Back to the task in hand, I've been working on my escapement mechanism today. I've put the final parts in place and it works. What a relief that was I can tell you! There is still a bit of work that needs to be done but, hey, it works! You can see from the photograph below that the pendulum isn't hanging vertically so I'll probably put a counter-balance on the straighten things out.
I had originally planned to using paper springs to keep the palette arms centred within their required movement. After leaving the prototype model for a couple of days the original spring had lost its oomph so I've replaced the springs with extra weights more details of which later. (Lower left coin on the picture below.)
The picture below shows a view of the back of the mechanism revealing the pendulum.
I'll now need to go through all the parts sheets and work out which parts I'm using and which have been abandoned. I'll then work out the counter-balance and make up another draft. This has been a fun model to design!
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More progress on the escapement model. I've been attaching the palette today, these are the parts that touch the tooth of the escapement wheel. In this model they are the connection between the pendulum (round the back - you can't see it) and the wheel.
There will be two palettes each joined to the pendulum via a long connecting rod. One will make the pendulume swing one way - the other the other. Tick - Tock. I'm adding them one at a time. The connecting rod needs to be positioned so that it lines up with the wheel as the pendulum swings past the centre line. To add complications, it needs to be able to swing back and forth but sit naturally in the centre of its range.
In clocks made from more traditional materials that would be done with a spring. In this paper model I've used a zig-zag of paper as a spring.
The spring sits inside a cover and holds the connecting rod central whilst the coin to the left of the rod returns it if it swings the other way.
Above is the finished assembly.
This bit has had me stumped for a while. How do I fit in the second palette? There simply isn't room. It need to go where it is in the picture but there is no space. I think I'm going to have to bite the bullet and fit a second wheel for it to drive.
I've been planning to do a YouTube video following the delvelopment of a model from start to finish showing the design process, the failures, the tears, the despair... finishing with a completed project. I could use a mix of film and animation to show how its all done, I think it could be quite interesting. This would have been a good project to have filmed as it has all sorts of interesting problems to be solved. Too late now though. Would you be interesting in such a video if I put one together?
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This is the third draft of the weight box for the grasshopper escapement mechanism. Rather than resorting to using cocktail sticks I have rolled up a piece of card really tight. By making the starting piece 'T' shaped I've made it so that it is stepped in the middle.
That way I don't need to add washers to keep the roller in place. Looking good so far!
Once complete I mounted it in a box...
...then fitted the paper belt as before. The result works rather nicely. Notice that rather than cutting a round hole which would have been very small and fiddly to do, I have cut a small cross and enlarged it with a pencil point.
Below is the result fitted into the main box.
I've had to increase the height of the box to allow space for the mechanism. I've then added what is effectively a bell crank for the palletes to attach too. The palettes are the the last part so hopefully the mechanism should be coming to life soon!
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Escapements are constructed from a collection of interconnected parts. Today, the weight.
My first draft didn't run very well. It stuck periodically as the weight moved down and the belt tended to drift to one side of the weight assembly. Today's draft, I narrowed the belt to 10mm from 20mm to reduce the friction. To keep the weight centred I added tabs on both side of the weight top.
As the weight drops down the belt slides under the curved surface at the top of the weight assembly. It still ran a little stiff so I thought I'd try adding a roller for the belt to roll over. It worked better even though the roller didn't actually turn. Weird. I suspect that the reduced diameter of the curve is reducing the friction on the belt making it run better. There are a couple of things I can try now. I'm pretty sure that the axle doesn't rotate because it is the proverbial square peg in a round hole. To make it work better I could use a cocktail stick as the axle however as I'm idealogically opposed to cocktail stick parts in paper models my alternative is to try reducing the diameter of the slip curve even further, making the weight assembly with no moving parts.
In other news. I've added a pendulum to the top of the box and added one of the two palette arms just so that I can begin to see how the geometry works. Looks like I can move the wheel up 20-30mm on the box.
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After all my experiments with ratchets and toothed wheels it is time to turn my attention to the escapement. The heart of many mechanical clocks, the escapement is the part that controls the time keeping. It has the dual function of driving the pendulum and dividing up time. There are a whole variety of different escapement mechanism from simple to complex. A quick search of youtube reveals many of them in action. After a bit of research I settled on the grasshopper escapement as an interesting mechanism that I thought I could recreate in paper.
First, the escapement wheel. I settled on a purely arbitary thirty teeth as a compromise between the teeth being close together and the wheel not taking ages to cut out. The wheel here is 120mm in diameter and made from doubled over card. To keep it flat I have added corrugations front and back at ninety degrees to each other.
I've mounted the wheel and axle on a tall box. On the top I've added a hinge to attach the pendulum and the rest of the mechanism. The pendulum will hang round the back of the box. The rest of the escapement mechansim will attack to the front side of the pendulum hinge - more of that later.
I had originally planned to wrap a paper strap round the axle and attach weights to the end of it. With the length of box I had chosen the wheel would turn just over two turns while the weight fell to the bottom of the box. Thirty tooth wheel, two and a bit turns, that would be around seventy ticks from one winding. By changing the weight so that it acted as a pulley I made it so that I got almost five full turns of the wheel from one winding. Almost 150 ticks!
This layout seem to work well though it will need to guides to keep the paper roll centred.
Looking good so far. Next step, the actual escapement.
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A working Peaucellier linkage to download and make. The simple geometry of the linkages is used to convert rotary motion into straight line motion. Members can download the parts for free. Non-members can download for a small fee.
Print the two parts sheets onto thin card. (230micron / 230 gsm) Solid lines show where to cut. Dotted/dashed lines are score lines. Grey areas show where the glue goes. Use white school glue (PVA) to glue the parts together.
Fold the support round and glue it together.
Fold over the top and glue it down as shown. Notice the dotted, valley fold line on the front.
Fold up the base to make two triangular tube sections as shown.
Glue the stand to the base using the grey area for alignment.
Glue together the parallelogram as shown. Notice the 'Top' label.
Glue the parallelogram to the stand using the centre link. The 'Top' is at the top of the picture (as you'd expect)
Glue the lower linkage between the triangle on the parallelogram and the triangular area on the top back of the stand. Notice that it should be roughly one millimeter from the stand.
Glue the upper linkage into place. Make sure that you don't get glue on the creases.
Glue the post into place. You might need to rock it back and forth a little so that it lines up with the path of the end of the linkage.
Fold the handle in half and glue it together then cut out along the grey lines to make a curve.
Finish off the mechanism gluing the handle into place. Let the glue dry.
Move the handle up and down and the left side of the parallelogram will move in a straight line parallel to the post. Clever stuff Monsieur Peaucellier!
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Invented in 1864 the Peaucellier linkage (poo-selli-yeah) linkage was created as a way of making straight line from circular motion. It was used in steam engines to control valves without the need to guides. The peaucellier linkages, invented by, you guessed it, monsieur Peaucellier, is mathematics in motion. The four red parts are all the same length, the circle radius is the same as the green link and the two yellow linkages are the same length.
Using Flash
As long as these ratios are adhered too, the grey dotted motion line will be straight.
I've been helping #1 Son with his mathematics revision so I've been in a geometrical frame of mind. Inspired by the maths, here's my paper version of the Peaucellier linkage. The end of the linkage moves up and down maintaining the same distance from the vertical bar with the arrow on. Animation below.
I'll be doing this as a download then I'll have to find a use for it in a model. Something that moves up and down in a straight line. A meerkat? Groundhog?
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A bi-directional ratchet to download, print out and make. As the rocker is rocked back and forth the two ratchets drive the wheel continuously in a single direction. Members can download the parts sheets for free, non-members can download the parts for a small fee.
Print out the two parts sheets onto thin card. (230 micron, 230 gsm) Dotted and dashed lines show where to score, solid black lines are cut lines and the grey areas show where to glue. Carefully score and cut out the holes in the parts before cutting out the pieces.
Assemble the two ratchet housings in the same way as each other. Note that they are mirror images of each other. Fold the main body of the piece in half and glue it together to make it double thickness. Fold the end of the long tab over and glue it together to make a double thickness ratchet pawl.
Carefully cut out the circle on the main piece with a sharp knife.
Cut along the two grey curves to make a semi-circular end to the ratchet housing.
Fold the two tabs at the top over and glue them down.
Fold the remaining tab over and glue it down. The ratchet pawl piece should be free to move up and down. Notice the colour of the square on the top of the housing, in this case, red.
Find the link point with the same colour square and glue it to the top of the housing using the two triangular grey areas for alignment. Notice that the dotted line on the link point is a valley fold.
Fold the gear in half and glue it down to make double thickness pieces. Notice that the four centre tabs are not glued down. When the glue is completely dry, carefully cut it out. Repeat this process with the other gear.
Fold round and glue together the square sectioned drive shaft. Glue one of the washers into place lining it up with the red line.
Thread a gear onto the drive shaft as shown. Make sure that the teeth are pointing in the same direction as the picture.
Find the same housing as the one in the picture. (remember that they are mirror images of each other) Thread the gear into place in the housing as shown above.
Make up the box and rocker stand as shown.
With the rocker stand to the left, thread the ratchet assemble through the hole on the box so that the housing is flush with the box.
Flip the box over. Thread the remaining housing onto the drive shaft. Thread the washer into place and glue it to the shaft lined up with the red line.
Fit the second gear lining it up with the blue line and making sure that the teeth are again pointing the right way.
Fold round and glue down the two long tabs on the rocker to make triangular sections as shown.
Fold round the end tabs and glue them down. Notice that they are valley folds.
Glue the two hinges onto the two grey areas.
Glue the hinges to the top of the rocker shaft.
Glue the linkage to join the ratchet housing to the rocker as shown above.
Repeat the process with the other linkage.
That's it. Once the glue is dry, rock the rocker back and forth and the wheel will turn. Use the Bi-Di-Rat as an interesting mechanism in its own right or as the starting point for your own design.
Have fun!
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After experimenting with a couple of different ways of connecting together the two ratchet in the dual ratchet model, I've settled (at least for now) on a 180º bell crank.
I must admit that it is all starting to look rather complicated for what is essentially a naked mechanism. Still, it looks like fun! So here's the plan. A 180º bell crank is basically a bar with a hinge in the middle. I'll locate it at a distance from the two ratchets and join it to the ratchets with a couple of linkages. Here's the first of the problems I forsee. The linkage that joins the ratchets to the bell crank need to be hinged in two different axes. Both ends need to be able to flex both up and down and side to side.
First axis of swing, side to side. I've added a couple of hinges lined up and down to the top of the ratchet housing.
The linkage has a hinge at each end and a twist along its length. The twist is more for artist effect than engineering need, looks nice though and does make a simple yet strong linkage bar.
I glued the linkage with its hinges running perpendicular to the ratchet hinges, that way it gives a solid joint which is still flexible. It moves easily both up and down and side to side yet still moves the parts effectively .
The prototype linkage is w-a-y to long, at least double the length it needs to be. Also, I think I'll move the bearing hole in the box further along to the right. I hope to have a working prototype tomorrow though I do have to take #1 Son into town for a quick look round the shops. Fingers crossed.
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The heart of many automata, both traditional and the paper variety, is the cam. The cam is perhaps the most flexible way of driving a mechanism. By changing the shape of the cam profile all sorts of different movements can be described.
But on its own, a cam just goes round and round. To use the movement the mechanism needs a cam follower, the part that runs along the cam's surface. In more traditional automata, made from wood and brass, it is quite possible to run the cam follower so that it is perpendicular to the cam, as in the first picture above. In paper based models this doesn't work so well. By their nature paper models have more flex and tolerance. A perpendicular cam on a paper based model will tend to flex and bend rather than running smoothly up and down, not what you want! Paper is at its strongest when it is under tension (being pulled) To use this strength, cam followers in paper models tend to drag across the cam surface (above right)
Using Flash
The design of the part of the cam follower that touches the cam is important. There needs to be a finger shaped end to closely follow the surface of the cam. More complex curves need a narrower finger but, as is often the case with engineering and design, there needs to be a balance between fineness and strength. The animation above shows how well the narrow cam follower follows the cam compared to a stronger wide one.
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