Bonus Challenge: The Puzzle of Structural Stability

Because I had a little time on my hands after completing the Lego car, I decided to try one of the bonus challenges: namely, the indestructible box. In this challenge, I had to construct a box that contained two weighted Lego bricks and could be dropped from a height of two meters twice without breaking (and without any touch ups in between the drops).

It was harder than it sounded.

My first iteration was a catastrophe. I built a huge block of solid Legos between two green Lego bases. It did not even survive a two foot drop. There were Lego bits everywhere. The design, I realized, was fundamentally flawed. There was not enough cushioning to allow the box to 'give' when it hit the floor. Because the center was made of weighted bricks instead of regular ones, the entire structure hit the floor with more force than I expected. All the force of the contact was directly felt by the Lego pieces. My second iteration tried to combat this problem.

Iteration two used axles and joining pieces to construct a cage around  the Lego bricks. Every axle was connected together in semi-solid hexagon. The axles would bend slightly when they hit the floor, and this combined with the extra bracing around each axle might help absorb the impact and keep the structure together.

The first drop was a success.

The second one...

What Remains of Iteration Two

Not so much.

The problem was, after the first drop, several pieces came loose, and although it was not enough to break the structure, it was enough to jeopardize its stability. Thus, it was not sound enough to manage a second drop without some tweaks.

If I had more time, I would have braced the axles even more than I originally did. The axles worked to cushion the impact much more than plain Lego bricks ever could. I also might try using longer axles, which would bend more with the impact.

Lego Racer: The Puzzle of Gear Ratios

Torque and speed are two very different things. Mathematically speaking, they are inversely proportional when discussing gears and gear ratios. A gear ration is a mechanism that can provide a mechanical advantage depending on its arrangement. Certain gear ratios increase the torque of a machine, while others increase the speed.

For this project, my partner Katie and I were challenged to build a race car that could support a one kilogram cargo, travel a distance of four meters on carpeted floor and move relatively fast. That meant we would have to find a medium between torque and speed with our gear ratio.

We began by reviewing the Physics of gear ratios. When a single gear is attached to one of our provided motors, it can only have the same torque and speed values as the motor itself. The old Lego motor has decent speed, but absolutely no torque. We would have to find a gear combination that would allow our car to support itself, let alone carry a one kilogram mass!

If we wanted to increase the speed of the car, we would have to gear it up. Gearing up is when the gear attached to the motor is larger than the gear it touches tangentially. For every single turn the large gear makes, the smaller gear rotates several times, thus increasing it's velocity. However, there is a drawback. This arrangement increases the speed, but decreases the torque.

Conversely, if we wanted to increase the torque, we would have to invert the gear alignment and gear down our gear train. In this orientation, the smaller gear is attached to the motor and the larger one connects tangentially to it. The large gear rotates once for every couple of small gear rotations, thus increasing the torque and making it easier for the motor to turn the larger gear's axle. However, with this arrangement, the speed of the apparatus is lessened. On one end of the spectrum, there's high speed and on the other end there's high torque: we needed to find the happy medium in order to achieve the highest power. Power is the product of torque (t) and angular velocity (w):

P = (t)(w)  where t = |F||r|cosx (for gears, F = = Ftanx) and w = v/r, where v = velocity and r = radius, F = applied force, and x = the angle formed between the force and surface

For this project, we would be able to have complete control over the torque and radius of the wheels.

We started by just building a simple model first. Since this project was more iteration based than plan-and-execution based, we decided that beginning with a basic design and editing it was the way to go. We started by choosing a 8/40 gear tooth ratio (1/5) and added a chain to give our pieces more wiggle room, figuratively speaking. They we so close to other parts that they couldn't spin freely, so the chain helped give all the components extra space.

Experimenting with Gears

Experimenting with a Chain

We balanced our car on four wheels at first, with the Pico Cricket motor perched over the main moving axle.

Iteration 1

All seemed well...and then we turned it on...

Well...THAT isn't very stable. 

It was back to the drawing board. The car could move, but the frame was not well suited to support the Pico Cricket on the front (which is why it keeps bobbing above). The front of the car kept coming into contact with the ground. This excess friction between the car and floor would only hinder the car's ability to support the kilogram. Our first iteration had failed, so we started to work on our second.

Iteration 2

To balance the car, we adjusted the position of the Pico Cricket to be more centered over the three-wheel design and added a small 'cart' behind it on which to perch the kilogram. This helped to both keep the car stable and remove excess weight from it, as the cart would insure the only force the car would have to overcome is the friction between the cart's wheels and the floor (this force was dramatically increased when the kilogram weight was placed on it, but it was probably less than if the kilogram was directly on the car).

Iteration 2 From Above

Well, this time the car could move itself just fine, once the mass was added, it was like someone hit the breaks. The torque was not sufficient to counteract the force of the kilogram. Thus, we began to work on iteration three. This time, the gear train would be altered along with the frame in order to account for the kilogram.

Iteration 3

We lengthened the base and made it a four wheel frame. The Pico Cricket was placed back over the main axle and the art was altered so that it connected to the upper side of the back bar, thus preventing the kilogram from ripping it free from underneath.

As we began to work on our third model, Katie and I also decided to experiment with other frame options using the same gear ratio in order to save time. In addition, we wanted to experiment with the placement of the kilogram. I worked with attached carts while Katie worked with mounted platforms. We now had two cars in the pipes. 

Early Model A

Early Model B

In addition, we added another eight tooth and forty tooth gear pair to our gear train. Now the ration was (1/5)(1/5)

or 1/25

New Gear Ratio: 1/25

We were certain that with this combination, the car would easily handle the weighted cart behind it. 

We gave it a try.

SUCCESS!

We now had a car that could handle itself, the kilogram weight and the friction of the rug all in one. However, despite this initial triumph, there was a major setback. The frame of the car was extremely rickety. One wrong poke or touch could make it fall to pieces. We knew our gear ratio and design was solid, but now we needed to in case it in a strong frame.

However, we forgot one major aspect about a car frame...keep it light. After we added several pieces to our little, wobbly car, it ceased to move. Whoops. It could not even move itself, even when placed on the non-carpeted floor.

The Pieces We Put On And Then Took Off

We promptly REMOVED the extra pieces. The car may have been more stable, but if it couldn't move, stability was a moot point. 

Thus, we kept on editing. After our failed frame design, we decided to alter the entire car to be lighter, but sturdier. That meant careful placement of Legos to support one another, as well as the motor controller, motor and Pico Cricket. We fiddled with the structure for a while before we settled on one that suited our needs.

Iteration 3

We kept the four wheel plus a cart design, but striped the structure down to the main support beams. It was stable and sturdy. There was just one problem. It STILL couldn't pull the cart while the kilogram was on it. We had already removed all the excess parts we could. Removing any more would jeopardize the structural integrity of the car. Then, after reviewing an earlier design by Katie, we tried a new approach to the wheel design. To add more support the the back, we made the back axle supported by one center wheel and removed the cart entirely. The kilogram would rest on a platform directly centered between all three wheels.

Iteration 4

Now all we had to do was test it.

It worked.

Quite well.

Even against other teams in the preliminary race. It crossed the finish line in thirty seconds. However, once we changed the batteries for a new set, it covered the distance in 15.5 seconds.

In addition to the success of iteration 4, we had also created a second functioning car. After lengthening Model B and reorienting the wheels, Katie had created a fully functioning car that achieved all the project goals and could pull the kilogram quite nicely.

Model C

1/25 Gear Ratio, Like the Original Car

Test Drive

Preliminary Race

Katie's car ended up pulling the kilogram across the four meters in 19.5 seconds. 

We were very happy with our little cars and their performances. We were not expecting them to go as fast as they did, seeing as how we decided to lean farther on the torque side of the spectrum than the speed side. On iteration 4, changing the back axle orientation must have reduced the frictional force more than we expected, both on the car itself and between the car and the carpet. Model C was also extremely light and held the gears together snugly.

Race Day

Everything we had achieved had led us to this moment *dramatic music*.....

Iteration 4 raced first and beat its opponent, finishing with a final time of 15.6 seconds.

Model C was not quite as fast as its opponent, but it still finished with an impressive time of 17.7 seconds, beating its old record by more than a full two seconds!

Overall, Katie and I were very pleased with how our designs turned out. Both cars carried the kilogram mass and handled well on the carpet, with impressive scores. It we had more time, I would have liked to have made Model C more stable, as some parts of it were only held together with a single Lego. I bet we could also strip Iteration 4 down even more and make it even lighter. Perhaps if we had, it would have won. Finally, we ended up striving for the greatest torque possible, rather than searching for a medium between torque and speed. I would have liked to experiment more with the gears to see if there was a higher ratio we could have achieved, or one lower, that could have improved both our cars speeds. We had fun, though. However, unlike the movies, instead of a need for speed, we developed a need for torque.

VROOM VROOM!

SciBorgs Day One: The Puzzle of Feedback and Control

Today in class, we explored the mystery of feedback and control. There is a lot more to engineering than just visually seeing if a product works. Some products, like robots, use sensors and programs to interact with the environment and make decisions based on the data the sensors gather. Although today we only used a few sensors, like the touch and ultrasonic, other aspects of the robots, called SciBorgs in our case, can be minutely controlled, such as what motors turn when, how many times they turn, how much power each motor gets and so forth.

When it comes to feedback and control, we can get really specific with what we want our SciBorgs to do.

We Can Make a Light Flash and Change the Color!

Today, we started with the basics. For motion, we had to make our Borg move forward, backward, brake, spin-right, spin-left, bear right, and bear left.

To make it go forward , all we had to do was use the blocks talk to abc > move foreword for (10)

Backwards was [reverse > talk to abc > motor on for (10)]

Brakes were [talk to abc > motor on > chirp > motor off ]. We later changed this to [talk to abc > motor off]. The chirp and initial movement block were there so we could be sure it was the stop block that was making the movement end.

Spin right was [talk to a > this way > talk to b > that way > talk to abc > motor on for (10)]

Spin left was [talk to a > that way > talk to b > this way > talk to abc > motor on for (10)]

Bear right was [talk to a > set power (100) > talk to b > set power (90) > talk to abc > motor on for (10)]

Bear left was [talk to a > set power (90) > talk to b > set power (100) >talk to abc > motor on for (10)]

Experimenting with Code

Some of Our PicoBlocks Procedures

PicoBlocks Procedures

 Overall, our SciBorg worked very well in these initial tests and managed to complete all the tasks in an organized fashion. Next we moved on to shaft encoders. The encoders (thanks to lego) were built right into the motors. All we had to do was program them. Our challenge was to make the SciBorg go forward until counta reached 1000 and then to have it back up until counta was 0.

We coded [talk to abc > motor on > wait until counta = (1000) > motor off > wait (1) > talk to abc > reverse > motor on > wait until counta = (0) > talk to abc > motor off]

The wait (1) is a precautionary piece. If the SciBorg reverses direction too fast, it can cause the cricket board to fail. The lowest recommended wait time between direction reversals is .2 s, but we made it 1s, just to be safe. The Sciborg started and finished exactly where it began, going forward 1000 rotations, stopping, waiting, and then returning along the same path. The only discrepancy was that when it started, it had tendency to bear right. Fortunately, it maintained this tendency all along the path in both directions, so it did not alter the start and end points.

Countb Moving Forward Until It Reaches (1000)

 Next, we did the same procedure, but substituting countb in place of counta. There was not real noticeable difference between the two, except that when the SciBorg was running the countb version of the program, it traveled in a more straight line. Originally, we thought that an axle hanging out a little ways on the right side was the cause for the curved path, as it seemed to be rubbing up agains the right well, and therefore slowing it down. However, with the new program, the problem did not manifest. Maybe it is a problem with the counting inside of motor a, or perhaps the two shaft encoders are aligned differently. Aside from this, counta and countb were practically identical. 

Final Product of Code for Today

Sienko Lecture: The Puzzle of Hidden Variables.

Just because a product works and it's cheap doesn't mean it's the best it can be. Professor Sienko demonstrated this extremely well in her presentation. Through her experience, medical devices in poverty stricken countries often do not work as well as they should, through no fault of the design, but because they were not correctly designed to fit the cultural and ritualistic needs that were required of them. For example, medical devices sometimes do not take into account that there will not be anybody who knows how to repair them immediately available. Oftentimes, when a machine breaks, rather than trying to fix it, local hospitals and clinics will use it for other purposes, like blocking off a broken elevator.

There is more to a product than functionality and cost.

Professor Sienko's presentation focused on Design Ethnography. In addition to studying the basic needs and requirements of the people for whom she was designing the product, she also took into account the local customs, culture and social practices. Rather than working with just a group of engineers and designers, Professor Sienko also worked with the residents of the community to solve their problems. Her lecture focused mostly on the tricky process of traditional male circumcision in Uganda. The practice has been deep rooted in the local culture for generations, but has a 35% complication rate. If something was not done to change this deplorable figure, then traditional male circumcision may have been outlawed and performed solely in clinics. For me, it was concerning that something hadn't been done earlier, but neither side was willing to compromise. Circumcision reduced the risk of cervical cancer, and even the spread of HIV, so from a medical standpoint it is extremely important. On the other hand, performing it the traditional way is a right of passage for the young men of Uganda, and to have it performed in a clinic would be culturally demeaning. I was not surprised by the conflicting ideas, but I was shocked that compromise was not an option earlier on.

Professor Sienko was the one who composed the compromise.

The basic design of her product was intuitive and drew upon the community's local knowledge of how condoms work. meaning that no instruction manual would be needed and non-experienced personnel could operate it. I was surprised by how easily the man of her focus group figured out the products purpose. More shocking to me, however, was the lack of information Professor Sienko had to begin the process. There was virtually no documented information about traditional male circumcision. She and her partners had to travel to various villages and collect the data themselves. The data included number of practicing cutters, speed of cut, and size. Once they had gathered their data, they had to edit their design to accommodate it. For example, medically it takes around 120 seconds to perform the cut. Traditionally, it takes about 10. The product had to be designed with speed in mind.

Professor Sienko's lecture dug deeper into the consumer/product relationship than I had ever thought about. I used to think that all a product needed to be was functional and cheap. However, functional and cheap describes clinical circumcision processes. In reality, the requirements go far beyond this into the realm of the human psychosis. From now on, I will try to think about a product in terms of its design, functionality, cost and cultural relevance.

Mechanisms: The Puzzle of Rotational to Linear(ish) Motion

In the world of Physics and engineering, there are certain mechanisms that can be very useful when it comes to the transformation of different types of motion. Motion along a straight line can be transformed into angular motion, and vice versa. After reviewing the various provided sources about mechanisms that convert rotational motion into linear motion, one mechanism in particular stood out to me: the elliptical gear pair.

Image from http://kmoddl.library.cornell.edu/model.php?m=689

The elliptical gear works by transforming steady axis motion into non-steady axis motion on an adjacent gear. In the above picture, the elliptical shape of the gears themselves is what enables this transformation. The gears can actually change the rate at which they spin depending on where they are in contact with each other. The ability to alter the rate of rotation was very intriguing to me, as it opened up all sorts of timing possibilities for different products. For example, if someone wanted a cranked door to open in a given amount of time, they could use an elliptical gear pair and save the material it would take to make a large, circular gear to achieve the same time difference. 

This variation in speed, as well as position of the gears, makes them extremely versatile. Elliptical gears have contributed to various flow rates in pumps and flowmeters. * The fixed points in an elliptical pair is constant, and as a result, the speed varies to keep this distance between the points equal at all orientations.

Image from http://www.cunningham-ind.com/ellipt.htm

The gears do not have to be the same size (or same shape, though that's an entirely different category of mechanisms) for this to work. Despite their oblong appearance, elliptical gears will rotate about their foci ('center') in a manner that allows them to stay in contact and their foci to be equidistant to each other in all orientations.

Speed variation in elliptical gear pair

This change in orientation to maintain the distance caused the speed variations along the edge of the gears, modeled here. It can range from as high as K to as low as 1/K, where K is the maximum gear ration possible based on the size of the gears. *












*for more information, see http://www.cunningham-ind.com/ellipt.htm

Well Windlass: The Puzzle of Retrieving Water

The Puzzle of the Well Windlass...

For those who do not know, a well windlass is a mechanism used to crank a bucket out of a well instead of pulling the rope up manually. This makes it easier for the operator to retrieve more water with less effort.

Image from http://upload.wikimedia.org/wikipedia/commons/1/1e/Ramelli_windlass_well.jpg

For this project, my partner Christina and I were challenged to construct our own well windlass while simultaneously applying our new knowledge of fastening and attaching as well as our previous experience with cantilevers and beams. The deflection equation,

(F(L^3))/(3EI)

Where F = the applied force, L = the length of the lever, E = Young's Modulus (or the ratio of stress to strain aka stiffness) and I = the moment of inertia (the lever's stiffness of its cross sectional area). In addition, we were given specifications that we had to work within in order for our windlass to be considered successful:

1.) We only had 500^2 cm of Delrin, 50cm of Delrin rod and 120 cm of string to use
2.) Our windlass had to span a gap of 12 cm and be able to lift the top 10cm of the bottle above the gap
3.) The windlass had to support the load of a 1 liter bottle of water without wobbling or breaking
4.) The crank to wind up the string could not be over the gap

Needless to say, this was a bit more of a challenge than the bottle opener...


We started by brainstorming. The Delrin rod was too flimsy to support the water bottle on its own, so we decided to support the entire windlass with two large bases connected at intervals by cut pieces of rod. The shorter the rod was, the less it bent. This was due to the lever arm length affecting the applied torque. Once we shortened the arm, we lessened the torque and made the rod more effective.

Not the sturdiest of rods...

We wanted something that would utilize the strength of the Delrin sheets...

 But that would also carry the string away from the gap, like a crank and pulley system...

 Additionally, it had to account for all the forces applied to it, such as gravity, tension, and friction. It had to have wide 'feet' to keep it well balanced...

Finally, the pulleys and crank had to be easy to use and apply, and since we could only cut out pieces, the pulleys had to consist of one small circle between two large ones.

This design would utilize the strengths of both the rod and the 3/16 in Delrin: the Delrin would act as a support while the rods transferred the string away from over the gap to the crank. The pulleys would help take some of the force from the bottle off the crank and make it easier to turn. Additionally, they would also be able to spin freely if the friction between the them and the string proved too great once the bottle was lifted.

Without extra support, the two connected bases would have been unstable and probably fallen over if the right force was applied in the wrong way. We designed two identical feet and fit them to the bottom of the bases on either side of the gap. We used press fits for their simplicity and so that we could disassemble the product if we needed to once more parts were cut and ready to be connected.

After our brainstorming session, we made a foam demo of our model...

Once we were happy with our design, we began to build the various pieces into Solidworks. Whereas the bottle opener only required on part file, the windlass was made of several different pieces, and required multiple.  It was tricky keeping our files organized, both on the desktop and within the group Dropbox file. We eventually resorted to naming our files by our first names to help differentiate them.

The stabilizing foot

The loose and tight bushing

The pulley pieces

The base 

Partway through designing the various pieces, we realized that the Delrin rod would never work as a sufficient crank and spindle for the rope. The rod was circular, with no distinguishing features that could give the rope the friction it would need to wind around it.

Well, THAT'S not going to hold it...

We had to pause and redesign a crank and spindle that would work for us, using Delrin sheet.

The second crank iteration

Eventually, we came up with the idea to use Delrin in place of the third pulley. The Delrin would be rectangular in shape with two smaller rectangles erupting from its ends. A hole through its center would allow the rope to be fastened tightly to it, and therefore provide the force needed to keep it in place. The  small extremities would be filed down to fit into circular holes. This would also make it easier for them to spin. Finally, using a press fit, the handle would be attached. We measured to make sure it would not be so long that it would touch the ground on each turn.

Besides the crank and handle, several other pieces underwent mild modifications in Solidworks (see above pictures). The bases went from a multi-part design, to two single arches with an area for the crank. This edit saved material and helped make the windlass more sturdy. The arch design strengthened the bridge over the gap, ensuring that the water bottle would not break it once the crank began to lift the bottle.

Before we sent our files to the laser cutter, we practiced making our own bushings and press fits to ensure that our pieces would fit together perfectly. Otherwise, we might have ended up wasting a lot of material.

Our final design began to fall into place. Our bushing and press fit measurements were spot on, thanks to the margin of error information we learned during our fastening and attaching session (see fastening and attaching post). We knew that any piece that needed to fit tightly would have to either have a .5 mm added/subtracted from it in order to actually fit snuggly.

It was time to start cutting.

The initial cut went very well, but we ended up having to re-cut several bushings and parts to the handle for size reasons. The handle's notches did not reach far enough to create successful press fits and several of the tight bushings ended up being more loose than expected and did not keep the pulleys pressed tight enough.

Otherwise, we were very frugal with our material and wasted very little.

Once all the pieces were cut, we began to assemble our 2D parts into a 3D windlass. All the press fits and bushing worked perfectly.

Using only 5 inch of the provided Delrin rod, we assembled our two pulleys, attached the string, placed it over the gap....and did our official (and probably only, given how little time we had left) test run.

Our presentation run (not the test run, but they are essentially the same)

We were pretty satisfied with our results...

The windlass worked better than expected. The pulleys kept the string aligned with the crank. The crank was easy to turn and never let the rope slip. The base remained mostly stationary and easily lifted and supported the weight of the bottle thanks to the double overhanging beam design, along with the arched sharp, which maximized its strength against the bottle by minimizing the affects of the two beam's moment of inertia. We could not control lever length, as the beams had to be a minimum of 12cm to span the gap, but we could control how well supported the two beams were, and made sure they would be strong enough to complete their task. All in all, we were two very happy engineers.

Side view with bottle

Looking through it

Long shot

Crank handle

Crank handle and spindle

Feet and base

Top view of pulleys

As a final edit, we connect the handle and the piece that attached it to the spindle with a heat stake, to ensure no amount of force could cause it to fall off mid-crank. Aside from this connection, the entire windlass can be disassembled into a neat, easy to transport pile.

In total, we used 12.7 cm of rod and 273.12 cm^2 of sheet.....well under our limit for the Delin. 

We had to use all of the 120cm of provided string, though, as the distance from the crank over the pulleys and down to the bottle lid barely left enough string to attach it securely. There was no way to adjust for this, so we used all of it. Because we kept our shapes basic, calculating the total Delrin used was simple. We used basic geometry equation, like the areas of a circle triangle. Our specific calculations and estimations can be seen below.

Geometry calculations

Geometry calculations, again

Even though our product worked extremely well, if we had enough time, there are still a few edits we would like to make. While we cranked the base moved slightly due to the force acting on the handle. If we could re cut the two base walls, we would add hooks to go over the lip of the gap on either side to make the windlass more stable and secure. Additionally, we would also make the spindle more like the pulleys, with a small gap in between two large buffers, so that the sting could not slip off it and become lodged between the spindle and the wall. This made the crank slightly harder to operate. As an extra edit, we could probably honeycomb our two bases, and thus use even less of the material we were given, but we did not want to compromise the strength of the bases, since they were supporting the brunt of the applied forces.

The demo and final product

I guess I won't have to lift my textbooks from my bag to my desk anymore.....assuming a one liter bottle weighs about the same as a Physics book.