go to the page above this one “Making helical gears” 


Making helical gears by rotary copying

Copying on round surfaces (I)

It is possible to use a milling machine to make a copy of a flat template by using a pin which follows the template to control the movement of the milling cutter. It is also possible to do this on round surfaces. The example shown is a system for cutting helical gears.

This idea goes back to the 1940’s and was based on work done by J S Eley and was written up in the Model Engineer. It was made to cut helical gears needed for internal combustion engines. This is normally done by a much more complicated system using a dividing head.

The idea is that a spindle with a chuck holding the workpiece also has a round drum on it. This drum can have a template fitted to it.

Fig.  Mike Sayers rotary copying device – xxx

As the user rotates the drum the workpiece is turned by a fixed pin acting against the template. At the same time the workpiece passes the cutter on an arbor in the vertical spindle.

The problem is the fixed pin. In the Eley/Sayers method, the fixed pin is fitted to the milling table. The rotary part is then mounted on a dovetail slide that is fitted to the milling table.

Somewhere else on this website there is a problem that requires a pin fitted to the column of the milling machine. If this can be done then the rotary part is fixed to the milling table. The rotary part then moves against the pin by simply moving the milling table along.

The rotary part is, in fact, a dividing head with the worm disengaged. On the back of it an extension shaft has been fitted. On this is mounted a drum.

x232 rotary copying - the drum

x232 rotary copying – the drum

fig the drum

The holes are for fitting the template.

On the drum if the template that the pin slides against. There is an indexing system so the workpiece/shaft/drum can all be turned round for each flute as it is milled.


fig rotary copying using a fixed pin

Fitting the pin was far more tiresome than expected so another version was tried. In this the rotary part slides on a dovetail fitted to the milling table.

fig rotary copying using a dovetail slide with pin fitted to milling table.

In either case the friction between the template and the pin is such that the system will not work. It is essential the the pin has a bearing fitted on it so it rolls against the template.

fig details of pin

      This only cuts one flute of the helical gear so the system allows for the workpiece to be indexed round though the drum stays in the same place. The spindle is moved forwards again and another flute is cut.


In the Eley design the whole of the spindle system is itself mounted on a slide which is mounted on a base. The fixed pin is mounted on this base. All of this is fitted to the milling table. This means that the whole process is self-contained – the milling table does not move.

Harrogate 2009 – Dave Fenner – mew 152 p39

Gadget for spiral milling – “a master spiral”

 Copying on a round surface (II)

Alternatively, some of this hardware is necessary because of the need for a fixed pin. Using the device used mentioned here, earlier, a pin is fixed to the column of the machine. This pin was shown earlier where it was used for copying a flat template. In this role it is necessary for the pin to be adjustable in the x and y directions since the position of the spindle on the device and the vertical spindle are fixed. The workpiece is held on an arbor. This is held in a chuck which is mounted on the spindle of the dividing head. At the other end of the spindle there is a holder for the template. There is also a mechanism for indexing the spindle relative to the template.


Fig. helix cutting device

In the figure the spindle is that of a simple dividing head. The geared drive to the dividing head is disengaged. All that has to be added is the indexing template carrier. This is fitted to the rear of the dividing head spindle. This spindle happened to have a spare length of thread on it. The drum is screwed onto this. It is essential that the drum and the spindle are locked together.

The vertical head spindle holds a gear cutter on a stub arbor and is tilted to the angle of the helix needed.

All of the movement of the table is limited by using the x-axis stops. One y-axis stop is set to limit of the depth of cut. During cutting the y-axis is locked.

For the first cut, the table is moved to the left. The spindle is locked on the zero position. The template is set by loosening it and letting rest on the height setting pin. It is then locked to the spindle. The cutter is turned on and the table is moved right with the template following the pin. When the first tooth has been cut the y-axis is unlocked and the workpiece moved away from the cutter and the table moved to the left. The template is loosened and the dividing head moved round to the next tooth. The template is placed on the height setting pin and then locked onto the spindle and soon on.

Making the template

Helical gears are covered in greater detail elsewhere. But this is a good place to cover one particular detail. This is the helix angle of the gear we are making and the shape of the template.

If a piece of paper with a straight edge is wrap round a round bar we can do it so the edge meets itself after having gone all the way round. In this case the angle of the edge to the axis of the round piece will be 90?. If we twist the paper the edge will be at a smaller angle and when it goes round it will not meet up with itself. If we draw a line along the side of the bar we will find the paper crosses it at one point and then another at some distance from the first.

The distance from the first to the second is the “lead”. Clearly the lead is a function of the helix angle and the diameter of the bar.

If the lead is L, the helix angler is alpha and the diameter of the workpiece is D


L = D x pi x cot (alpha)

This explains why on the above device the angle on the gear is clearly 45?. But the angle on the template is not. The reason is that the lead of the gear and the lead of the template are what matter. In spite of the different diameters the lead of the gear and the lead of the template are the same.

From this we can work out the angle of the template. The template is equivalent to the edge of the piece of paper. It is a straight line – when flat. When this is wrapped round the drum it forms part of a helix. We can work this out as follows:

L                 The length of the                   gear and the                              template

D(gear)                 diameter of gear

D(template)       diameter of                         template

Alpha(gear)       helix angle of gear

Alpha(template)   helix angle of                      template

D(gear) * cot (alpha(gear)) = D(template) * cot(alpha(template))


D(gear) * cot (alpha(gear)) / D(template) =     cot (alpha(template))

Helix angles greater than 45? ****

Helical gears are covered in greater detail later. But an interesting feature of all of these sorts of devices is that it does seem more difficult to machine helix angles that are greater than 45?.

However, if the milling machine is being used in the horizontal mode, i.e. using the horizontal socket, but with a stub arbor, then with the Sayers device on a sub-table it might be possible to cut helix angles greater than 45?. This is possible because the Sayers device has it own sliding movement – it does not depend upon the ability of the milling table to move at a large angle (or any angle at all).

A video of a similar system can be seen here:


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