Cut 2D Inlay toolpaths

In the new desktop version of Cut 2D they have added several additional features to improve its functionality, included in these, is the new Inlay Toolpath commands.
I was interested in this particularly as it was a further way of adding numerals to the clock dials.
To test what it could do and to ensure that my new CNC router was capable I designed a small test piece that is shown below. It is simply 3 separate numerals and a small rectangular plaque with numeral shaped pockets, machined to fit the numerals into.

First step was to set up Cut 2D with a blank size and a thickness, which in this case was 90mm x 90mm x 6.2mm thick, and then load the DXF file and centre it in the blank using F9 function key.

The Inlay Toolpath command, is the new addition to the Toolpath operations menu shown below.
Clicking on the end icon brings up sub menu allowing you to choose which operation you want to do first. The first two choices are for the numeral itself in either a stepped or a straight form, with the second two choices for either a pocket or straight through cut.
One of the main advantages of using the Inlay tool path option is that when a pocket is programmed it takes account of the cutter size being used and adds the appropriate radius to the internal square corner on the numeral, if it didn't do this the numeral would not fit in the pocket without post machining operations.

First select the Pocket option and fill in the details required, including the Pocket allowance box highlighted below. The Pocket allowance is there to give you some clearance between the pocket and the numeral to be fitted into it, it is useful for giving space to fit if there is any post machining finishes to be added, paint or varnish etc.0.25 mm is a good starting Point.

Next select the Straight inlay option and fill in the details required, this time leave the Allowance offset at zero, its probably best to keep all your adjustments for the fit on the pocket. This time you will need to add tabs to hold the numerals in place when you cut through.

Next select the outline for the plaque and choose a normal 2D profile toolpath and fill out the details as you would normally, to cut straight through, again using tabs.

Now select all the tool paths and click on the preview  toolpaths to make sure it is going to cut what you require. Once that's OK the you can click on save toolpaths, now you are ready to machine.

Once that's OK the you can click on save toolpaths, now you are ready to machine. The image below shows the sample I machined and put together.

Remontoire for Woodenclocks

After developing the design of the Woodenclocks Gravity escapement to the point where it was working quite accurately I had started to think if there might be something else I could do with the clock design to improve the the overall efficiency of the clocks. I had always had problems with the gear train working smoothly and consistently, so this seemed a reasonable area to look at more carefully.
By the nature of a clock the gear train is going to have to start and stop with each action of the escapement, so when the escapement is engaged, the gear train stops moving and when it releases it will start moving again, this happens with every tick of the clock. The problem here is that each engagement of the escapement involves a certain amount of friction, and two types of friction at that. There is static friction which applies when you try to get an object to start moving and sliding friction which occurs whilst the object is moving, and it is the static friction that has the greater value. If you could reduce the number of times that the gear train has to stop and start then you can reduce impact of the static friction. This is important because one of the largest variable affecting the smooth running of the clock, is the friction in the gear train. This is going to vary all the time because the fit between the mating teeth in the train will constantly vary due to the small variations in both tooth geometry and the surface smoothness of the teeth we make for the wooden clocks. These variations are likely to be a lot bigger in our home-made clocks than those manufactured on industrial scale equipment, so if we can reduce the static friction we can improve the clocks running.

Remontoire action
One the ways to reduce the static friction in the drive train is to introduce a remontoire , the simplest type of  remontoire invented by Robert Robin in 1772. This invention is based on the endless rope system for winding clocks invented by Christiaan Huygens nearly hundred years earlier, and is deceptively simple in the way that it works.

The remontoire literally means 'to wind' and is used to separate the motion of the gear train from direct contact with the escapement. Where the gear train itself is driven by the main clock weight, the escapement is driven directly by a separate smaller remontoire weight, with this remontoire weight being reset periodically by the gear train. The secret of its operation of the Robin Remontoire the latch holding back the rotation of the gear train is released when the descending remontoire weight  touches down on a lever system connected to the latch. The gear train now begins to turn again, and lift the remontoire weight to its topmost position where it is once again restrained by the latch, the whole cycle now repeats.
The gear train only moves once every 30 seconds or so depending on where it is operating in the gear train, so not stopping and starting every second, thus reducing the amount of static friction in the system.
For more information on the Remontoire see  http://www.my-time-machines.net/horz_2_train4.htm.

The Remontoire therefore has all benefits needed to reduce Static friction from the clock, and reduce the variations in friction generally from effecting the action of the Escapement . The next thing to do is to design and build a test rig to find which approach would best.
Four approaches were identified as being feasible and are listed below.

Remontoire - Design 1 - Cord Drive

The first approach was a direct implementation of the Robin Remontoire. In the diagram shown above the basic design is laid out in a simple manner and I have used this as the starting point for the first rig.

In this rig the drive is coming from the drive train indicated by the large arrow on the left, the drive train's rotation is halted by the latch shown in green at the top right.
At this point the Escapement is being driven by the small weight shown in the centre-bottom, it is supported on the endless cord shown in blue. This cord is wrapped around two equal size pulleys, one behind the small gear on the left and one behind the escapement. The small weight in the very centre keeps the cord in tension.
With each incremental rotation of the escapement the small escapement weight drops down closer to the green lever below it. When the weight touches down on the green lever, it pushes up the red strut on the left and lifts the latch at the top holding back the drive train. The gear train is now free to move and it lifts the small escapement weight back up as it rotates 1 revolution, stopping when gravity drops the latch to its rest position. This winding of the escapement weight takes place in the space of 1 tick of the escapement.
This is the Robin Remontoire in action, but it has problems, the major one is that it is difficult to stop the cord slipping, and even the smallest slippage will cause the clock to lose time. In practical terms I tried wrapping the cord around the pulley one and a half times, this failed as the cords kept getting locked up, I also tried lining the pulley with coarse grit emery cloth, this worked much better but did not keep the two sides exactly in sync. There was also an anomaly with the actuating of the latch release, sometimes it would take two goes by the escapement weight to complete the release, so for these reasons the Robin design driven by a cord was not going to work.
What it did show was that it could work if a chain or belt was used and the latch actuation was driven directly by the escapement. This was to be the route taken in the next design..

Remontoire - Design 2 Ladder Chain Drive

This next rig was designed so that a finger attached behind the Escape wheel, would actuate the latch directly and a ladder chain would be used in place of the cord used previously.

This arrangement worked much better, the finger shown above in red moves with the escape wheel and touches on the green latch to lift and release the drive train. The design of the finger/ lever action is arranged so that the lever is lifted and released inside one incremental movement of the escape wheel. That means that the drive train and the Escape wheel will always stay synchronized.

The only problem to emerge from this design was that the ladder chain would sometimes snag on the sprocket driving it, and then completely stop all movement.  This was probably due to the design of the sprocket itself, and as these were purchased as a pair, I didn't want to spend time designing a new one when there were other options to try.

Remontoire - Design 3 - Timing Belt drive.

I only really included this for the sake of completeness as I didn't particularly want include something as obviously modern into a wooden clock. I just think it would look odd.
Any way the arrangement is exactly the same as the previous one but the belt and pulley were used in place of the ladder chain and sprocket.

I only had 2 pulleys available for this test so the tension pulley was left off, in retrospect this was probably a mistake, as it was difficult to keep the teeth on the belt engaged with the pulley on the rewind. I used some small guide pulleys instead and in the main they worked but occasionally it would slip and lose sync.Had I used a third pulley and a tension weight it would have worked fine.


Remontoire - Design 4 - Clock Chain drive.

I probably should have started with this one as, chains have been used to drive clocks almost from the very start. I used a Chain /Sprocket Grandfather clock repair kit that worked quite well fitting it into the rig. https://www.cousinsuk.com/product/conversion-chain-kits?code=L33579

It worked straight the way and never slipped, jumped or went out of sync, its only problem was that it may have been a bit coarse being a 33 links/foot chain so next time I would use a 42 links/foot and redesign the sprocket to suit.

To clarify where the remontoire would sit in a finished clock.

Conclusion

In conclusion then it seems clear that the concept can work alongside the woodenclocks gravity escapement, and would add an interesting visual feature to the clock when built.
Clock 26 will now be designed with the Remontoire shown in design 4 included.


A video of all 4 of the escapements in action can be viewed here https://youtu.be/FIBXzdK0y7A

Compound Pendulum

After writing the article on the simple pendulum calculation, I had fully intended to follow it up with an article on the Compound pendulum, but as it turned out my efforts to do the calculation for this proved to be based on the wrong equations so after struggling for some time to find the right solution I finally appealed to the many clock builders on my mailing list for help.

It didn't take long to get 4 responses with suggestions as to how to do it. 

The first was from Roger Bunce who sent a page from his copy of  'Workshop Calculations, Tables, and Formulae by F. J. Camm'. 

You use the formula to calculate the equivalent pendulum length of a simple pendulum from the lengths a and b in the compound pendulum. The resulting length can then, of course, be used in the simple pendulum formula to calculate the period.

It should be noted that the length b in the diagram should be to the centre of the top weight.

Next was a link from Rus Thomas to an Excel file on Paul Rogers website for his 'compound pendulum period calculator'. This is an excellent resource offered by Paul and allows you to calculate both simple and compound pendulums. I have used this further down to illustrate how it can be used for your own calculations.

Next came a suggestion from Robert Miller who suggested searching on the works of Henry Kater, which I did but must admit I struggled to understand how to use the data provided.

Finally from Guy Winslow who provided a link to a calculator called  Eureqa. I watched a couple of the videos and couldn't figure out how I would actually be able to use it. 

So, in the end, I have settled on using the Excel file from Paul Rogers.

Excel Calculator

The reason for wanting to do this calculation was to use a much shorter 'seconds' pendulum in a mantle clock is a clock that could sit on a shelf without having the 1-meter long pendulum protruding through it. The double ended pendulum allows this because when you put a second weight above the pivot point it slows the clock down so you can shorten the length to main weight quite considerably.

If you are interested in doing this you can download a copy of the Excel file here. I have modified this slightly so that only the cells that you need to interact with are visible.

The image above shows my modified file with the inputs in the pale orange and the calculated values in green. 

My first calculation assumes that both are going to be equal which simplifies the initial setup, but this is not necessarily how it will finish up as you can always make the bottom weight larger than the top which is quite normal. Not sure that it would work so well in practice if you make the top larger than the bottom.

It should be noted that the weights are assumed to be cylinders so you need for a start to input the diameter and length of the weights you are going to use. If your weight is not a cylinder in this orientation then you need to adjust the values of diameter and length to the proportions of your weight and adjust until you get it approximately right. 

Now input the values for H1 and H2 and you should see immediately a value for the Period in seconds. 

I have a value of 2 seconds for the period (well almost)  which is 1 second to swing in one direction and then 1 second to swing back again. I have achieved this by inputting the value for H2 which is the maximum length I can have for the clock that I am designing, and then keep on adjusting  H1 until the value is reached.

At this stage, you could also introduce some changes to the sizes of the weights to arrive at a solution that produces a better aesthetic to the pendulum.

A couple of things to note here are that the values for H1 and H2 are assumed to be to the centre of mass, in reality, should consider the weight of the rod as well, but it is a quite small difference so it has been ignored here.

The other thing is there may be other factors that will affect the movement of the pendulum over time, and in the way, the clock is constructed, so adjustment should always be allowed for in positioning the weights on the pendulum when it is finally built and running.

Generally speaking, the following rules apply:-

To increase the period:

Reduce H2

Increase H1

To decrease the Period:

Increase H2

Decrease H1

Keep H1 smaller than H2

Keep M1 smaller or equal to M2

Goal Seek

Too enable you to more quickly adjust the values for length and or weight, Excel has a function called Goal Seek that can be used to quickly zero in on a value that you are seeking. For instance, I require a value of 2 seconds for the period but it would take a lot of time to manually increment the value of H1 to achieve this so Goal Seek can be used to speed up this process.

To get there go to the Data tab and click, then go to 'What-if Analysis' and then click on 'Goal Seek', that will bring up the screen shown below.

To fill out the Goal seek box first click in the 'Set cell' box and then click in the box containing the value for the Period. 

Next, enter the value you want in seconds in the 'To value' box.

Now click in the 'By changing cell' and then click in the box containing the value for H1.

Finally, click OK and it will work out the value for H1.

The result is shown above, the period is now very close to 2 seconds and the H1 dimension has been reduced to 196.6784399 to achieve it. You can do the same thing for H2 or the weights.  

It seems to work better if you fix H2 and recalculate for H1 than the other way around.

The photograph above shows the test rig for the woodenclocks gravity escapement fitted with the double ended used to test the calculated results from the Excel file.