Introduction: Perpetual Motion Machine: the Real-life Version of M.C.Escher's Waterfall
Here's a video shows the completed model. This video was released at April 1st and we called it "Perpetual Motion Machine" on that day.
Step 1: Tools & Materials
1mm ABS plastic plate;
PVC tubes in 3 different diameters;
PP textured sticker;
Small electric water pump;
Power supply with adjustable voltage；
Angle square, T Ruler (replaceable with straightedge & triangle);
Hot glue gun;
Step 2: 2 Analysis on the Drawing
Waterfall, 1961, M. C. Escher
Waterfall, by M. C. Escher, with the delicate structure of a Penrose triangle creating the visual paradox, has been winning admire all over the world. First of all, take a close look at it....
A dimensional geometry merged from 3 hexahedrons is placed on the top of the Left Tower. And on the top of the Right Tower placed another dimensional geometry merged from 3 octahedrons. And we call the part under the waterwheel the Pool，and from the Pool there is the "1st flume", the "2nd flume" and so on. Water falls from the Platform in the upper part of the Left tower.
As the aim of this project is to re-establish the marvelous scene of Waterfall from plane to 3D and present us a vivid show, it is important that: first, how to realize the impossible architecture structure; second, how to realize the water circulation within flume-waterfall circle.
There are many different ways to approach the aim and here is just one of them. You may keep on your own probing and come up with some cool ideas~
And before the project starts, you have to convince yourself that:
1. Perpetual motion is impossible;
2. Perpetual motion is impossible;
3. Perpetual motion is impossible;
Well....and still you have to accept that:
1. Water always flows to a lower place;
2. Seeing is not always believing.
Step 3: 3 How to Start
The whole model is mounted on a table.
It is a continuous flume going lower and lower from the 1st flume to the 4th. Water flows into a pool hidden beneath the table from the end of the 4th flume. The 3rd level of the left tower is the highest part of this model and from where water falls to the waterwheel. Water will be pumped up to the 3rd level to accomplish this circulation.
A proper angle to observe would provide a perfect visual experience which makes you visually connect the waterfall platform and the end of the 4th flume, thus achieve the very circulation. We have to rely on the differences of width and height of pipes to approach an acceptable perspective.
We marks on the drawing here that the blue words show water circulation, the orange words show the impossible structure and the green words indicate other non-functional details.
Step 4: 4.1 Design Process 1
Before establish the 3D model, software modeling assisted design is an economic and effective choice. Most 3D design software can help, but i recommend here Google SketchUp, which is the most convenient to use. Free version is available, aiming at drawing blueprint for architectural design. The very difference distinguish it from other 3D CAD software is that : SketchUp is designer oriented , allowing you to adjust your blueprint during the design process ,forming the final version gradually.
On the Help Page of Sketchup you can find the youtube video for primer tutorial .
on establishing the model, we use the "Match Photo" function. We regard the work of Escher as a picture we take of the building from some point of view. Then use it as background to establish a 3D model precisely like the building in the background picture.
This is the collation map between original work and the established model. Take a close look, there is a semi-transparent part blocking in front of the building in left picture. We ignore the backgroud on the right side..
Step 5: 4.2 Design Process 2
Here we put forward the idea of "Observation Point". While modeling in SketchUp, choose "Perspective" ,in "Camera" options. In perspective view,we simulate the effect of a camera shooting the buiding .All of the visual illusion is based on the settled position and angle of camera, which is the so calld "Observation Point" ,what to be discussed later is all about "how to cheat the spectator at observation point".
While observing on another angle, reality comes to light.
This 3D model neglects two main parts of final version, the button surface of water stream and the supporting columns which dimensional illusion stems from. I provide the SketchUp model file(without supporting columns) of waterfall perpetual motion for download(http://www.guokr.com/article/18649/#sketchup). The unit is meter since SketchUp is for architectural design. Too huge model is a trouble for transportation and reservation. On the other hand, too small a size contributes to the difficulty on processing, so it's crucial to choose a proper zooming ratio!
Step 6: 5 Build the Waterfall
As the processing of mapping is paralleled with model building, you might find some parts of the model have already been mapped.
With the marking tool, all the sizes here are accessible in the SketchUp file, so sizes will not be talked from on.
Step 7: 5.1 Base Plate
The base plate is cut from ABS plastic plate with a paper cutter knife. It would be much efficient with electric tools like angle grinder.
In the photo, the left-lower part is the "pool" and from that goes the 1st, 2nd, 3rd and 4th flume to the right-upper. You may noticed that the 3rd flume is wider than the 1st and the 4th wider than the 2nd. Thanks to perspective these flumes would be looked as if they have the same width. Later we will talk about the differences of the tubes' diameter and of the two dimensional geometries and both are meant to enhance this obligatory perspective.
Step 8: 5.2 Wall of Flume
The wall of the flumes is composed by two ABS plates indicating the shape of "walls" and 5~6 PVC pipes limiting the width of flumes.
To avoid leakage we need to stick PVC sticker on the top of wall. It also helps when we do the mapping later.
Step 9: 5.3 the Third Floor of the Left Tower
It can be seen from Google Sketch Up, only the third level of the left tower is at the highest level for the whole ‘waterfall’ model. This design is to facilitate the falling down of the water and therefore to make a great impaction against the waterwheel.
Initial results were worked out. However, we are not supposed to put on those texture at this time.
The figure presents the discharging point of the Waterfall in the third level of the tower.
Two PVC pipes were used to set up the discharging point of the waterfall. The connection place was glued using hot sol gel. We must ensure that the PVC pipe in the right hand side should be blocked by the one in left hand side from observation. This is to avoid being seen through.
In order to get close to the original effect of the waterfall, a transparent plastic film has been placed in the discharging point of the waterfall. The water will then flow down along this film.
Step 10: 5.4 Bottom Surface of the Water Streams
The PVC pipes were cut into suitable heights and glued on the base plate. They were used to support the bottom surface of the water stream. Since the water try to find its own level, the height of the pipes should gradually lowered down and make sure they were tilted in same direction.
The figure shows the effect after pasting all the supporting columns.
Cut the ABS plastic plate into suitable shapes and paste them between the walls of two flumes. For easy fabrication purpose, the bottom surface of the water is not as a whole. A separate ABS plate was used as the bottom of water surface for each flume. Note the seam in the middle portion of the figure; it will be blocked by the column in front if seen from the observation point. The concept of cheating in the observation point is used for the whole project.
Since the surface of the ABS plastic plate is very smooth, when the water flows over, the water surface won’t be flat, instead, it will converge into water streams. In order to achieve the original effect, polishing processing of the plate is necessary. In the left side of the figure, we can observe the polished effect of the plate.
Step 11: 5.5 Circulation of Water
For those who have seen the video, you probably know what the blue liquid is. Yes, it’s toilet detergents.
We are going to make a tank for primary storage of the water, in order to ensure the smooth flow of the water streams. The shape of the tank can be any.
A plastic box was used to serve as secondary storage tank of the water.
The white stuff in the figure is a small pump, which is used to pump the water up to the discharging point of the waterfall. Of cause, there is no perpetual motion existing; the model is actually driven by electricity.
This pump works at 12 Volt, and is able to pump the water up to 2 meters. In order to make the water flow out gradually but not erupt out, we need to adjust the water velocity. This can be achieved by altering the voltage of the pump or you may control the speed of the motor.
From the video at beginning of this article , we can see that the whole process is as follow: water flows out of the water sink�flows through four flumes�collected in a transparent bowl�flows into the water tank along the pipe�pumped the water up to the third level of the left tower�water flows down, into the sink again.
Up to now, the circulation of the water flow has been achieved. The following steps will focus on creating visual illusion as well as the steps to make mappings which are close to the original picture.
Step 12: 5.6 Monitoring System of Visual Illusion
From now on, all the later steps are based on the real time effect of visual illusion feeding back by a spectator at observation point. Here we use camera + video output.
Step 13: 5.7 Supporting Columns Generate Illusion
We stick PVC pipes of different sizes on the bases according to perspective. To generate visual illusion, we need to cut some part of PVC pipes. This picture shows how to draws the part to be cut. Actually we use output on video to guide the place of marks.
Step 14: 5.8 the Waterwheel
At first, we made this mill model, to match the shape in original work.
But while put it into use, we find this shape need a precise position to burden the rush, and the part dipped under water suffers larger friction.
This is improved version, 2 sides are made from ABS plate and blades are out of 1/4 PVC pipes. Glued by epoxy. Silver acrylic paint is used to approach original work.
This is waterwheel fixed on the house.
Step 15: 5.9 House on the Left
We made half model of the house.
Why its ”half house ”? Look at this angle……Keep in your mind——cheat camera.
Step 16: 5.10 Geometry on Top of the Tower
To learn more about marvelous characteristics about these two geometries, refer to this article Gifted Escher: unveil the geometries on tower (http://www.guokr.com/article/19538/)
This is the one on the left. Download the blueprint ,print and glue it.
This is the one on the right. Size of it is larger than the left one, since it's positioned farther.
This geometry is combined by 12 same octahedrons.
Step 17: 6.1 Texture Mapping: Flume Walls
Construction finished, but decoration is also an essential part to reestablish the marvelous scene of Waterfall.
In order to consistent the appearance with Waterfall, we plan to copy the original texture to the model.
To keep our plan simple enough, we use Photoshop instead of unstable hand painting work. Firstly pick out the texture pieces in the original work. Then adjust size and perspective of the chosen piece. Finally print the texture out on Water Resist Vinyl.
Since foreground and background pictures are not in close contact with the model, print them on A4 paper is convenient and economical.
Build a new file. Setup units to centimeter; choose the 90 X 60 size.
Use bricks on the wall as the fill pattern, notice to intercept as more bricks as possible and fix irregular flaws may appear.
Draw reference lines following Google Sketchup’s dimension analyze.
Draw outline of walls according to the reference line.
Fill outlines with the fill pattern set in step2. As the layers of brick in Waterfall are all the same, fill pattern’s size could be easily adjusted. It’s worth noting that the brick thickness on pillar base and wall are not the same, this could be helpful to cause visual deception.
Draw some light grey texture for side face of the mill.
Make some additional copies in the spare space in case need backup.
Before printing the file, change the picture in to grayscale mode to prevent color distortion. Texture picture for download( file Hyperlink
Step 18: 6.2 Background Pattern
the white lines here reminds me the murder scene.... lol
The not big background in original work is actually far more big than model in regard of perspective effect. Our background wall is 50cm behind model, with a size supposed to be 145cm *100cm under computation.
some part of the background is ward off by waterfall. Theoretically , if only you settle the model in the right position and angle, the blank part can be covered up. But since you don't always lucky enough to find the "perfect place", you'd better fill up the blank (by ps , or just use your brush).
Blank on table also need to be conceal. I use some piece of background pattern……not that perfect though.
Background pattern download:
Step 19: 6.3 Blueprint of Roof
Cut the original pattern of roof and adjust to be rectangle. As long as the angle of roof matches what appears on original work,the chimney on the adjusted roof also present a straight effect.
Step 20: 6.4 Pillars and the Rest Texture
In our ideal design, the pillars should by no means be a mapping but 360° model, but since the effects of 2 means look the same, we choose the simpler one.
There are 3 groups of pillars with 3 different lengths away from camera, so the mappings copied has also 3 sizes, making it possible for all the pillars look the same in cemara.
Foreground is a picture of deep sea paradise. Take reference of what we do to the background.
Step 21: 7 How to Make This Footage of the Waterfall
Remember, we mean to cheat you spectators. If you think you are quite talented in "cheating" you can just skip this reminder~
Hide all pipes within screen! Especially, in order to make the water flow visually continuous, it is necessary to slightly lower the water level from the falling place by pump voltage tuning before shooting. You need to tune up the pump voltage to push the water at a proper time point; this operation is sophisticated and exercise is needed.
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