Oct 17, 2016

Kinematic Coupling Pen Fabrication

This is the Kinematic Coupling Pen! I'm showing the finished photo first, after three coats of walnut oil to bring out the cocobolo sheen. The metal bits are steel, and the pen cartridge is the same as the one in my brass pen

This completes my 2.750 Kinematic Coupling Lab, and here is my writeup for the class. The following blog post goes more into detail about fabrication and test setup, and is slightly more handwavey about analysis. It otherwise has the same info. 

Fabrication of the kinematic coupling started with steel round stock turned to a final outer diameter and a 6mm clearance hole for the pen cartridge. I bandsawed the shaft into halves after turning diameters to ensure they were a matched set, then faced them flat. 

Both the socket half and the grooved half used the indexing head on the mill to align features at 120deg angles. The 45deg V- grooves were made with a small endmill followed by a 90deg countersink (start with the endmill for stress-relief!), and the hemisphere sockets were made with a 1/8" ball-endmill.


I then turned some alignment offsets in both halves, but didn't really plan how I was going to cut my parts off the excess stock. Sloppy bandsawing and attempts at salvaging parts left my alignment offsets significantly shorter than I had hoped and my actual kinematic coupling (KC for now on) parts really dinged-up with tool marks.

I cleaned up by first press-fitting a 1/4" dowel into the 6mm hole, then gently filing away the tool marks by hand. This means the parts aren't perfectly circular anymore, but you wouldn't notice unless you spun them at high speeds. Kinematic coupling part of the lab now completed; moving on to the pen itself!

The wood phase of this project took place at the Hobby Shop, because I needed its wood lathe, dust collection system, and expert advice. 

Expert advice: Hayami is an awesome guy. I show up with a block of pain-in-the-ass wood, and he showed me everything I needed to complete my pen. He even set up an additional orientation period when I completely forgot to show up to the first one.

Dust collection system: Fun fact, cocobolo dust is super allergenic. You are highly likely to develop skin rashes from prolonged contact, and it's toxic if you breath it in. The wood itself is fine, but the dust is yikesy stuff. Hobby shop gave me a personal respirator mask, and I ran a vacuum at every machine station I touched. I'm pretty happy to say that I haven't developed an allergy to the stuff yet, because I still have plenty of pieces left.

But let's talk about the wood lathe. I was pretty happy to finish the actual kinematic coupling part early on, because then I had an excuse to spend lots of time (2 weeks) learning woodturning. My 2x4 scrap of cocobolo got bandsawed to two rough rectangular pen-blanks, then I found the rough centers and drilled a 1/4" through-hole.

The 1/4" through-hole served two purposes: one, I needed a through-hole for the pen cartridge; two, the Hobby Shop pen-turning kit consists of a 1/4" bolt and a thumb-nut that clamps the workpiece to the lathe.

The woodturning process has three parts. First, the pen blank is made cylindrical and roughly even using a scallop-shaped rough gouge. Then, a hemisphere-shaped gouge turns the proper outer diameter and shapes contours. Finally, a parting tool forms tongues for alignment with the pen tips and cuts my parts off the original stock.

After the wooden parts were done, it was back to MITERS for the steel pen-tips. The tapered front was made using similar methods as the brass pen, except this time I didn't bother dealing with cutting threads in steel. Drilling tiny through holes was bad enough (I broke 1 drill bit and 1 centerdrill in the process, but 3rd try is the charm!)

Once all the components were complete, they were glued together with 30min epoxy and brought to 2.750 show and tell the next day! Following that, I sanded all the components' edges flush and cleaned off all remaining epoxy residue. Officially finished!

Of course, there's still science to be done. I evaluated the kinematic-coupling part of the pen with two tests: a repeatability test and a stiffness measurement. In both cases, I wanted to better simulate a freely-waving pen solely held in place with magnets, which meant I had to avoid standard laser pointers (since I'd be doubling the weight of my pen!) My test setup consisted of a disassembled laser diode taped to the top of the pen in an attempt to add as little weight as possible.

     An aside about this laser diode - it's a really fantastic 400nm blue experimental laser diode
     Bayley let me borrow so that I can eventually make a shiny knurled case for it for science, 
     where the normal application is for something like ridiculously-specific X-ray equipment.
     But more importantly, the laser diode emits a very beautiful blue hue.

Given my contact surfaces of steel and neodymium alloy, I expected both high stiffness and high repeatability, so my test setups required magnifiying small errors over long distances - Abbe Error!

image credit: Matt Rosario

Basically Abbe error (sine error) takes advantage of magnifying angular error over distance to make observing tiny errors easier. In my case, that meant clamping my pen in the mill and observing laser pointer errors 24.5 feet away (giving me a magnification factor of 840:1)

I got an average error of 8μm, which was the expected order of magnitude for a steel-steel manually-machined object. I could have probably cut down on error if I had invested more effort than just taping the laser pointer on, or if I had been more careful machining the ball sockets in the kinematic coupling (one is noticeably shallower than the others)

Setting up laser diode for repeatability test

Laser pointer is blue dot in center of blue circle
For measuring stiffness, I used the same laser diode and attached it mostly parallel to the bisector of the magnet-triangle, and pointed it at a wall 15' away (528 magnification factor). Then I pushed on it perpendicularly with a force sensor (approx. 1N) and measured laser error on the wall.

I got an average deflection of 3.5μm after 5 trials, which resulted in a measured stiffness of 0.30 N/μm. This was twice the stiffness predicted from the kinematic coupling spreadsheet (0.14 N/μm), but is pretty close. Discrepancies could come from many sources, ranging from assumptions in the spreadsheet to again user error with the laser pointer, so it's unclear how closely my pen follows the theoretical model.

Finally, I've been doing some user testing over the past week. It writes! Unfortunately, due to the size of the kinematic coupling it has the ergonomics of an expo marker. The size of the pen threw me off initially but I got used to it eventually.

Additionally, the magnets used in this pen are not so strong that they perfectly resist my hand, so the back of the pen wobbles a bit if I write too quickly or squeeze the joint. This means my hand is located further down the pen than it normally would be when writing with an expo marker or a different pen.

I also experienced the fun thing where the tip of my pen cartridge is also steel and will therefore adhere to magnets, so I have to take care when removing the ink cartridges. The pen cartridge-tip gets press-fit in the pen, and the first time I tried pulling it out I accidentally separated the ink reservoir from the steel tip. Ink got everywhere! So, in order to remove ink cartridges I have to tap the pen-tip with the steel back of the pen.

A happy side-effect of the pen-tip getting press-fit within the pen is that the pen-tip stays put under normal writing conditions, even though there is space in the back of the pen. That means I don't need to make a cap for this pen, and can instead tap the writing-tip inside the pen-body if I want to store it in my bag.

Oct 13, 2016

2016 EC Rope Bridge Construction

East Campus has a long tradition of building large wooden structures and improving/ building off of previous years' large wooden structures. This past year, I set out to make a better way of building our rope bridges. This rope bridge project ended up being a small part of Elena's & my Clubhouse structure, itself a small part of the East Campus 2016 REX Fort. (she has a blog too!)

Photo credit: Wesley Lau

An issue we had with the 2015 East Campus rope bridges was that their nylon-webbing cables were directly tied to steel eyebolt anchors, and as the bridge bounced up and down the steel eyebolts would fray their cables. We had to conduct periodic maintenance on the rope bridge to replace cables that frayed too much. In addition, the bolts themselves would bend from the weight of the bridge and the people bouncing on it. It was impossible to observe the effects and extent of bolt bending until we removed the bolts during deconstruction, so I decided to devote my 2.671 (Measurement and Instrumentation class) experiment to bolt bending.

A short explanation of theory:
Pulling on a rope
Any amount of load present on a rope (including the rope's own weight) will cause the rope to sag. You can express what forces this rope imposes on its anchors with the equation
where each anchor supports half the load (vertical component) as well as opposing tension from the rope (horizontal component). The upwards force component applies a torque on the anchor scaled by the span of the bridge, 

When a person walks across the bridge, the load shifts from being mostly supported by one anchor, to being equally supported by both anchors, to being unequally supported again. 

Additionally, every time someone walks across a rope bridge, its anchors are yanked at an angle. So why does this matter for our steel anchors?

Turns out bolts really don't like being pulled at anchors. In fact, eyebolt strength drastically decreases the greater the angle becomes.
graphic from http://farmallcub.com/phpBB2/viewtopic.php?p=208393

It's actually rather terrifying. Below are the manufacturer specifications for the bolts used in the 2015 EC Fort, my 2.671 project, and the eventual 2016 Fort/Clubhouse.
Manufacturer specifications for decrease in strength with angular loads

Bolts are optimized for strength in the axial direction. If not loaded along their axis, they lose all mechanical advantage from compressing the substrates and instead become just a simple rod of "bolt steel". Thus when loads pull at extreme angles, you can expect bolt strength to drop to as low as 25% of their advertised strength.

Not only that, but if you pull on things long enough with enough force you can weaken them even more. The hope for this rope bridge was that we wouldn't keep it running long enough to run into this problem, and luckily we didn't! But fatigue concerns still gave us some panic.

Zhu, Y. "Fatigue Strength", Strength of Mechanical Components Course Notes
My 2.671 project focused on validating whether our bolts were in fact as compromised as the spec sheets suggested. If your rope yanks on an eyebolt at an angle, how will the bolt fail? How severe of an angle can you actually get away with?

I approached the problem by looking at stress-strain curves. For most materials, you need to put some amount of force into yanking on stuff for it to stretch. Both aluminum and nylon rope will behave like a spring - they will stretch linearly with force. But if you keep pulling with steadily increasing force, the material structure will get compromised and no longer behave like a spring (or return back to its original position!) For our rope bridge's sake, we treat this phenomenon as structural damage.

I fabricated a jig to anchor eyebolts 0°, 30°, and 45° offset from a vertical loop of webbing, and then conducted pulling experiments using the Instron machine. 

Rope and eyebolt-jig set to fix the bolt at a predetermined angle

Different kind of fixture to characterize the bolt without including rope

I made a rough, but functional angle jig from a block of hexagonal aluminum stock

You can see the point where applying steadily increasing force suddenly makes the bolt stretch more than usual. At this point the bolt is damaged. 

It turned out that while experimenting on bolts resulted in expected graphs, introducing another compliant object - rope bridge - produced weird graphs that were difficult to relate back to physics.

You can see the final paper here.

One thing was for sure - a rope bridge that didn't need to worry about angular loading was going to be a very nice bridge. Wesley introduced us to the idea of saddle joints - create a protrusion to move the location where the rope changes angles away from the eyebolt itself and on something more forgiving.

Critical design requirements of this saddle joint were to 1. ensure that the rope was in line with the eyebolt axis, 2. sustain high compressive forces without crushing its wooden frame, and 3. allow enough space to tie knots!

#2 in particular required a bunch of structural calculations. We also needed to calculate how much abuse our wooden towers could sustain in order to determine how many people could use the bridge at a time.

This particular saddlejoint used sch. 80 black steel pipe with a quarter-circle cut out. It sat ~1.75" above the wood, which provided enough vertical clearance to mount eyebolts and their washers. It just barely cleared enough horizontal space to allow knot tying and rope tensioning, which forced creative thinking when tying the bridge cables together. Future saddle joints should consider having more horizontal space.

As you can see in the video below, movement of the bridge is redirected by the saddle joint into just axial tension. Because the ropes do not rub against the eyebolt surface, we saw no visual damage even after a large dance party and subsequent week of near-constant use. Even better, this saddle joint performed ideally enough at allowing only angular displacement that we couldn't visually find any rope damage at all, which indicates very little allowed extension or side-side motion of the ropes.

The rope bridge itself consisted of two double-rope main cables of 4000-lb nylon webbing, woven through 2x6 foot planks. We relied heavily on Liz, Thomas, Maya, and SNP's ropes expertise to choose knots and provide the required amount of tension.

Polypropylene 3/8" rope strands were used for the railings. The upper hand railings consisted of three braided strands, in order to be thick enough to grab comfortably.

We had expected either the bolts or the rope to be the strength-limiting factor of the bridge, but in practice our bridge 2x8 spandrel was the weak link. With enough people (5 bouncing up and down) we saw the spandrel flexing. Future bridges would probably have better performance using a bridge spandrel consisting of two paired 2x8 beams bolted through the 4x4 columns and some 2x4 flexion bracing.

However, during operation we didn't have to actively limit the bridge occupancy at all. Our bridge was sufficiently creaky and scary-looking that rarely more than 4 people were on the bridge simultaneously, and no one tried to use it as a dance platform.

Photos of the completed rope bridge below!

Oct 5, 2016

Kayak at NY Maker Faire

Kayak has been on 
     - 1 ocean
          - 1 river
               - 1 lake
                    - 1 plane ride
                         - 1 road trip
and now, it has made an appearance at NY Maker Faire!

Without conducting any maintenance since the California adventure, I tossed the kayak bag into the trunk and joined MITERS in showing off our silly projects.

It still has the mussel-inspection tag from Santa Clara county!

Assembly took something along the order of 15-20min, where I was grateful I had made the frame assembly order non-critical (I couldn't remember whether I needed to build the front first or the back) Sometime soon I will need to switch to a longer-lasting pole marking method, and get a stainless replacement allen wrench.

Once I had the kayak set up, I could help assemble the rest of MITERS's booth. Most of our visitors fell into three categories:
     - People who like shiny metal objects and robots
     - Kids who wanted to drive the go kart
     - Old boat enthusiasts who were excited to see a non-3D-printed object / robot at Maker Faire

I'm glad my kayak did its part to entice tourists to talk to us!

Seeing MakerFaire for the first time was really cool, too. There was plenty of PowerWheels racing:

Also car-art, a la Mad Max:

A nice relaxing weekend of hanging out with MITERS:

And other silly projects. (I was puzzling for so long whether this violinist was controlling the hubwheel-skateboard with pitch or amplitude. Turns out there was another person behind her with the remote!)

But most notably a never-ending line of small children wanting to try out the go-kart. Some of them even considered building one after riding it!