With the head completed, I can judge how much mass I'll be dealing with for the head. The neck is identical in concept to those wooden art horse models that you may have seen: three cables threaded through multiple cutaway sections. It allows for the neck to bend in all sorts of fun directions while resembling a a knife rack. I opted to go with this design over any others since there's not much else that works and looks any better. Also, it works, period.
I split the neck into 20 minor sections composed of 5mm thick sections, and one large 30mm long section. From my understanding, the three bones near the head don't have much movement and the head will likely block the movement when angled down, so there's no point adding articulation that won't be utilized. I originally thought of making the sections 10mm thick, but it would look terrible and have poor movement.
Each section is composed of four cards thickness, so they're stiff enough for shape but not entirely rigid as an eight card thick layer. They taper from 30mm wide x 55mm long to 38mm wide x 80mm long. Approximately 10 stacks were used, so 40 cards total. The neck pivot required its own special assembly, which took 3 stacks, or 12 cards.
In order to get the neck to retain a pose, I selected some conduit that I happened to have lying around. Why do I have conduit lying around, you ask? Who doesn't have conduit lying around, I say! It's one of the fundamental building tools for paper modeling, next to sheet metal and and epoxy. Anyone who says otherwise still uses glue sticks and 100% post consumer content paper to make model La Pietàs. I originally chose three bundles, but that proved difficult to bend. The top and bottom rows need to slide within the 3.175mm diameter holes I made, and the conduit was just enough to not allow for smooth movement. For now, I made the center wire a conduit bundle, and opted for a twisted pair of two regular 20 gauge electrical wires for the top and bottom. I'll probably add a third after some more testing.
The head-neck assembly will be done with a hinge, secured by a nut and bolt. I needed to make an assembly to interface with the hollow head, so I made a partial bucket shaped thing and glued it to the hinge top. Not much to say about my lack of planning here, except that it worked out fine.
The head adapter fits inside the hollow head. I had to modify the head to allow for the adapter to fit in properly. That meant reducing material in the front of the neck and about 10mm from the back, shaped to adapt to the curvature of the adapter and neck. There's some part of the adapter still showing, but that will be trimmed to fit.
Here's the inside of the head. Looks a bit more professional than sanded Hand of Emrakuls bonded together with printer paper.
To attach the neck to the body, I used another 4 card stack to make a mounting plate. Right now, I jammed in the conduit end and it's being held in place by that alone. I'll need to make some stabilizer structures to keep it from wobbling. I'll also need a more permanent and sturdy means of providing neck articulation for the top and bottom wires. For now, the neck can do some decent poses, but can't do a straight extend. The weight tends to make it curve.
Total costs so far: 124 cards on the neck assembly + 122 cards on the head and body= 246 cards. It's looking unlikely that I'll hit the under 300 mark with the remaining parts left. Then again, a smaller scale horse still costs more than the equivalent of 300 commons. If I increase my budget to 400 cards, it'll be about $100 at the rate of $0.25 a common (or $40 at $0.10 a common), which is still better than what they'd fetch if I tried to sell someone a stack of Kurgadons or Ingenious Thiefs.
Showing posts with label structure. Show all posts
Showing posts with label structure. Show all posts
Sunday, May 22, 2011
Sunday, May 01, 2011
This Month's Project: Horse Legs
Been about a two months since I decided to build a horse. After much time of not trying, I made some progress. I've finished drafting up plans for the legs and am happy with the overall status. No point posting plans since you will never want to build these. I also still have no plans for the neck and head so far.
The leg system is largely unchanged from other endeavors: 16 card thick hinge pieces with screws.I should be using larger fasteners, but I still have a good stockpile of parts remaining. Only difference is the overall larger size of each component, and less modular nature. What you see here is a sense of how many cards were destroyed to build the horse's legs. Quite a bit this time. A set of forelegs and hind legs used 22 sheets of 4 card stacks, for a total of 88 cards. Already close to my original arbitrary goal of 300 cards. I ruined one part due to drawing errors, adding eight more cards to development costs. Sixteen cards were used to build the templates, with four being scrapped. That brings up the total expenditure (including the four used in development two months ago) to 116 cards used. In case there's any doubters that I am not using basic lands, and am, in fact, using crap commons, here's some of the templates used to build the legs:
Good old crappy Ice Age. Seems that I accumulated a stack of oddly glossier Ice Age cards. I never liked them due to their odd finish that ruined and came off easier than the regular coat and used them for templates. Turns out that they were sort of uncommon in print run, but nothing worth celebrating about. A glossy Pyknite is still useless.
I spent some time figuring out the leg range of motion for each part using various photos and references. I'm probably off by a good margin, but I have the general movement mapped out. If you're interested, you're better off buying a book on horse anatomy (which I didn't), or studying one properly (which I didn't). My measurements aren't the most reliable.
The most important parts of the project are the legs, neck, head and, for a lack of a better term, chassis. Everything else will be freehanded like the camel, and skinned with a coat of card, hopefully. Right now, it's going to be a horse made of scaffolding.
This is where the horse currently stands. The joints can be tightened enough to allow me to do this, and hopefully retain this pose with additional weight from the rest of the horse's body. As a test of joint strength, I added some test mass to the neck region to give a good estimate on what to expect. What better to simulate the mass of 60 more magic cards than someone made of about 60 Magic cards?
Hotaru proved that the hinges need a lot of tightening. I could stack the Heavy on the front and provide a more rigorous test. I had some difficulty keeping the rear legs angled correctly with just Hotaru, and it will be trickier once there's more mass to work with. I'll have to readjust the center of mass once I develop the head, much like the camel.
It'll probably be a while before I figure out the neck and head components. Until now, it's a glorified barricade horse. I now have a good idea of how crazy of a size this thing is going to be, fully built.
The leg system is largely unchanged from other endeavors: 16 card thick hinge pieces with screws.I should be using larger fasteners, but I still have a good stockpile of parts remaining. Only difference is the overall larger size of each component, and less modular nature. What you see here is a sense of how many cards were destroyed to build the horse's legs. Quite a bit this time. A set of forelegs and hind legs used 22 sheets of 4 card stacks, for a total of 88 cards. Already close to my original arbitrary goal of 300 cards. I ruined one part due to drawing errors, adding eight more cards to development costs. Sixteen cards were used to build the templates, with four being scrapped. That brings up the total expenditure (including the four used in development two months ago) to 116 cards used. In case there's any doubters that I am not using basic lands, and am, in fact, using crap commons, here's some of the templates used to build the legs:
Good old crappy Ice Age. Seems that I accumulated a stack of oddly glossier Ice Age cards. I never liked them due to their odd finish that ruined and came off easier than the regular coat and used them for templates. Turns out that they were sort of uncommon in print run, but nothing worth celebrating about. A glossy Pyknite is still useless.
I spent some time figuring out the leg range of motion for each part using various photos and references. I'm probably off by a good margin, but I have the general movement mapped out. If you're interested, you're better off buying a book on horse anatomy (which I didn't), or studying one properly (which I didn't). My measurements aren't the most reliable.
The most important parts of the project are the legs, neck, head and, for a lack of a better term, chassis. Everything else will be freehanded like the camel, and skinned with a coat of card, hopefully. Right now, it's going to be a horse made of scaffolding.
This is where the horse currently stands. The joints can be tightened enough to allow me to do this, and hopefully retain this pose with additional weight from the rest of the horse's body. As a test of joint strength, I added some test mass to the neck region to give a good estimate on what to expect. What better to simulate the mass of 60 more magic cards than someone made of about 60 Magic cards?
Hotaru proved that the hinges need a lot of tightening. I could stack the Heavy on the front and provide a more rigorous test. I had some difficulty keeping the rear legs angled correctly with just Hotaru, and it will be trickier once there's more mass to work with. I'll have to readjust the center of mass once I develop the head, much like the camel.
It'll probably be a while before I figure out the neck and head components. Until now, it's a glorified barricade horse. I now have a good idea of how crazy of a size this thing is going to be, fully built.
Sunday, November 07, 2010
Assembling a Sentry Gun
Doing some more clean up with documentation. The TF2 Sentry Gun paper model is very under documented. Magically jumps from a base stand to a level 3 within four days.
I've recently uploaded revised schematics to replace the very ineffective ones posted about two years ago. However, there's no documentation of how the parts were assembled. Time to fill in those gaps.
Building a Sentry base
The base needs to be stiff. 110lb cardstock without special treatment methods will be ineffective in supporting the loads this model will encounter. Recommend using 110lb cardstock only for tubing and using thick laminates of Magic: the Gathering to assemble every part on the base.
Magic cards offer good strength for little material. Treat them like sheet metal when building the front legs. Use thicknesses of 8 cards to create 2.5mm thick sections. The curved side frame posts were built in that manner. A thickness of 4 cards was used for minor sections like the upper parts of the front legs.
110lb cardstock is weak when used as a plane sheet, but when rolled up with or without support of a 3.175mm wooden rod, it's sturdy. The main post and rod running through it were done with both methods: using a wooden inner rod and without.
These rear legs are very troublesome. You're going to have minimal adhesive holding these parts together. Recommend making biscuits and joints to connect the sections. Super glue is recommended for these parts.
Tubes, Tubes, Tubes
A lot of the sentry will be large sections of material. The trick is to lighten up the material as best as possible. The ammo drum was built almost like a papercraft model, with lots of empty space inside. Making the drum solid would contribute excess weight to an already unstable model. Here, there's the inner drum (left), outer support drum (middle), and the outer shell (right), which is composed of a tapered cylinder. The outer shell fits alongside the outer support drum to stiffen one side, while providing the tapered shape on the other side. Magic cards were used for the flat backside, offering good planar stiffness with minimal warping.
I built the ammo drum support arm in sections. Don't do that. Build this section as stiff as possible, and out of as few pieces as possible. This part is very problematic as it supports a lot of load and will be subject to constant bending for the rest of the life of the sentry. Don't even try using 110lb cardstock without some inner support material. Stiffer the better.
The minigun assemblies are designed to spin, but also designed for weight reduction. The arch shaped supports are fleshed out using tubes on the curved ends, and troughs made of Magic cards. Tubes offer stiffness with shape, and the cards offer stiffness with flat surfaces. The only time something needs to be completely solid is for shapes 3-4mm thick or less.
For the barrels, they span a length of 40mm, but you can support them on the edges with 12-16mm of material. This lightens up the parts significantly.
For this build, I considered using pre-existing plastic tubes to minimize friction when rotating. Not a big issue in the long run since it won't see much rotation. The tubes offered strength and volume for little effort. The barrels themselves need rework, but I've drafted new plans for a stronger set in the newer plan revisions.
There's a bit of sag from the barrel weight, since rolled up 110lb cardstock is still heavy. There's little room for a counterweight, but adding more mass to the supports only loads the center mounting plate more. The goal is to minimize overall weight as well as keeping it balanced. The first objective helps with the second.
The Turret
The rocket turret is another part that requires lightening. The image above demonstrates how it was built: four tubes running along the length, with tabs on the sides to allow for a cover to be placed around it. Build this like sheet metal and not like a milled object.
These support arm parts for the turret were built light and stiff. They may appear thick, but they're mostly hollow inside.
The amount of "large mass supported by a thin strut" situations on this model are numerous. Luckily, this is the least severe of the situations. The white support base is made of several layers of 110lb cardstock, but can be done with Magic cards. The trick is to use the thickness of the material to your advantage for small details.
Wiring the Sentry
This wire assembly can be tough. You'll need to find wire with a sleeve diameter of 3mm, or make your own by rolling printer paper around some thin wires. Printer paper is soft and bends easier than 110lb cardstock when rolled. Goal is to keep the rolled thickness to a minimum. Thicker the walls, harder to bend.
Attaching the wires to the plate can be done by leaving bare wire on the ends and threading it through a sheet. Just glue another sheet to sandwich the wire ends in, and they should remain in place.
I've documented the ammo belts here, and with the rest of the new diagrams, that should cover all the miscellaneous aspects of building the sentry gun.
Now.. Just need to properly present the completed model this time around.
I've recently uploaded revised schematics to replace the very ineffective ones posted about two years ago. However, there's no documentation of how the parts were assembled. Time to fill in those gaps.
Building a Sentry base
The base needs to be stiff. 110lb cardstock without special treatment methods will be ineffective in supporting the loads this model will encounter. Recommend using 110lb cardstock only for tubing and using thick laminates of Magic: the Gathering to assemble every part on the base.
Magic cards offer good strength for little material. Treat them like sheet metal when building the front legs. Use thicknesses of 8 cards to create 2.5mm thick sections. The curved side frame posts were built in that manner. A thickness of 4 cards was used for minor sections like the upper parts of the front legs.
110lb cardstock is weak when used as a plane sheet, but when rolled up with or without support of a 3.175mm wooden rod, it's sturdy. The main post and rod running through it were done with both methods: using a wooden inner rod and without.
These rear legs are very troublesome. You're going to have minimal adhesive holding these parts together. Recommend making biscuits and joints to connect the sections. Super glue is recommended for these parts.
Tubes, Tubes, Tubes
A lot of the sentry will be large sections of material. The trick is to lighten up the material as best as possible. The ammo drum was built almost like a papercraft model, with lots of empty space inside. Making the drum solid would contribute excess weight to an already unstable model. Here, there's the inner drum (left), outer support drum (middle), and the outer shell (right), which is composed of a tapered cylinder. The outer shell fits alongside the outer support drum to stiffen one side, while providing the tapered shape on the other side. Magic cards were used for the flat backside, offering good planar stiffness with minimal warping.
I built the ammo drum support arm in sections. Don't do that. Build this section as stiff as possible, and out of as few pieces as possible. This part is very problematic as it supports a lot of load and will be subject to constant bending for the rest of the life of the sentry. Don't even try using 110lb cardstock without some inner support material. Stiffer the better.
The minigun assemblies are designed to spin, but also designed for weight reduction. The arch shaped supports are fleshed out using tubes on the curved ends, and troughs made of Magic cards. Tubes offer stiffness with shape, and the cards offer stiffness with flat surfaces. The only time something needs to be completely solid is for shapes 3-4mm thick or less.
For the barrels, they span a length of 40mm, but you can support them on the edges with 12-16mm of material. This lightens up the parts significantly.
For this build, I considered using pre-existing plastic tubes to minimize friction when rotating. Not a big issue in the long run since it won't see much rotation. The tubes offered strength and volume for little effort. The barrels themselves need rework, but I've drafted new plans for a stronger set in the newer plan revisions.
There's a bit of sag from the barrel weight, since rolled up 110lb cardstock is still heavy. There's little room for a counterweight, but adding more mass to the supports only loads the center mounting plate more. The goal is to minimize overall weight as well as keeping it balanced. The first objective helps with the second.
The Turret
The rocket turret is another part that requires lightening. The image above demonstrates how it was built: four tubes running along the length, with tabs on the sides to allow for a cover to be placed around it. Build this like sheet metal and not like a milled object.
These support arm parts for the turret were built light and stiff. They may appear thick, but they're mostly hollow inside.
The amount of "large mass supported by a thin strut" situations on this model are numerous. Luckily, this is the least severe of the situations. The white support base is made of several layers of 110lb cardstock, but can be done with Magic cards. The trick is to use the thickness of the material to your advantage for small details.
Wiring the Sentry
This wire assembly can be tough. You'll need to find wire with a sleeve diameter of 3mm, or make your own by rolling printer paper around some thin wires. Printer paper is soft and bends easier than 110lb cardstock when rolled. Goal is to keep the rolled thickness to a minimum. Thicker the walls, harder to bend.
Attaching the wires to the plate can be done by leaving bare wire on the ends and threading it through a sheet. Just glue another sheet to sandwich the wire ends in, and they should remain in place.
I've documented the ammo belts here, and with the rest of the new diagrams, that should cover all the miscellaneous aspects of building the sentry gun.
Now.. Just need to properly present the completed model this time around.
Labels:
Build progress,
paper model,
sentry gun,
structure,
Team Fortress 2
Sunday, July 25, 2010
This Weekend's Project: Annual Hip Surgery
This weekend, I tackled on a problem that's been plaguing the girls since their first iteration: deficient hip structures. The current build utilizes ball joints. I had some time to think of a new solution, assisted by the plethora of new construction methods I've learned from building the Team Fortress 2 doll set.
The hips have been a problem for one reason: they required to bear significant load on a small region of material. The hip requires a good deal of stiffness to resist torsion, bending/fractures, and friction to keep position under load. Prototype build 1 utilized screws and pins to hold the hip together using a hinge joint linked to the body by a pin. Really primitive, and the movements were restrictive and counter intuitive to the user.
Hip Iteration 2 played with ball joints. I had them aligned in two configurations (cup axial and perpendicular to the ball/shaft) and under three total designs. The problems with the ball joint were apparent: Friction was unreliable. To obtain the correct amount of friction, I had to balance the diameters of the ball with the socket ( often done by shimming with scrap paper) with the friction of the ball and the connector shaft.
Here's the current build. Note the paper used to shim the gap between the socket and ball.
The goal was to allow for maintenance by allowing the leg with the socket to be removed from the ball, and if needed, the ball could be removed from the shaft. This was critical back then due to the way the ball was constructed: poorly. I required a method of allowing maintenance in case the ball sheared apart or deformed significantly, or if I required a complete mechanism overhaul. Handy that I designed for interchangeability and easy modifications back then.
The ball's biggest problem was that despite being able to craft them with a relatively decent degree of accuracy diameter-wise, they were very difficult to make respectably spherical. It was more like building an octagonal cross sectioned polygon. When moved, the "sphere" had more friction in some positions than others.
The second problem was the nature of the material itself. Paper does compress to some degree, and the irregular sphere deformed a lot. It deformed from moving around the socket, with the thicker sections of the ball compressing the socket, making a depression with low friction. The whole setup was susceptible to expansion effects. I noted a fluctuation in friction over the year, attributed best to humidity. Naturally, water will expand paper. The socket was made of Magic: the Gathering (for the smooth finish to assist movement) and the ball was made of 110 lb cardstock. The dissimilar materials caused a more drastic change of dimension than if they were similar. I'm presuming the 110lb cardstock deformed the most, but I have not been certain.
As a result of the problems, I encountered another problem: shaft torsion. Friction was uneven from the ball/socket and ball/shaft interfaces. Some cases occurred where the friction was fairly strong and a degree of torque applied to the system did not transfer to overcoming static friction of the system and went to torquing the shaft. As a result, I had a fair degree of axial play that no amount of shimming could correct.
Now we have the major problems identified:
Iteration 5 is similar to the traditional hip structure in that it uses a hinge joint and a rotating shaft connected to the hip in a "T" fashion. It however opts to put the rotation within the hinge than at the hip. Iteration 5 uses the strength of the screw hinge system to allow for easy adjustable friction and bypasses the ball-and-socket system and its resultant problems. Shaft torsion has been reduced by shortening the connector shaft. Less length, less torsional effects.
The system has the shaft inserted to a 6mm deep cup located on a notched region on the center movement disc. Disc is shown above the finished assembly. The hinge system resembles a "Pac-man", with an arc removed to allow for clearance of the cup. The cup moves along the arc, limited by the hard stops. Friction is easier to control, as there's only one factor for the rotational aspect. However, the engagement is less (10mm from the ball and socket, 6mm in this configuration) so the shaft needs to have extra friction to hold the same positions as the previous iteration did.
After some initial tests, I decided that my design was worth implementing, at least to one of the girls. Since I'm rather fond of Hotaru having legs, and Aelia isn't really doing anything important, I chose Lia as the test subject.
To construct the legs, I did the usual bit of tubes and shells. I however tried a new method of filling out the spherical void needed to cover the screw/nut part of the hinge: solid hemispheres.
These were made with the handy paper solids maker from long back. I built them in cylindrical steps and sanded them down aggressively with a Dremel. The tube and shell method will be glossed over here since it's fairly simple: glue tubes and reinforce with a sheet of Magic card.


So, how do the finished legs/hips look?
"Don't get any ideas, I'm technically only 2 years old."
Gratuitous upskirt photo time. The new joints solve a cosmetic problem of filling in a small unsightly gap between the thigh and the hip structure. I've left the port covers for the fasteners unsanded for easy access/maintenance.
As for evaluation: they are fairly stiff to allow the legs to retain their position. I'm going to see how humidity effects affect the system before retrofitting them to Hotaru and Aelia. Lia will be testing the system and finding any flaws over her next few months. The system does have drawbacks. The mechanism only works for fairly large sphere/hinge joints (mine was 18mm in diameter, and does not work for smaller diameters) and there's a good chance of the torque from moving the legs unrooting the shaft from the hip. I had to re-attach the shaft to the body after noticing the new hips had twisted the shaft out of place.
The hips have been a problem for one reason: they required to bear significant load on a small region of material. The hip requires a good deal of stiffness to resist torsion, bending/fractures, and friction to keep position under load. Prototype build 1 utilized screws and pins to hold the hip together using a hinge joint linked to the body by a pin. Really primitive, and the movements were restrictive and counter intuitive to the user.
Hip Iteration 2 played with ball joints. I had them aligned in two configurations (cup axial and perpendicular to the ball/shaft) and under three total designs. The problems with the ball joint were apparent: Friction was unreliable. To obtain the correct amount of friction, I had to balance the diameters of the ball with the socket ( often done by shimming with scrap paper) with the friction of the ball and the connector shaft.
The goal was to allow for maintenance by allowing the leg with the socket to be removed from the ball, and if needed, the ball could be removed from the shaft. This was critical back then due to the way the ball was constructed: poorly. I required a method of allowing maintenance in case the ball sheared apart or deformed significantly, or if I required a complete mechanism overhaul. Handy that I designed for interchangeability and easy modifications back then.
The ball's biggest problem was that despite being able to craft them with a relatively decent degree of accuracy diameter-wise, they were very difficult to make respectably spherical. It was more like building an octagonal cross sectioned polygon. When moved, the "sphere" had more friction in some positions than others.
The second problem was the nature of the material itself. Paper does compress to some degree, and the irregular sphere deformed a lot. It deformed from moving around the socket, with the thicker sections of the ball compressing the socket, making a depression with low friction. The whole setup was susceptible to expansion effects. I noted a fluctuation in friction over the year, attributed best to humidity. Naturally, water will expand paper. The socket was made of Magic: the Gathering (for the smooth finish to assist movement) and the ball was made of 110 lb cardstock. The dissimilar materials caused a more drastic change of dimension than if they were similar. I'm presuming the 110lb cardstock deformed the most, but I have not been certain.
As a result of the problems, I encountered another problem: shaft torsion. Friction was uneven from the ball/socket and ball/shaft interfaces. Some cases occurred where the friction was fairly strong and a degree of torque applied to the system did not transfer to overcoming static friction of the system and went to torquing the shaft. As a result, I had a fair degree of axial play that no amount of shimming could correct.
Now we have the major problems identified:
- ball irregularity
- friction irregularity
- shaft torsion

After some initial tests, I decided that my design was worth implementing, at least to one of the girls. Since I'm rather fond of Hotaru having legs, and Aelia isn't really doing anything important, I chose Lia as the test subject.
To construct the legs, I did the usual bit of tubes and shells. I however tried a new method of filling out the spherical void needed to cover the screw/nut part of the hinge: solid hemispheres.
Gratuitous upskirt photo time. The new joints solve a cosmetic problem of filling in a small unsightly gap between the thigh and the hip structure. I've left the port covers for the fasteners unsanded for easy access/maintenance.
As for evaluation: they are fairly stiff to allow the legs to retain their position. I'm going to see how humidity effects affect the system before retrofitting them to Hotaru and Aelia. Lia will be testing the system and finding any flaws over her next few months. The system does have drawbacks. The mechanism only works for fairly large sphere/hinge joints (mine was 18mm in diameter, and does not work for smaller diameters) and there's a good chance of the torque from moving the legs unrooting the shaft from the hip. I had to re-attach the shaft to the body after noticing the new hips had twisted the shaft out of place.
Sunday, December 06, 2009
J.Norad Makes Paper Ball Joints
This post is more for personal reference than of possible use to any of you. Today, I'll be covering some parameters for designing a ball joint. A ball and socket joint provides excellent movement capabilities but isn't an easy element to build with paper.
The key to building a robust ball joint with paper is to have the appropriate materials needed. A good ball joint should provide adequate joint stiffness, but it may vary on your application.
Designing the Ball and Socket
You'll need to know a few things first:

First, we must acknowledge that the support rod diameter 2P and the lower socket height Hl limit our angle. This is because the rod hits the edge of the socket, defined by how deep (Hl) the socket is. Second, we'll define the angle the joint provides as the angle that the center of the support rod makes with the line parallel to the bottom of the socket. This angle will be phi.
From Figure 1:
The angle we actually want is the complimentary angle to Phi, since that determines the angle relative to the null position. So we take twice the compliment to Phi (two directions) to find the angle of our joint.
Total angle range for the ball and socket joint = 2(90° - Phi)
Where Phi = arctan(Hl/r1) + arcsin(p/sqrt(r1^2 +Hl^2))
This equation tells us some obvious relations, which help support the validity of the result:
The Socket
The socket should ideally consist of a durable material. 110lb cardstock will not work, as it wears out fast and easily over a few cycles. The smooth varnished surface of a Magic: the Gathering card is an excellent material. It will withstand more cycles and is fairly strong. Since paper (and Magic cards) does not have "negligible" thickness anymore (you're now working with a system that will requires a few thousandths of an inch in terms of tolerance to work well), you need to account for the overlap of paper. Magic cards have a thickness of 0.30988 mm (experimentally measured), which translates to 0.0122 in. This is enough to make your cylinder a slight oval if there's overlap. (If you consider that the accuracy of hand building has a tolerance in the range of half a millimeter anyways, it might not matter in the long run. And you can always correct for it later...)
By acknowledging paper overlap, we form our socket by cutting out a strip of Magic card of a length equal to our projected ball diameter so that when we curl it up, both ends sit flush with each other, thereby eliminating the overlap. Once you have your cylinder, you can freely complete the cylinder with additional layer of Magic card without worrying as much about overlap. Removing overlap helps reduce wear of the ball and socket over time, since the raised edge is most likely to wear first.
Remember: paper is not incompressible. You'll lose a few thousandths over time. Adjust accordingly.
The Ball
The ball part is perhaps the most difficult part to build. Not also do you need to have the dimensions as close as possible for a tight fit, it needs to be built well and uniform.
First, you'll need a decent support rod to use. 1/8" (3.175 mm) diameter bamboo sticks are a good choice. They're usually $2 for a pack of 100. Pick one with low eccentricity if possible, and look for non-slivering/splintering ones. Those will snap first over time.
Next, you'll need to use the excel sheet for making cylinders. I suggest using 110lb cardstock for the ball, since it's easier to work with and tears less than printer paper. However, printer paper glued together with superglue will provide a nice solid sphere. I like to sand the ball after it's made, so I use 110lb.
To make the spherical shape, you need to taper the strip to a triangular shape. If using the 1/8" rod method, start the taper from 5cm from the starting edge and taper it linearly to 3mm to the other side.
Roll the paper around the rod as tight as possible. Any gaps or loosely bonded sections will result in failure in the rod axial direction, meaning it will start to deform and separate as you push it in the socket.

After you've finished, your sphere will be somewhat octagonal in cross section. Break out those calipers and sand that sphere down to as best as you can to a uniform diameter throughout. Irregularities will result in uneven performance, where certain positions are looser than others. You ideally want the ball to be a few thousandths (0.003-0.010 in) larger than the socket for a nice snug fit.
Adjusting the Fit
Your ball and socket joint may be loose or come loose over time due to thermal expansion, humidity, wear or other factors. You can easily adjust the joint to regain stiffness. Options include:
If there are any other adjustments or updates, I'll add them as necessary to this page.
The key to building a robust ball joint with paper is to have the appropriate materials needed. A good ball joint should provide adequate joint stiffness, but it may vary on your application.
Designing the Ball and Socket
You'll need to know a few things first:
- Figure out how big your joint is going to be.
- Figure out how much mobility you want.

Figure 1: The Ball Joint Schematic
For a given set of construction variables, r1, Hl and 2p, you can figure out how much motion your ball joint will provide. We'll use some trigonometry to solve for the angle phi, and use this to determine the total angle your joint will provide.There's four design parameters that dictate the performance of your ball joint:
- Ball radius (r1 in Figure 1) (You'll hopefully know this value first)
- Socket depth (Hl in Figure 1) (somewhat adjustable, has a lower limit)
- Support rod diameter (2P in Figure 1) (adjustable, has a lower limit)
- Range of motion (phi in Figure 1) (defined by values 1-3)
First, we must acknowledge that the support rod diameter 2P and the lower socket height Hl limit our angle. This is because the rod hits the edge of the socket, defined by how deep (Hl) the socket is. Second, we'll define the angle the joint provides as the angle that the center of the support rod makes with the line parallel to the bottom of the socket. This angle will be phi.
From Figure 1:
- The red angle Beta formed from the point of contact with the socket edge (Hl) and the support rod walls is less than our desired angle, phi. Since it's a right triangle, we know from the pythagorean theorem that the length of from the center to the tip of Hl is the square root of r1^2 + Hl^2.
- The angle formed from the line OP to the support rod centerline is the difference between angles phi and Beta. We know the thickness is 2P, and that OP forms the hypotenuse, and half the rod thickness P forms the opposite wall. Therefore, the angle Phi- Beta = arcsin(P/sqrt(r1^2 +Hl^2)).
- From trigoneometry, the angle Beta =arctan(Hl/r1)
The angle we actually want is the complimentary angle to Phi, since that determines the angle relative to the null position. So we take twice the compliment to Phi (two directions) to find the angle of our joint.
Total angle range for the ball and socket joint = 2(90° - Phi)
Where Phi = arctan(Hl/r1) + arcsin(p/sqrt(r1^2 +Hl^2))
This equation tells us some obvious relations, which help support the validity of the result:
- If Hl is longer than r1, the angle decreases
- if p increases, the angle decreases
- increasing r1 increases the angle.
The Socket
The socket should ideally consist of a durable material. 110lb cardstock will not work, as it wears out fast and easily over a few cycles. The smooth varnished surface of a Magic: the Gathering card is an excellent material. It will withstand more cycles and is fairly strong. Since paper (and Magic cards) does not have "negligible" thickness anymore (you're now working with a system that will requires a few thousandths of an inch in terms of tolerance to work well), you need to account for the overlap of paper. Magic cards have a thickness of 0.30988 mm (experimentally measured), which translates to 0.0122 in. This is enough to make your cylinder a slight oval if there's overlap. (If you consider that the accuracy of hand building has a tolerance in the range of half a millimeter anyways, it might not matter in the long run. And you can always correct for it later...)
By acknowledging paper overlap, we form our socket by cutting out a strip of Magic card of a length equal to our projected ball diameter so that when we curl it up, both ends sit flush with each other, thereby eliminating the overlap. Once you have your cylinder, you can freely complete the cylinder with additional layer of Magic card without worrying as much about overlap. Removing overlap helps reduce wear of the ball and socket over time, since the raised edge is most likely to wear first.
Remember: paper is not incompressible. You'll lose a few thousandths over time. Adjust accordingly.
The Ball
The ball part is perhaps the most difficult part to build. Not also do you need to have the dimensions as close as possible for a tight fit, it needs to be built well and uniform.
First, you'll need a decent support rod to use. 1/8" (3.175 mm) diameter bamboo sticks are a good choice. They're usually $2 for a pack of 100. Pick one with low eccentricity if possible, and look for non-slivering/splintering ones. Those will snap first over time.
Next, you'll need to use the excel sheet for making cylinders. I suggest using 110lb cardstock for the ball, since it's easier to work with and tears less than printer paper. However, printer paper glued together with superglue will provide a nice solid sphere. I like to sand the ball after it's made, so I use 110lb.
To make the spherical shape, you need to taper the strip to a triangular shape. If using the 1/8" rod method, start the taper from 5cm from the starting edge and taper it linearly to 3mm to the other side.
Roll the paper around the rod as tight as possible. Any gaps or loosely bonded sections will result in failure in the rod axial direction, meaning it will start to deform and separate as you push it in the socket.
After you've finished, your sphere will be somewhat octagonal in cross section. Break out those calipers and sand that sphere down to as best as you can to a uniform diameter throughout. Irregularities will result in uneven performance, where certain positions are looser than others. You ideally want the ball to be a few thousandths (0.003-0.010 in) larger than the socket for a nice snug fit.
Adjusting the Fit
Your ball and socket joint may be loose or come loose over time due to thermal expansion, humidity, wear or other factors. You can easily adjust the joint to regain stiffness. Options include:
- Adding some additional material to pad out the socket to reduce the inner diameter. I suggest using a small section of paper (printer or 110lb works, depending on the looseness) inserted into the joint
- Thickening the ball with superglue. Make sure the ball is dried completely before re-inserting.
If there are any other adjustments or updates, I'll add them as necessary to this page.
Friday, August 28, 2009
J.Norad's Guide to Building Stuff With Magic: The Gathering Cards
Time to gather all my development notes and techniques all into one post.
First a primer:
Magic: the Gathering is a convenient, abundant work material in some cases, despite the steep initial material costs. A card costs anywhere from $0.26 from a booster pack to $0.13 from a tournament pack. Found in many a gaming shop and teenager's closet, you can secure large quantities of "chaff" cards for little cost. I shall be dealing with non-foil cards, as I have yet to find a use for the foil "premium" cards.
If the idea of cutting up common and uncommon rarity cards scares you, lands are cheap and practically free from most shops and post-tournament gaming. I use anything that I deem "unplayable" or in gross excess, except lands, which I find useful. I particularly have a hatred for Centaur Veteran, from Torment.
Preparing the Cards:
Magic: the Gathering has a nice sheen/varnish to each card. It is slightly waterproof and resistant to some paints and glues. You'll need some sand paper, about the 80 grit range, to get rid of the coating. Once the card has some white showing, you've sanded enough. You may in some cases leave the surface on one side unsanded to take advantage of the smooth surface. Two unsanded surfaces have a drastically lower friction and wear rate than two sanded surfaces in planar shear. I take advantage of this property when making hinge and pin joints with Magic cards.
Elmer's glue is sufficient for working with Magic cards. Loc-tite can be used for emergency "quick drying" jobs or plastinating sections of Magic cards. That involves applying a thin layer of Loc-tite and letting it dry, forming a hard layer of glue on the surface. This is useful for increasing part thicknesses for joints. If you use Elmer's glue to form boards, they will require 2-4 days of drying time to fully stiffen. While they dry, they are relatively bendable and easy to cut.
I've experimentally determined a few ideal card thicknesses for use in construction. A minimum of 4 (four) cards is needed for a rigid structure of small size. For larger components like doll joints, 8 (eight) layers is recommended. Four layers conveniently is the thickness where you can still manage to cut the stack of cards with regular scissors. If you wish to cut cards with a tool, I would suggest cutting four layers at a time, gluing the stacks together, then work on the part as one solid piece for sanding/finishing purposes.
Material Properties- Thicknesses
A Magic card is approximately 0.012 inches thick, or 0.27mm. Depending on how well you apply glue (a thin coat spread evenly is recommended: excess will cause warping when drying), the thickness of the glue is negligible. With the sanded cards, I like to glue four cards together to form Magic: the Plywood. I keep a stack of these boards around for quick access. I do most of my work in increments of four cards for simplicity. Less variance in stock materials.
I have a chart to assist in gauging how much material I need to use for making a solid object.
With this, I can quickly gauge how many times I need to trace a part out before I achieve the required thickness. Keep in mind: Magic cards are not incompressible, nor are they static in thickness. You can easily thicken the edge of a 4-card board with aggressive Dremel sanding by up to 0.5mm. Significant, considering it's 1.2mm to start with. This occurs by delaminating the card's individual layers with frayed edges. This is why you should Dremel AFTER gluing laminates together.
Tooling and Cards
Now you have some 4-card boards, you're ready to make stuff. Treat these boards like wood. Really bad wood. Do not inhale the dust generated from cutting. The dust is a fine particulate.
For making holes, hole punches work for 2-3 layers deep before you encounter significant resistance. This allows you to make 1/4" and 1/8" holes with ease and precision. For other holes, you'll need a drill. Start off with a manual 1/16" drill to make a pilot hole. Don't bother making a hole in a material deeper than a couple millimeters by hand, otherwise it won't be perpendicular to the plane. A pilot hole is key to prevent edge fraying. With a Dremel, use your desired drill size and drill halfway through the material using the pilot hole as a guide, and repeat for the other side. Going straight through causes the other side to flare up like a volcano.
Material Properties: Stiffness
You may find yourself making something longer than the card is. In this case, put the necessary length of cards together and alternate the break between cards with a solid card, like a brick layer. Except, in this case, you want to alternate where the breaks are so they're not all stacked near each other. This weakens the structure significantly. Refer to the figure below for proper stacking.
Material Properties: Bend Radius
A 4-card board can be bent to some degree to form a curved surface. For smaller bend radii, you'll need to roll the card around a dowel first to prevent cracking. You can achieve small cylinders with Magic cards, but anything smaller than 1/4" is difficult. Magic cards are not recommended for tube making, unless the surface finish must be smooth as possible.
This post will be edited as necessary.
First a primer:
Magic: the Gathering is a convenient, abundant work material in some cases, despite the steep initial material costs. A card costs anywhere from $0.26 from a booster pack to $0.13 from a tournament pack. Found in many a gaming shop and teenager's closet, you can secure large quantities of "chaff" cards for little cost. I shall be dealing with non-foil cards, as I have yet to find a use for the foil "premium" cards.
If the idea of cutting up common and uncommon rarity cards scares you, lands are cheap and practically free from most shops and post-tournament gaming. I use anything that I deem "unplayable" or in gross excess, except lands, which I find useful. I particularly have a hatred for Centaur Veteran, from Torment.
Preparing the Cards:
Magic: the Gathering has a nice sheen/varnish to each card. It is slightly waterproof and resistant to some paints and glues. You'll need some sand paper, about the 80 grit range, to get rid of the coating. Once the card has some white showing, you've sanded enough. You may in some cases leave the surface on one side unsanded to take advantage of the smooth surface. Two unsanded surfaces have a drastically lower friction and wear rate than two sanded surfaces in planar shear. I take advantage of this property when making hinge and pin joints with Magic cards.
Elmer's glue is sufficient for working with Magic cards. Loc-tite can be used for emergency "quick drying" jobs or plastinating sections of Magic cards. That involves applying a thin layer of Loc-tite and letting it dry, forming a hard layer of glue on the surface. This is useful for increasing part thicknesses for joints. If you use Elmer's glue to form boards, they will require 2-4 days of drying time to fully stiffen. While they dry, they are relatively bendable and easy to cut.
I've experimentally determined a few ideal card thicknesses for use in construction. A minimum of 4 (four) cards is needed for a rigid structure of small size. For larger components like doll joints, 8 (eight) layers is recommended. Four layers conveniently is the thickness where you can still manage to cut the stack of cards with regular scissors. If you wish to cut cards with a tool, I would suggest cutting four layers at a time, gluing the stacks together, then work on the part as one solid piece for sanding/finishing purposes.
Material Properties- Thicknesses
A Magic card is approximately 0.012 inches thick, or 0.27mm. Depending on how well you apply glue (a thin coat spread evenly is recommended: excess will cause warping when drying), the thickness of the glue is negligible. With the sanded cards, I like to glue four cards together to form Magic: the Plywood. I keep a stack of these boards around for quick access. I do most of my work in increments of four cards for simplicity. Less variance in stock materials.
I have a chart to assist in gauging how much material I need to use for making a solid object.
Tooling and Cards
Now you have some 4-card boards, you're ready to make stuff. Treat these boards like wood. Really bad wood. Do not inhale the dust generated from cutting. The dust is a fine particulate.
For making holes, hole punches work for 2-3 layers deep before you encounter significant resistance. This allows you to make 1/4" and 1/8" holes with ease and precision. For other holes, you'll need a drill. Start off with a manual 1/16" drill to make a pilot hole. Don't bother making a hole in a material deeper than a couple millimeters by hand, otherwise it won't be perpendicular to the plane. A pilot hole is key to prevent edge fraying. With a Dremel, use your desired drill size and drill halfway through the material using the pilot hole as a guide, and repeat for the other side. Going straight through causes the other side to flare up like a volcano.
Material Properties: Stiffness
You may find yourself making something longer than the card is. In this case, put the necessary length of cards together and alternate the break between cards with a solid card, like a brick layer. Except, in this case, you want to alternate where the breaks are so they're not all stacked near each other. This weakens the structure significantly. Refer to the figure below for proper stacking.
A 4-card board can be bent to some degree to form a curved surface. For smaller bend radii, you'll need to roll the card around a dowel first to prevent cracking. You can achieve small cylinders with Magic cards, but anything smaller than 1/4" is difficult. Magic cards are not recommended for tube making, unless the surface finish must be smooth as possible.
This post will be edited as necessary.
Sunday, July 12, 2009
Why No One Built a 1:1 Scale Sentry Gun
Only half a year, and I've figured out all the issues that anyone trying to make a 1:1 scale exact copy of the Team fortress 2 sentry gun would have. I would like to point out first that if you do for some reason decide to build a 1:1 scale model, you're going to enjoy all the problems I've had, but on a larger scale.
This is the TF2 sentry gun in its current repaired state. I've completed all six legs and corrected for the bending issue caused by the inherent design flaw of placing a massive weight on a thin moment arm.
Figure 1: A Force Analysis
Figure 2: Support arm
I still feel that the sentry gun's legs are ridiculous. The rear legs with the large circular feet are almost purely cosmetic. They cannot bear a load well, due to the fact that they are not bearing loads axially with the leg supports, but actually causing a bending moment around their attachment point. This causes a great potential for shearing at that region. The middle two legs are actually the most important legs of the 6. They bear the greatest load being near the base of the support column, and don't have a tendency to split away from the other legs like a ladder without the center folding bracket.
What of the sentry gun's front legs? They're slightly worse than the rear legs, since they are actually held onto the main column with pin supports that are actually not rigid in position. Their structural strength lies in the support struts connecting the base of the front legs to the bottom of the support column. I would advise anyone making a 1:1 scale model to put extra consideration into the strength of the strut brackets and to actually convert the pin connections at the top of the front legs to fixed joints.

Figure 1 illustrates the crux of the problem with the design. What looks aesthetically pleasing in the virtual world doesn't necessarily correlate to a practical design in reality. Left, we have the side profile of the sentry gun. The middle shows what the model essentially looks like from a force analysis: two "real" ground supports, one distributed load, and one concentrated load with a pivot at the intersection of both leg supports. The right shows the resulting problem: the rear assembly starts to deflect if the support isn't properly reinforced.
Figure 2 demonstrates all the key points of interest in making the arm that supports the ammunition housing for the sentry gun. Due to the angled shape of the arm, there are multiple points of interest where the builder will need to take into account material shear and deflection. The bottom pivot pin takes on a substantial lateral load and not much concern for axial loading. Threading a rod through a circular ring solves the problem of shear located where the pin meets the support arm.
At a small scale, there are not many ways to reinforce a series of thin rods connected to cylinders. I've resorted to Loc-tite glue to be a pseudo welding compound. Works fine, but for larger versions of this model, the rods would need to be solid components with the cylindrical sections. The right half of figure 2 illustrates the only method of corrective action taken to counter the lean: reinforcing the arm base with a wooden rod. The component in that region had begun to deteriorate and delaminate. The rod strengthened the region.
At a small scale, there are not many ways to reinforce a series of thin rods connected to cylinders. I've resorted to Loc-tite glue to be a pseudo welding compound. Works fine, but for larger versions of this model, the rods would need to be solid components with the cylindrical sections. The right half of figure 2 illustrates the only method of corrective action taken to counter the lean: reinforcing the arm base with a wooden rod. The component in that region had begun to deteriorate and delaminate. The rod strengthened the region.
Labels:
paper model,
reworked projects,
sentry gun,
structure,
Team Fortress 2
Saturday, June 27, 2009
Insights Into Magic Card Doll Making, Part 2
Welcome back to part 2 of documenting Lia.
Figure 1: Finished legs
Figure 2: Hip structure
Lia at this stage sported Rev. B hips. Rev. A was too loose and was enclosed so any maintenance was destructive. I eventually changed her design to Rev. C which sported an open socket system with the opening parallel to her hip connector, which allows me to pop the ball joint out easily for repair. The rods are made with a bamboo stick used for barbecues. Approximate diameter is 1/8". These were bought specifically for use for building Hotaru and have lasted me to this current date.
Lia at this stage has her hip completed.
Figure 4: End caps for limb joints
I used the cone frustum maker to build these caps. The washer for the screws are glued down to the card face, and the nut is expoxied onto the washer so I have a false permanent thread to anchor the screws in. This allows me to adjust the tightness of her joints and easily change components.
Figure 5: Completed torso.
The body gets a coating of printer paper and 110lb cardstock to get as best of a surface finish a piece of sandpaper can get. Which in this case, isn't much. Fortunately, Aelia doesn't suffer from surface defects like Lia and Hotaru due to a more aggressive sanding.
Figure 7: Foot construction, end stages
I changed the foot from an epoxied mess to a proper construction that could actually be painted. The foot is made of tubes stacked together until the form was present. After the tubes were secure, I coated the entire foot with 110lb cardstock, sanded it down, and cut out some toes.
Figure 10: Components ready for painting
Lia at this stage sported Rev. B hips. Rev. A was too loose and was enclosed so any maintenance was destructive. I eventually changed her design to Rev. C which sported an open socket system with the opening parallel to her hip connector, which allows me to pop the ball joint out easily for repair. The rods are made with a bamboo stick used for barbecues. Approximate diameter is 1/8". These were bought specifically for use for building Hotaru and have lasted me to this current date.
Lia at this stage has her hip completed.
I used the cone frustum maker to build these caps. The washer for the screws are glued down to the card face, and the nut is expoxied onto the washer so I have a false permanent thread to anchor the screws in. This allows me to adjust the tightness of her joints and easily change components.
The body gets a coating of printer paper and 110lb cardstock to get as best of a surface finish a piece of sandpaper can get. Which in this case, isn't much. Fortunately, Aelia doesn't suffer from surface defects like Lia and Hotaru due to a more aggressive sanding.
I changed the foot from an epoxied mess to a proper construction that could actually be painted. The foot is made of tubes stacked together until the form was present. After the tubes were secure, I coated the entire foot with 110lb cardstock, sanded it down, and cut out some toes.
This stage, the parts have been rounded out. I used the technique outlined here for making the twig-like limbs not so thin. Now, I have implemented a better system where I first add the tub reinforcements, cover them with a sheet of Magic card, then coat it with 110lb cardstock. I then cover the seams with printer paper, sand them smooth, then get them ready for paint.
The head was built using an out of date system that I've now abandoned in favor for a more sculpted process using a Dremel to carve out facial details. The previous method can be found here. I'm now using this process to make doll heads.
Hands were constructed in the same manner depicted here for Aelia.
The head was built using an out of date system that I've now abandoned in favor for a more sculpted process using a Dremel to carve out facial details. The previous method can be found here. I'm now using this process to make doll heads.
Hands were constructed in the same manner depicted here for Aelia.
Development log:
6/25/2007: Initiated building the development unit, based off an Obitsu ball jointed doll structure.
7/12/2007: Completed exterior build of development unit, Revision None.
7/27/2007: Hotaru officially completed.
9/13/2007: Hip design moved from hinge swivel joints to ball joints. Entered Revision A.
6/10/2008 to 6/15/2008: Lia built and completed. Entered Revision B. Feet and shoulders changed.
June 2008: Hotaru and Lia upgraded hip structure to Revision C.
2/28/2009: Aelia project initiated. Body enters Revision D. Changed shoulder joint and chest assembly for structural strength and reliability. Body shaped to resemble BBI proportions.
6/6/2009: Aelia project completed.
That wraps up two years of doll making. (Amazing that it's only been two years since I started. A lot has changed in skill level since then. ) I hope this has been insightful into the level of work needed to produce a doll made from Magic: the Gathering cards. I don't expect anyone to be able to replicate my work or even do close to what I do. I hope that by showing you this process, you can use this for ideas of how to build your own creations.
A lot of the building techniques used in building Hotaru and Lia were critical in the construction of the Team Fortress 2 related things. The sentry gun and Sasha would not exist if it weren't for those two.
6/25/2007: Initiated building the development unit, based off an Obitsu ball jointed doll structure.
7/12/2007: Completed exterior build of development unit, Revision None.
7/27/2007: Hotaru officially completed.
9/13/2007: Hip design moved from hinge swivel joints to ball joints. Entered Revision A.
6/10/2008 to 6/15/2008: Lia built and completed. Entered Revision B. Feet and shoulders changed.
June 2008: Hotaru and Lia upgraded hip structure to Revision C.
2/28/2009: Aelia project initiated. Body enters Revision D. Changed shoulder joint and chest assembly for structural strength and reliability. Body shaped to resemble BBI proportions.
6/6/2009: Aelia project completed.
That wraps up two years of doll making. (Amazing that it's only been two years since I started. A lot has changed in skill level since then. ) I hope this has been insightful into the level of work needed to produce a doll made from Magic: the Gathering cards. I don't expect anyone to be able to replicate my work or even do close to what I do. I hope that by showing you this process, you can use this for ideas of how to build your own creations.
A lot of the building techniques used in building Hotaru and Lia were critical in the construction of the Team Fortress 2 related things. The sentry gun and Sasha would not exist if it weren't for those two.
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