This first sketch shows the mid saggital shapes of all five lames that were used in the modeling.



The first shows what we might get with a lame that reaches the center of the cop. The resulting half angle is 28°. This would yield a total included angle of 56° if both ends of the joint were flexed. The supplementary angle of 124° (which is how a physiologist would measure the flexion of the organic knee joint) is clearly more than enough for a fully armored limb.



The next two model show a slightly narrower lame, and the possible flexion is somewhat reduced. In both of these, the flexion is reduced significantly, but they are probably still within authentic parameters. The articulation between the lames and the cannons can probably be optimized to get a few more degrees of flexion, but that was outside the scope of this particular series of models.





In the last two, the lames are too narrow to get enough flexion to be useful.





In the next post, I hope to show some variations of the other side of the lame and how they effect articulation with the cannons.

Mac

[Scott Martin]

Hi Mac

Sorry I didn’t jump in earlier, it’s been a very busy year so far!

I recall our discussions at the Texas hammer-in, and that really helped me with artulation, particularly with the “droop” for gauntlets.

One of the tricky points to making the articulation “shallower” is that in general the articulation is an arc. Most of the “short throw” articulations tend to be things like gauntlets or sabotons where the middle of the arc is compressed or truncated. I think one of the major reasons for the “knuckle folds” on a classic gothic gauntlet is to compress the arc: your articulation arc segments are on the outside of the knuckles, and then you have a “wv” which acts as a straight line (rather than an arc) but because it is “corrugated” it retains strength. This “arc cheat” is also apparent on 16-17 century gauntlets, which have very flat backs and a deep (but narrow in width) knuckle rider. If these were full arcs then the middle of the knuckle plate would need to be much deeper, and look more like a poleyn than a rectangle.

I’ll see about posting pictures but you can see that in general “short throw” articulations tend to have minimal (or no) arc across the central section of the articulation, while “deep throw” articulations are almost spherical (or steeply arched) in their aspect.

Thanks for the illustrations (and methodology) I’ll post more once I figure out how to articulate my thoughts a bit better.

Scott

[Mac]

Hi Mac

Sorry I didn’t jump in earlier, it’s been a very busy year so far!

I recall our discussions at the Texas hammer-in, and that really helped me with artulation, particularly with the “droop” for gauntlets.

One of the tricky points to making the articulation “shallower” is that in general the articulation is an arc. Most of the “short throw” articulations tend to be things like gauntlets or sabotons where the middle of the arc is compressed or truncated. I think one of the major reasons for the “knuckle folds” on a classic gothic gauntlet is to compress the arc: your articulation arc segments are on the outside of the knuckles, and then you have a “wv” which acts as a straight line (rather than an arc) but because it is “corrugated” it retains strength. This “arc cheat” is also apparent on 16-17 century gauntlets, which have very flat backs and a deep (but narrow in width) knuckle rider. If these were full arcs then the middle of the knuckle plate would need to be much deeper, and look more like a poleyn than a rectangle.

I’ll see about posting pictures but you can see that in general “short throw” articulations tend to have minimal (or no) arc across the central section of the articulation, while “deep throw” articulations are almost spherical (or steeply arched) in their aspect.

Thanks for the illustrations (and methodology) I’ll post more once I figure out how to articulate my thoughts a bit better.

Scott

I am having trouble understanding. Can you add some diagrams which illustrate what you mean? You know what they say.... "a picture is worth a thousand words".

Mac

[Scott Martin]

I am having trouble understanding. Can you add some diagrams which illustrate what you mean? You know what they say.... "a picture is worth a thousand words".

Yup, I'll pull these from one of your sections since they illustrate the point (I continue to be envious of your drawings...) When I build these, they start as a smooth arc, and then I "knock down" the middle sections so that I get the end points of the arc, and then a "flat" center section (the zig-zag can be thought of as "corrugated flat") the actual articulation is defined by the "arms" where the picots are located.

Within limits this all holds true for things who's section is not semicircular. In the upper example below, I have drawn a cross section through a typical mitten gauntlet lame. Like the example of the voider, I have shown the typical two dimensional model on the left. The highest point is marked "A", and the "shoulders" of the lame are marked "B". Even though the section is very different than the that of the voider, the same relationship holds for points plotted on the model. That is to say, what works in the middle will work at the shoulders, and by extension, everywhere in between.

In the lower example, I have shown a gauntlet with a zig-zag section of the sort we sometimes see. The two high points are marked "A". The corners and the central "valley" fall at about the same height and are marked "B". The two outer valleys are marked "C". Like our previous examples, all of these points will trace out approximately the same angle between the primary and secondary locks when modeled in two dimensions.



The take away here is that the two dimensional model works for armor of various sections, and even for complex sections.

Mac

So my point is that the middle section is effectively irrelevant - whether it is a smooth arc (like a poleyn) or a "truncated" arc like the gauntlets you have presented here. You could consider these two gauntlet mitten articulations to be equivalent, the smooth vs "waffled" center is "artistic interpretation" rather than a functional difference (although your angle clearances are more "exciting" for the gothic, particularly if you are slotting the rivets)
The more "arc" you have the deeper the articulation needs to be to provide the appropriate angle, and this is based on the radius of the outer arc, which is farther on a couter than a gauntlet for a similar degree of movement, because the arc length of a 5" diameter radius (couter) is much larger than the arc length of a 1.5-2" radius (gauntlet) even if the width of the "joint" is similar. My gauntlets use ~6" wide lames, while my elbows typically use an 8" wide lame.

I hope that this is clearer, we lack the words to really describe what we are talking about, so I may need to take pictures of armour since my drafting skills are terrible!

Scott

[Mac]

The more "arc" you have the deeper the articulation needs to be to provide the appropriate angle, and this is based on the radius of the outer arc, which is farther on a couter than a gauntlet for a similar degree of movement, because the arc length of a 5" diameter radius (couter) is much larger than the arc length of a 1.5-2" radius (gauntlet) even if the width of the "joint" is similar.
Scott

I'm afraid I got lost right at the end.

It's easy to imagine that a verbal description is somehow easier than a diagram. After all, we talk and write all the time. It seems like it should natural and effortless. The fact is that it's very difficult to write about something in a way that's comprehensible to someone else. Someone famous once said something like "Don't write so that you can be understood, write so that you can't be misunderstood". When I find myself in a place where I can't be sure that I won't be misunderstood, I resort to diagrams. It's just easier that way. It's not that drawings simply fall effortlessly from my hands. I really have to work at it. In the end, though, it's easier than trying to do it with writing.

(That paragraph took about 15 minutes to write. Writing is hard. I wish I could have just made a drawing. )

Mac

[Scott Martin]

I'll take some pictures - I suck at drawing, so I'm building some example armour instead. Slower (especially with my current IRL project actively on fire) but less prone to mis-interpretation and confusion.

With the added benefit of having folks tell me how to do things better

To be fair Mac, we've been having this conversation for over 10 years now(!). The "writing is hard" factor forces one to discover what we can't explain well, and that brings attention (at least for me) to areas I don't really understand.

Mac is doing waaaay better than I am at explaining, so I'm mostly trying to fill in the holes (or point at the holes and hoping someone else can fill them in). Unfortunately there are a lot more people interested in owning armour than making it, and fewer still interested in teaching, so it's not surprising that this sort of discussion is so often on "the back burrner".

This is probably a good time to thank all the folks who have helped me understand this craft better, I really appreciate the time many of you have spent explaining things to me (and showing me your work as well as how to look at "the real stuff").