The self balancing bookshelf:

What a conversation starter, I think when I move next I might just have to make space to build one of these…

The best video tutorial on the differential gear:



I love this video, right down to the 1930′s voice and the use of the motor cycle stunt team!

The customisable public bench:

Basically, using a utility box located near the bench, anyone can alter their urban environment. Talk about power to the people, designed by Carmela Bogman and Roger Martens it means to put a DIY urban design element back in the hands of the broader public.

The gear ring:

For fidgets everywhere

Folding concrete!

Designed by Dror Benshetrit, these blocks work based on 4 elements cleverly joined that use gravity to hold them open. The applications are huge, as part of the research for this design the tried out wooden and metal frame versions and found that with a few additional elements you could have almost instant temporary housing that would be structurally sound, strong and would last, new innovation in refugee camp building?

I love the book version, I want to build a book case using them

And finally… in flight!

(sorry Dean didn’t have access to my video editing software!)

You can see he’s still got a bit of clank and clunk in the movement but I think that it’s caused buy the weight rather than the mechanism. The Pegasus was made out of thin brass sheet where as mine is made of 3mm acrylic, once you add up the weight of all the layers that make up his body it’s going to put strain on the mechanism. I also think I should have taken time to re-make the box, some of the stiffness is caused by the lever having too steep and angle to turn around. Overall I’m really pleased with him though, he flies! I want to have a go at making a brass version though, very pretty and I want to get that smooth motion, yet another project then

So, first, what is going to make my dragon fly?

As a said before I think that the best mechanism to replicate the movement of the Pegasus will be a crank. A crank is basically a lever attached to a rotating shaft, the diagrams below are from a great book ‘Cabaret Mechanical Movement’ by Aidan Onn and Gary Alexander, highly recommended if you want to do any work with mechanisms!

(scan of crank images, label parts)

I don’t think I’ll have enough time to cut my parts out of brass, no matter how beautiful the end result will be. To save time it would be quickest to draw the components in 2D Design and manufacture them on the laser cutter.

Fist things first, what do I have to make the pivots for everything to move around? Looks like I’ve got 3mm acrylic rod to work with, so what size hole do I need for this to work? I’ll need a tight fit for fixed points and one for moving points but not too loose, I don’t want any rattle:

Using 2D Design it was easy to manufacture test pieces, looks like it’ll be 3.2mm for the moving points and 3mm for the fixed points. Even though the results seem obvious you never know if the laser cutter will melt a little extra away from the cutting line, it all depends on how the machine is set up.

Next, the length of the lever connected to the dragon. This is all linked together with the size and position of the cam for the crank so…

The part of the drawing to the right is an accurate representation of the dragon at it’s lowest point on the crank. There appears to be enough room for everything to move so I think I can go ahead an design the rest of the dragon:

The additional pieces are all to make up the layers that move against each other. So now I have my dragon, the box size and shape and the cam drawn, I think I’m about ready to start construction!

Clang!! first problem, I’ve not left enough space for the vertical rod to fit through the top of the box! Back to the drawing board:

Right got there in the end, time to do a test fit:

Looking good till I tried the mechanism

Crud, he’s all floppy and moving way too far back and forth, I tried fitting some scraps to close the hole in the top up a bit to see if it made a difference:

Hmm it’s a bit better but not by much, I’ll need to alter the mechanism if I’m going to make much of a difference. To reduce the ellipse that the crank describes at the top there are a few things you can do, make the cam smaller, move the shaft and pin points closer together on the cam or to move the guide higher up. As I’ve already cut the box and I don’t want to waste material re-cutting it I’m going to ry a combination of the first two:

The one on the left is my new design, I’ve also included a couple of new components to limit the size of the guide hole in the box lid, time to test again:

Much better! I’ve made the hinges for the wings out of some acrylic tube cut into three pieces, the middle stuck to the wing and the other two sides stuck to the body with a piece of rod in the middle for the pivot, to stop it falling out I ran a little acrylic cement in the end of the tube at each end. It’s still a little clunky but hopefully the linkages will reduce a lot of that.

I’ve always loved dragons so I’m going to have a go at making an automata of a dragon flying. I got most of my inspiration from an automata made by a guy called Keith Newstead:

I love the smooth motion! I think I’ve worked out that it’s made from a crank to describe the elliptical movement of the body of the horse and linkages to make the rest of the movement. Hopefully I’ll be able to replicate the smooth, graceful movement…

There are two types of drives: positive and friction. Gears fall into the positive category as they are made up of inputs and outputs locked together and synchronised. Pulleys and belts fall into the friction drive category as they rely on the friction of the belt against the pulley to transfer the movement.

A good example of a friction drive is the inside of a wood turning lathe:

The pulleys have no teeth and the belt is driven by friction. For positive drives you can have toothed pulleys and belts or a chain an sprockets. Toothed belts have notches cut along their inside edges that engage with teeth cut in the surface of the pulley, like the rather fetching treads on this hummer tank:

Chain and sprockets work the same way except the teeth are on a sprocket wheel and fit into the gaps in the chain, like the gears on a bicycle:

So there’s the types and some examples but what about the detailed stuff?

In a any drive system you have a driver gear or pulley and a driven gear or pulley, the relation ship between them is determined by their size, for example:

In this system the driven pulley , being smaller than the driver, would go much faster and have much less torque acting on it.

Where as in this system the driven pulley would go a lot slower and have more torque acting on it, the technical term for the relationship between the two is called the velocity ration and it can be worked out using another mathematical equation.

As I said in my post on mechanisms a wheel (or pulley or gear) is just like a lever that moves through 360° so your looking at the equivalent of…

distance moved by effort ÷ distance moved by load

This translates into…

distance moved by the driver pulley ÷ distance moved by the driven pulley

Which is made much easier to work out by finally turning into…

Velocity Ratio = diameter of driven pulley ÷ diameter of driver pulley

Note the driver and driven have changes places in the final equation.

So the velocity ration for this system is 0.5:1. It works in a very similar way for geared systems:

So the velocity (gear) ratio of this system is 2:1

So what if you want to work out how fast a pulley is turning? You use the (rather long worded) equation below:

Rotary velocity of driven pulley x Diameter of driven pulley

                                                   =

Rotary velocity of driver pulley x Diameter of driver pulley

Or:

RV D1 x ØD1  = RV D2 x ØD2

So I want to find out the rotary velocity of the driven pulley here, again using the transposing formula techniques I spoke about in my previous post you end up with:

There is so much more I could go into, cams, cranks, shafts, ratchets, springs, the list is huge! I really want to get my teeth into making a mechanism so I’m going to move on and have a go at building an automata. I’ve always loved moving toys and I’ve not made one of these since I was little playing with paper kits

So, ready for more mathsy goodness?

There are three important formulas to remember when dealing with mechanisms…

Mechanical Advantage

This is basically a comparison of the effort put in to the load moved, this leverage is the ration of the distances of the effort and load to the fulcrum. When you work out this ration you can tell how the lever will work:

You work this out by using this equation:

For example the effort taken to lift a load in a wheel barrow:

Any number greater than one is a mechanical advantage and the higher the number the better the advantage.

Velocity Ratio

The velocity ratio is the distance moved by the effort divided by the distance moved by the load. An easy way to remember it is that it’s the opposite to mechanical advantage, so effort over load rather than load over effort.

Using the same example of the wheel barrow:

Efficiency

Last but not least efficiency is exactly what it says on the tin, how efficient is your mechanism?

You need the previous two worked out to get this as the equation is:

So our wheel barrow is…

196% efficient! This is because you can lift more than you normally would be able to by using a wheelbarrow.

Really useful stuff

The right hand side is turnign clockwise and the left hand side is turning anti clockwise.

To balance the scales or bring them into equilibrium the clockwise turning motion has to balance the anticlockwise motion. To work this out you need to use a famous equation:

Force x Distance = Moment 

A moment is a turning force and is measured in Newton meters or Nm.

You can turn our set of scales into a lever of the first order to better understand this equation:

You have to do the equation for both sides to get them to balance so in this instance our unknown is the load on the left hand side of our scale so our equation would look like this:

 F1 x 2m = 2N x 3m

By breaking this down into two separate equations we can work this out:

2N x 3m = 6Nm

 F1 x 2m = 6Nm

You have to do something very mathsy now called transposing formula, basically moving the elements of the formula around to get F1 in the right place. As long as you do the same to both sides of the equation it remains true, here’s some examples:

3 + 4 = 7

2 + 3 + 4 = 7 + 2

√3 + 4 = √7

You also need to remember this rule : is you change the side you change the sign! For example:

3 x 4 = 12

3 = 12 ÷4

So our moments formula needs to undergo a bit of a transformation before we can use it:

So we end up with:

By using this result we now know that to bring out imbalanced set of scales into equilibrium we need to add an extra 2 N to the left hand side!

In Archimedes’ book called ‘On the Equilibrium of Planes’ he wrote out the ‘Law of the Lever’. He wrote that a lever is used to convert a small effort into a large effort and vice versa, he famously said ‘Give me a long enough lever and a place to stand and I will move the earth’. He also divided levers into three groups or orders depending on the relationship between the fulcrum, load and effort.

Levers of the First Order

By moving the fulcrum closer to or further away from the load you change the distance that the lever must move and the amount of effort it will take to lift the load. A lever of the first order always has the fulcrum between the effort and the load. Levers in this class are things like a children’s see saw, a spade or a pair of scissors.

Levers of the Second Order

Levers are classed as belonging to this group when the load lies between the fulcrum and the effort. It’s can be described as a force magnifier, it has very good mechanical advantage, something I’ll be talking about in my next post. A good example is a wheelbarrow, lifting the handles uses relitivly little force but can move a heavy load, in this example the fulcrum is the axle of the wheel. 

Levers of the Third Order

In a lever of the third order the effort is applied between the fulcrum and the load, this acts as the opposite of a lever of the second order, it’s a force reducer. The effort used will always be bigger than the load. doesn’t sound very useful does it? It does, however, have a big advantage, the load moves faster than the effort, you could call it a movement amplifier. Your arm is a good example of a class three lever using your elbow as the fulcrum, the effort comes from your bicep muscle and the load is held in your hand. To move the load requires the effort of your muscles to pull up against the fulcrum of your elbow.

Linkages

You can get really cool effects by combining levers, this creates linkages!

Here’s a collection of levers connected to form a linkage that will give parallel motion:

A bell crank transforms vertical motion into horizontal motion using rotary motion around a fixed point (phew, what a mouthful!):

You can change the action of the linkages by where you apply the force:

Onwards to the scary maths bit!

After doing a bit of research I’ve found that there are only 5 basic mechanisms!

1. The Inclided Plane
2. The Wedge
3. The Screw
4. The Lever
5. The Wheel

On a closer look you can reduce this list to just two basic mechanisms, a wedge is like an inclined plane, or two joined together and a screw is like an inclined plane wrapped round a shaft. The wheel is like a lever that moves through 360°. So the remaining two are the inclined plane and the lever…

Wonder what you can make with these?…

Irregular

This is motion with no discernible pattern, you can get this effect using an irregular cam and follower.

Intermittent

This describes motion that starts and stops regularly, like a Geneva stop mechanism.

Linear

This is simply motion in a straight line, like a train or going down a slide

Rotary

 This is the motion you’ll see most used in things like automata, it’s motion in a circle, like turning a handle on a wooden toy.

Oscillation

This is back and forth motion around a pivot point, like a metronome or somebody waving.

Reciprocating

This describes a continuous back and forth motion between two points like a piston in an engine.