Pen-Dragon Mechanical Fractal-Drawing Device, version 2

[Splat]

This is an amazing model, very mesmerizing to watch, and creates beautiful mathematical artwork. Great job

[aeh5040]

Ldraw instructions are now available! The file is here. Obviously, it is quite a challenging build.

In the process of creating it I tried to rationalize the construction in a few places, so it is not identical to the model in the video. (Hopefully it is better.)

I would of course appreciate any feedback on the file. I expect there will be a few errors.

Edit: I have corrected the positions of the cams in the file and the picture below.

Edited July 24, 2015 by aeh5040

[Blakbird]

Yes, that looks challenging all right. I like a good challenge. I'll go through the file and see if I can make it any more "buildable".

One difference I note in the file is the tires. The file has the knobby tires because I think the smooth versions are not in LDraw.

Some of the lift cranks use cams, and others use 1x3 thin liftarms. Why the difference?

[aeh5040]

Yes, that looks challenging all right. I like a good challenge. I'll go through the file and see if I can make it any more "buildable".

One difference I note in the file is the tires. The file has the knobby tires because I think the smooth versions are not in LDraw.

Some of the lift cranks use cams, and others use 1x3 thin liftarms. Why the difference?

Nothing escapes Blakbird's eagle eye, I see :) I did indeed use

Tire 81.6 x 14.2 Motorcycle Z Racing Tread

in the model, because I had a suspicion it might make it more accurate. This tire is quite rare and not available in LDraw.

I'm pretty sure it will work fine with the knobbly one, as the size is very very close and the knobs probably have no effect, but it's possible the smooth one is slightly better!

Regarding the cams, there is a reason for it, although again it is probably unnecessary. As you go along to the later Geneva mechanisms, the torque becomes less, but the need for precise actuation also becomes less, because the later mechansims advance very quickly for a small turn of the first one. Early on, you want a "sharp" cam so that the actuation happens at a predictable point; later you want a "blunt" one, so that it requires less torque to lift the rocker beam. Hence I used the 1x3 lift arms for the first two, then the "sharp end" of the cam for the middle two, then the "blunt end" for the last two. Again, I was probably being overly cautious, and it would likely work with any arrangement, but I was trying to throw everything I could at making it work well (and this was more necessary in earlier versions that had other issues).

Edited July 21, 2015 by aeh5040

[aeh5040]

For anyone who wants to try their hand at making this (perhaps Blakbird is the only one crazy enough!), one issue is that the pen needs to be shorter than typical pens, otherwise it will obstruct the Geneva mechanisms. The ones that I used are called Crayola Pipsqueaks. They are readily available in toy stores, at least in the USA. They are water soluble (useful in case of accidents) and the right size - the pen holder in the model in designed to accommodate their thickness. For the video, I cut the point of the pen a little with scissors to make it blunter, and get a thicker line.

Edited July 21, 2015 by aeh5040

[skppo]

Have you tried running it with the pen attached in a "wrong" place? I wonder how the pattern would change with such offset.

[aeh5040]

Have you tried running it with the pen attached in a "wrong" place? I wonder how the pattern would change with such offset.

That's a great idea! It might produce some interesting effects...

[BachAddict]

That's a great idea! It might produce some interesting effects...

It would make all of one direction of curve larger and all of the other curve smaller or even negative, right?

On another note, are you going to submit this to Rebrickable? If not, would you give permission for someone else to do it?

[aeh5040]

It would make all of one direction of curve larger and all of the other curve smaller or even negative, right?

That's right, if the pen is off-center in the left-right direction. But it could also be off-center in the forward-backward direction, which would give a different effect.

On another note, are you going to submit this to Rebrickable? If not, would you give permission for someone else to do it?

Yes. I'd like to see how Blakbird and others get on with the file first.

[Blakbird]

As I am wont to do, I have dissected the file and simplified it by removing all the structure and leaving all the moving parts. In the case of this model, it looks almost the same with only the functional parts included. Then I separated the functions into logical groups and color coded them. The results are shown below. This helps a lot in understanding how everything works. The more I look at it, the more I understand and the more impressed I am. In the future, I will step through each of the colored functions and explain how I think they work.

The phrases "Geneva Mechanism", "Scotch Yoke", and "Tomy Armatron" are all mentioned in the description, but it may not be at all obvious to many how those things work or how they work together to achieve the desired result.

[aeh5040]

As I am wont to do, I have dissected the file and simplified it by removing all the structure and leaving all the moving parts. In the case of this model, it looks almost the same with only the functional parts included. Then I separated the functions into logical groups and color coded them. The results are shown below. This helps a lot in understanding how everything works

Nice!!! Thanks for doing this - it looks great! I actually started trying to do the same thing myself, but it got way too tedious trying to select the right parts in MLCad. How exactly did you go about doing it, may I ask?

A couple of minor points to consider about the coloring:

1. You might want to make the 3 little linkage parts on each side that connect the top half to the bottom half either yellow or gray, or even just make these and the yellow and gray all one color - they move together and are essentially part of the same mechanism.

2. The light blue gear trains on the bottom could do with splitting up into several colors. There is the part from the Armatron that goes over the top of the wheels and into the add-subtract mechanism, and then there is the part from the add-sub to the wheels. These deserve two different colors, as they perform different functions, related by a linear transformation performed by the add-sub (comprising the two differentials). Perhaps the add-sub mechanism itself should be a third color.

In the future, I will step through each of the colored functions and explain how I think they work.

The phrases "Geneva Mechanism", "Scotch Yoke", and "Tomy Armatron" are all mentioned in the description, but it may not be at all obvious to many how those things work or how they work together to achieve the desired result.

Quite so! I suspect your explanations will be clearer then anything I could produce, and of course I'm happy to help with any issues...

Edited July 22, 2015 by aeh5040

[Blakbird]

Nice!!! Thanks for doing this - it looks great! I actually started trying to do the same thing myself, but it got way too tedious trying to select the right parts in MLCad. How exactly did you go about doing it, may I ask?

No special tricks, just patience and a lot of practice. I start by inling the whole thing with MPD Center, then I create a blank submodel for each function and just cut-paste parts into them from the top level. Of course, I can't do any of that without first understanding which parts move with which other parts, and that can take quite a while if I've never built the model.

A couple of minor points to consider about the coloring:

I thought about all that coloring stuff. The pictures I have posted so far are just an attempt to use colors to group the functions, not the explain everything. If I tried to do that all in one image, there would be too many colors and it would actually be harder to follow instead of clearer. As I go through each individual function, I'll add more colors to explain the details of that function. I hope that makes sense. I did the same thing with my review of Akiyuki's ball factory.

[Blakbird]

The model is split into two main modules: top and bottom.

The bottom contains the motor, the drive system, and the pen. It waits for a command and then executes either a right or left turn.

The top is the brain and controls the logic of the model. It's input is a rotating axle from the motor, and it's output are two links which command either a left or a right turn. So the whole function of the top is to determine whether a left or right turn should come next, and then to command it at the appropriate time. Let's take a closer look at the top.

In green we see the input gearing which is powered by the motor. In orange and purple we see the Geneva mechanisms. In blue we see the cams which drive the yellow rockers. Let's start with the input:

The blue axle comes from the motor and drives a worm gear. This provides for a large 1 stage reduction and also prevents any backdriving. There are 4 stages of gearing here: blue-red = 8:1, red-yellow = 1.67:1, yellow-green = 3:1, green-orange = 5:1. Overall ratio is therefore 200:1. This means there is LOTS of torque available to drive the Geneva mechanisms, and that's important because they are not as efficient as gears.

The orange gear drives the first Geneva mechanism. There are a total of 5 Geneva mechanisms in series. Let's take a closer look at them:

A Geneva mechanism is like a gear system in that there is a rotating input which drives a rotating output. However it is different than a gear system in that the rotation of the output is intermittent. In this case, the purple assembly is the driver and the orange assembly is the follower or wheel. As can be seen in the animation, each revolution of the driver rotates the follower 180 degrees, so it is something like a 2:1 reduction. However, the follower stops at a 45 degree angle and then waits for input before rotating 90 degrees to the next stopping point. The 2x2 macaroni piece serves to hold the follower in place during the portion of the cycle when it should be stopped.

The Geneva mechanisms are arranged in series with the output of each driving the input of the next. Each is connected to a pair of cams shown in blue.

Each cam pair is clocked so that they face opposite directions. This is important because you don't want to command both a left and right turn at the same time. As Alexander previously explained, the cams are shaped differently to provide sharper lift in the early stages and more gradual lift in the later stages. The very last cam (shown upper left) is different than the others. The others are designed to lift only for about 1/4 of their rotation, but the last is designed to lift for 3/4 of a rotation.

So what's the point of all these cams, intermittendly commanded by Geneva mechanisms? The cams serve to lift the rockers, shown in yellow.

There are two rockers, one for a left turn command and one for a right turn command. ANY of the cams on a given side can command a turn by lifting the rocker. The cams bear against 2x2 round rollers to minimize friction.

After going through the logic of the top assembly, but without the benefit of having actually built it yet, I find myself wondering about a few things:

• What drives the need for the Geneva mechanisms? What if you just used 2:1 gearing at each stage instead? I think the problem would be that all the cams would be moving all the time, and this would make for duplicate commands. The model needs to sit still while waiting for the next command. This leads me to the next question:
• Is there ever a time when more than one cam is commanding a turn at the same time? For example, could two cams on the left side both be pointing up? It seems like this would be inevitable.
• Is there evere a time when a right and left turn are commanded simultaneously? The last 3/4 turn cam leads to believe that this must happen while it is engaged. What is the effect of this?
• Why was it important that the Geneva wheel stop at a 45 degree angle instead of a 90 degree angle? Is this because Technic axles are cruciform and you don't want a cam "up" and commanding a turn when a wheel is stopped?

I think it would be quite interesting to watch an animation or video of the top assembly alone running at high speed, perhaps with the 40 tooth gear as direct input. There is a snippet of this in the main video, but it is not long enough to see the motion drive all the cams. Sadly, such an animation is more complicated than I have the time to simulate manually.

[aeh5040]

Awesome work so far, Blakbird.

Overall ratio is therefore 200:1. This means there is LOTS of torque available to drive the Geneva mechanisms, and that's important because they are not as efficient as gears.

Actually, the Geneva mechanisms move quite easily, so there is not so much need for torque here. (The locomotion requirements of the lower module are what prove to be the limiting factor in terms of torque). Much more important here is that the Geneva wheels turn slowly enough that the lower module has time to do a complete operation between "instructions" from the upper "brain".

That said, the Geneva mechanisms ironically involve some gearing UP - in your lovely animation, you can see that the orange wheel actually moves faster than the purple one, at its moment of maximum speed. Consequently, the last few Geneva wheels provide very low torque, no matter how hard you push the first one. Therefore, all moving parts of the brain layer need to be very light, loose, and low friction. (Thus: the round rollers, and the counterbalances on the rockers). And the lower layer will need to do a lot of "signal amplification" to do its job properly...

After going through the logic of the top assembly, but without the benefit of having actually built it yet, I find myself wondering about a few things:

• What drives the need for the Geneva mechanisms? What if you just used 2:1 gearing at each stage instead? I think the problem would be that all the cams would be moving all the time, and this would make for duplicate commands. The model needs to sit still while waiting for the next command. This leads me to the next question:
  

No, 2:1 gearing would not work at all. Think about the last axle - it is turning at an average speed of (maybe) 1 turn every 30 minutes. If it did so at a uniform speed, as would happen with gearing, then it would hold a rocker in the up position for maybe 5 minutes at a stretch, and furthermore the precise time interval would be very unpredictable. Throughout that time, the bottom would be receiving constant instructions to turn. We don't want that!

• Is there ever a time when more than one cam is commanding a turn at the same time? For example, could two cams on the left side both be pointing up? It seems like this would be inevitable.
  

No, there is not. The "rest position" for all the axles is with the cams at 45 degrees to the vertical. Because the cams line up with the 2 pegs of the peg wheel, whenever an axle advances from one 45 degree position to the next, it either actuates one of the rockers itself, or it advances the next axle (but not both).

• Is there evere a time when a right and left turn are commanded simultaneously? The last 3/4 turn cam leads to believe that this must happen while it is engaged. What is the effect of this?
  

Again, no, there is not. (If there was, it would result in the machine moving straight ahead for a step). The effect of the last special cam is that whenever this last axle would cause the next axle to advance (if there was a next one), we instead get a right turn. (The last cam does not just provide lift 3/4 of the time - it provides 3 separate lifts, with gaps between them.) This is what causes the curve to join up and form a twin dragon.

• Why was it important that the Geneva wheel stop at a 45 degree angle instead of a 90 degree angle? Is this because Technic axles are cruciform and you don't want a cam "up" and commanding a turn when a wheel is stopped?
  

It's nothing to do with the shape of technic axles specifically (except in combination with the shape of the cams), but your second explanation is essentially correct.

I think it would be quite interesting to watch an animation or video of the top assembly alone running at high speed, perhaps with the 40 tooth gear as direct input. There is a snippet of this in the main video, but it is not long enough to see the motion drive all the cams. Sadly, such an animation is more complicated than I have the time to simulate manually.

Good idea, I'll try to set this up at the weekend (with the real model). In the mean time, perhaps this picture will help. Each row on the right is an illustration of the cams viewed from the left side of the vehicle (with the triple cam at the end), at a point in time between steps. From each row to the next, the first axle advances 90 degrees clockwise, perhaps causing some others to advance. The little red vertical line shows that exactly one axle actuates a rocker at this step. It will be the left side rocker if the cam moved across the top, or the right side rocker if it moved across the bottom. This corresponds to a right or left turn respectively, and you can see the corresponding place in the dragon curve.

Edited July 23, 2015 by aeh5040

[afol1969]

At first:

Again a masterpiece of technic MOC! I have made it on my build list I wonder how much experience it needs to build models like this.....a Fractal Drawing Device!

@Blakbird: You're really talented to document very complex models, it makes a lot easier to understand the functions, which is necessary to build the model.

Hope I'll find the time to build it in further time.

Greetings

Alex

[Captainowie]

I'm also really enjoying the back-and-forth between Blakbird and aeh5040 - by the end of it we'll have a pretty comprehensive record of exactly how this marvelous machine does what it does.

[aeh5040]

I'm also really enjoying the back-and-forth between Blakbird and aeh5040 - by the end of it we'll have a pretty comprehensive record of exactly how this marvelous machine does what it does.

Thanks for saying that! I was worried most people might be getting bored...

[mahjqa]

Absolutely not getting bored. Reading this with the utmost fascination.

[Blakbird]

Actually, the Geneva mechanisms move quite easily, so there is not so much need for torque here. (The locomotion requirements of the lower module are what prove to be the limiting factor in terms of torque). Much more important here is that the Geneva wheels turn slowly enough that the lower module has time to do a complete operation between "instructions" from the upper "brain".

I had wondered about the timing aspect. So the brain needs to run slowly just so it doesn't issue commands faster than the mechanical part can execute them. And the Geneva wheels are necessary so that the commands are discreet and never overlap eachother.

Again, no, there is not. (If there was, it would result in the machine moving straight ahead for a step). The effect of the last special cam is that whenever this last axle would cause the next axle to advance (if there was a next one), we instead get a right turn. (The last cam does not just provide lift 3/4 of the time - it provides 3 separate lifts, with gaps between them.) This is what causes the curve to join up and form a twin dragon.

I see. I was thinking that the last cam resulted in a continuous 3/4 turn actuation, but it must actually be 3 discreet actuations (the three 2x2 plate stacks).

In the mean time, perhaps this picture will help. Each row on the right is an illustration of the cams viewed from the left side of the vehicle (with the triple cam at the end), at a point in time between steps. From each row to the next, the first axle advances 90 degrees clockwise, perhaps causing some others to advance. The little red vertical line shows that exactly one axle actuates a rocker at this step. It will be the left side rocker if the cam moved across the top, or the right side rocker if it moved across the bottom. This corresponds to a right or left turn respectively, and you can see the corresponding place in the dragon curve.

Thanks for the diagram; I was actually going to ask if you had something like this. For example, when you start a new drawing it is important to know where you can set the model to get a result that will fit. That requires a knowledge of where the current state of the machine lies on the final curve. Do you always set the machine to a particular state before starting a drawing? The state shown in the LDraw file (with all the Geneva mechanisms horizontal) can actually never happen in normal operation.

[Blakbird]

Time to talk about the lower half of the model: the power and drive system. Although my initial focus was on the Geneva mechanisms on the top, now I think the bottom is even more interesting.

The motor input is shown in green, the "switches" in dark tan, the "Tomy armatron mechanism" in red, the Scotch yokes in tan, the transmission in turquoise, and the output to the wheels in white. Let's start with the easy part, the input gearing.

The central horizontal axle is the input from the Power Functions L motor. The bevel gears go up to the vertical axle and up to the brain. The additional 1.67 ratio here means that the total ratio between the motor and the Geneva mechanisms is 333:1. The lateral horizontal axle powers the "Tomy armatron mechanisms", my favorite part of the model. The 20 tooth double bevel gear is an idler and doesn't change the ratio. The drive axles are turning at all times when the machine power is turned on.

The "Tomy armatron mechanism" converts commands from the brain into a fixed number of rotations of the output wheels and then stops. How does it do that? It's really hard to explain so I spent all day yesterday making some animations which make it much clearer. (The green axle and gears in the animation should really be moving, but that was too much work to do manually and wouldn't work at this frame rate anyway.)

The red assembly serves as a clutch of sorts, engaging and disengaging itself from the downstream components. The green drive axle runs through the middle driving a 16 tooth spur gear. This in turn drives the two dark gray idler gears. When this mechanism is held in the starting position by the dark tan cam stop, the idler gears are not attached to anything and just spin. One of the two idler gears spins almost frictionlessly on an axle, but the second is mounted on a friction pin shown in yellow. This friction causes drag which tends to make the entire assembly want to rotate. When the dark tan stop is released by the brain, the red mechanism is free to rotate. It spins 1/4 turn and then stops against the tan slider. In this position, one of the 16 tooth idler gears is connected to the transmission and drives the wheels. In parallel, the tan slider is also powered and starts to translate. When the slider moves a certain amount, the red assembly is again free to rotate another 1/4 turn. It keeps driving as the second idler gear engages. When the tan slider oscillates back to its starting position, the red assembly is again released to rotate 1/2 turn back to its starting position to stop against the dark tan cam.

I've given some thought as to why the yellow idler gear support is a 3L axle pin instead of a regular 3L pin. Axle pins are made of a softer plastic than regular pins, so my suspicion is that this was chosen to achieve a particular amount of drag.

So what makes that tan slider oscillate? A Scotch Yoke!

When the "Tomy armatron mechanism" is driven, it in turn drives the Scotch yoke. The Scotch yoke controls the motion of the "Tomy armatron mechanism", so the system forms a feebdack loop. The animation shows how a 1 revolution rotation of the red axle produces one oscillation of the tan slider and therefore one drive cycle of the "Tomy armatron mechanism".

The whole point of all of this is to drive the wheels a particular amount, so let's look at how this attaches to the transmission:

At start, the whole transmission is in neutral because nothing is connected to it. To be more precise, any rotation of the wheels is locked by the worm gears. The yellow gears are driven by the "Tomy armatron mechanism" when engaged. They drive the blue mechanisms through the worm gears which power the Scotch yokes. The orange axles power the right wheel drive system and the red axles the left. In both cases they drive the ring gear of a differential. Let's look at the left side. The red gears drive the ring gear of the tan differential. Since the orange gears are locked by the worm gear, the opposite white differential ring gear cannot rotate. The white and tan differential outputs are linked together. Since the white gears cannot rotate, one of the tan diff outputs (the white one) cannot rotate. This causes the output to be driven to the turquoise at 2x speed and then out to the left wheel. The right hand wheel also moves in the opposite direction, but instead of the ring gear being driven the tan spider gear is driven. This means the torque goes straight through to the purple output to the right wheel but at half the speed.

The gear ratios are extremely important here not just for torque, but because the output must have a very precise number of rotations in order for the drawing to work. Let's trace the gears to a wheel and see how it comes out. The yellow gears could be any ratio that provides enough power from the motor. One "cycle" is defined by one brain command which results in one trip of the dark tan stop, one rotation of the "Tomy armatron mechanism", and one oscillation of the scotch yoke. Therefore we can use one rotation of the blue gear as the definition of a cycle. Blue-red stage = 3:1. Red gear to diff ring gear = 1:1. Diff ouput = 2:1. Turquoise 1st stage = 1:3. Turquoise second stage = 1:1. Final stage to wheel 36 tooth gear = 1:3. So total for the left hand side is 2:3. This means that the left hand wheel rotates 2/3 of a revolution for every cycle. The other wheel rotates half as much in the opposite direction. Voila, right turn! (The left hand side rotating results in a right hand turn).

There are various sources of backlash or lost motion in the system that could result in the slight loss of accuracy.

• The gears themselves have some backlash.
• The worm gears can translate a small amount on their axles before being restrained. This results in a slight loss of wheel rotation.
• The "Tomy armatron mechanism" is briefly disengaed while rotating from the first idler gear to the second. This might result in missing a gear tooth or two on the output. However, even if this happens it would slow down the Scotch yoke which would cancel out the loss. Hooray for feedback!

I've really got to get some parts and start building this thing ......

[MaxSupercars]

OMG it's simple and complex together... Really great work aeh5040! And thank you Blakbird for yor even great explanations, images and animations!

Max...

Edited July 24, 2015 by MaxSupercars

[BusterHaus]

Blakbird, your animations are extremely helpful in trying to understand how this works. Are you planning on making instructions, too? Or will you just be doing a breakdown of all the mechanisms in this device?

[aeh5040]

Once again, Blakbird has figured out how everything works essentially perfectly! Very impressive without building anything. The armatron animation is awesome! Just a few clarifications:

I've given some thought as to why the yellow idler gear support is a 3L axle pin instead of a regular 3L pin. Axle pins are made of a softer plastic than regular pins, so my suspicion is that this was chosen to achieve a particular amount of drag.

Oddly enough, I didn't give so much thought to this. It's possible a blue 3L friction pin would work just as well. Perhaps it is an axle pin just because of some previous version of the design in which the axle went into an axle hole. (I don't remember exactly).

One point to add about the red Armatron wheel: it is important that it is well balanced on the central axle, with the center of mass as close to the axle as possible - otherwise it might come to rest in the spot where the center of mass is lowest, and not rotate any more. The reason for the extra axle with lots of half-bushes is to adjust the weight distribution appropriately.

To amplify Blakbird's final point about backlash, the crucial property is that the cumulative error is literally zero. 3000 consecutive actuations of the mechanism on the left side would result in exactly 3000 revolutions of the Scotch Yoke, and exactly 2000 of one wheel and 1000 of the other. As I tried to explain in another post, by happy mathematical accident it turns out that the (considerable) backlash inherent in the transition from a left turn to a right turn does not seriously affect the final drawing. I have put some computer generated pictures here in attempts to illustrate this.

One final point about accuracy. As explained, a "turn" consists 2/3 of a rotation for one wheel and 1/3 of a rotation in the opposite direction for the other. We want this to correspond to a 90 degree rotation of the vehicle, but this depends on two things: the diameter of the two wheels, and the spacing between them. Get either wrong by even 2% and the picture will not be so good (see the link above). I managed to adjust the wheel spacing to sub-half-stud accuracy by using a technic plate turned sideways and an old style 8t gear nestled into two axle holes. (The latter trick is also used to get the casters on the bottom of the vehicle the right height).

One problem with version 1 of the machine was that the constant turning creates a big sideways force on the wheels, tending to push them off their axles. Even if they don't fall off, this quickly results in lost accuracy. Hence, the two turquoise cantilevers that you see on top of the wheels play an important role.

Edited July 24, 2015 by aeh5040

[aeh5040]

Thanks for the diagram; I was actually going to ask if you had something like this. For example, when you start a new drawing it is important to know where you can set the model to get a result that will fit. That requires a knowledge of where the current state of the machine lies on the final curve. Do you always set the machine to a particular state before starting a drawing? The state shown in the LDraw file (with all the Geneva mechanisms horizontal) can actually never happen in normal operation.

It looks as if I got myself confused about this. What I said earlier about it being insensitive to initial conditions was not correct. As you say, the initial set-up in the LDraw file does not match anything in the schematic list of diagrams, and is NOT the correct way to set it up. One possible correct initial setting is to have the cams on one side pointing towards each other in pairs. I will edit the LDraw file to reflect this. Other initial settings will produce DIFFERENT patterns, generally less interesting than the dragon, but also quite nice. E.g. the incorrect set-up in the file (all cams pointing one way on one side) gives a space-filling curve that fills a diamond shape (according to my computer program).

Edit: I think the LDraw should be correct now!

Edited July 24, 2015 by aeh5040

[Lipko]

This is all totally amazing. The idea, the mathematics, the implementation and development, the programming, calculation conditioning (this stuff). This all seem to be a pretty good thesis work material. About how many workhours went into this?

(These threads lately make me think that I picked a wrong profession, and this mechanical engineering is just not my thing. It's a bad feeling to feel that I suck at something I love and picked as a profession)

Edited July 24, 2015 by Lipko