The gears used in all of my clocks have geometry based on the standard gear profile formulae with some adjustment to the tooth profile to thin them down a little to make it a bit less sensitive to the inaccuracies inherent when using hand cutting methods to produce them. When designing clock gears I generally use the metric system to define the teeth but both metric and imperial can be used interchangeably. The chart shown below shows the formulae I use for gear calculation. For the gear teeth to engage with each other they must both be calculated using either the same Diameter Pitch (DP) or the same Module these two terms relate to the way the teeth are spaced around the Pitch Circle Diameter (PCD). You can see from the chart below that as the Mod increases so does the size of the tooth, and visa versa for the DP. If you are working with metric dimensions you will use the MOD and if you are working in imperial dimensions you will use the DP. Generally speaking, if you are building a wooden clock then you will be using Mod 1.5 or above. Once you have decided on the DP or Module you are going to use that to calculate all the other features using the formulae in the chart at the top. Both these charts come from the Technical section of the HPC Gears catalogue There are two main gear trains in a clock, the minutes train that requires a total ratio of 60:1 this runs between the shaft carrying the minute hand and the escapement wheel. The escape wheel normally turns once a minute and it connects through the train with the shaft holding the minute hand, which turns once an hour, hence the 60:1 ratio. The second train runs between the minute hand and the hour hand which requires 12: reduction. This ratio normally has to 2 sets of gears with ratio's of 3:1 and 4:1 and the centre distance of each are normally the same as the gears are mounted on the same pairs of shafts, I always use a 8 teeth and 32 teeth pair along with a 10 teeth and 30 teeth pair, as it allows the shafts to be shared. With the 60:1 ratio there are many more options open to you and will to a large extent depend on the design you are trying to achieve, so I must leave that up to you to decide. Having said that a simple set of 3 gears using 3 pair sets with ratio's of 3:1 4;1 and 5:1 works quite well as when multiplied together they will give you a 60:1 ratio. Having decided on the gear arrangement I normally try to determine the Module value I am going to use and that relates to the size of the gears I want. To determine that I would normally work out on CAD or on paper what size I want the largest gear to be, so in my case this is usually a 60 tooth gear. As an example I have decided the gear needs to be about 125mm (5ins) diameter so from the chart above I can work out a value for the module. Module = Outside Diameter mm / ( Number of teeth +2) This gives a value for the Module of 2.016 so round that down to 2.0 and you can now use that value to calculate the sizes for all of your gears. If you are an organised person you would use a spread sheet to enter all your values to work out the relevant gear sizes, I never got round to doing this so finish up working them out on a calculator. The chart below shows a typical gear pairing for a 3:1 gear ratio and a Module of 2 using a 60 tooth and a 20 tooth gears. The tooth thickness is slightly less than the normal 50% of the CP value I have used between 44% and 48% of that value depending on what looks to work best in the CAD simulations. There is another section of the Gear train that has not yet really been mentioned and that is how power is transferred into the system to get it to start ticking. Mostly this is going to be through a weight attached to a cord wrapped around a barrel on the drive shaft. The Drive shaft can be the Minute shaft but this is generally not a good idea as it is going to apply a very high load to the shaft which will eventually lead to early wear to the shaft and bearings so I recommend we use a second more robust shaft to carry the load from the Drum to the Minute shaft. This is shown in all the illustrations below. This has another advantage as well which is to increase the run time of the clock, introducing a ratio between the two connecting gears of around 2 to 1 double the run time. You can run your own changes on this to increase the run time even more. Do remember that by doubling the run time you also need to double the weight. The problem with this is that at some point you will need to rewind the clock as the weight will hit the floor and stop the clock. There are a couple of ways to do this and the first is to introduce a Rachet arrangement shown in the illustrations below. This illustration with the back of the clock removed shows the type commonly used, it consists of a Ratchet and a Pawl where the Pawls move under gravity to lock into the ratchet at the top, this type needs no springs, so it is fairly simple. What it does is effectively disconnect the drive when you turn it backwards so that you can rewind the clock. A different clock this time with a 2:1 ratio between the drive gears and a rather unusual double drum that feeds the cord from both sides effectively balancing out the adverse effects of offset loading on the frame. A different approach this time not using a ratchet and Pawl arrangement to provide the winding ability, instead a 'Needle roller clutch' is used. The internal rollers are encouraged into a locking position against the inside walls of the shell making it lock in one direction and free in the other. these are normally designated with an HF as in HF0612 as used in the case shown above in Clock 51. You do need to be certain to secure the Clutch within the gear so there can be no relative movement, by either clamping or glueing. Another method of increasing the running time of the clock is to use a simple pulley system as shown above which will also give you another 2:1 mechanical advantage resulting in a further doubling of the running time and of course a further doubling of the weight.

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In an interactive and game-like manner, students learn about the mechanical advantage that is offered by gears. By virtue of the activity's mechatronics presentation, students learn to study a mechanical system as a dynamic system under their control as opposed to a static image. The system presented is of two motorized racing cars built using the LEGO® MINDSTORMS® robotics platform. The altered variable between the two systems is the gear train; one is geared up for speed and the other is geared down for torque. Students collect and analyze data to reinforce particular aspects and effects of mechanical advantage.

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The drive train of the BR 55 engine. In order to get the see through between boiler and chassis and also keep the boiler narrow I had to put the motor in the fire box. The best place for the gears down to the wheel axles however seemed to be between the cylinders. The 16L axle runs through the (open) bottom of the boiler. For the connecting and coupling rods I'm using Ben Coifmans custom gear. The connection between connecting rod and piston rod sits beside the coupling rod which caused some issues with the two snagging and locking the mechanism. The sliding mechanism you see here resolved that issue and kinda looks the part as well ;-)

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