The operating heart of a pinwheel calculator is a cylinder made up of a series of disks or wheels stacked side by side. Every wheel has a setting lever and a series of nine pins, each of which can be made to protrude or retract according to the position of the setting lever.
In the illustration, the
setting lever is set to five and five pins protrude from the
surface of the cylinder. When the whole cylinder is rotated, the
protruding pins mesh in turn with a transfer gear which advances
the output register by five divisions.
The pinwheel
cylinder of a Brunsviga calculator with 4 set in the ninth
position. Once set, the whole cylinder can be locked together and
rotated as a single unit.
A close up of the four
protruding pins on the cylinder.
To perform a very simple calculation such as adding 3 to 5, the action is as follows:-
This is the principle of operation. To perform a subtraction, the handle is cranked in the opposite direction. Multiplication or division is carried out by repeated addition or subtraction.
For all but the most simple of calculations, it is necessary to allow for a carry from one decade to the next. Unfortunately, it is difficult to implement a carry on a mechanical calculator.
Why?
The carry process requires input from two sources. A given figure wheel has to decide:-
Implementing this sort of thing in brass and iron would quickly result in little heaps of gear teeth in the bottom of the calculator and a jammed mechanism.
A problem is that the carry has to be added sequentially from right (units) to left, one digit at a time. This is because a carry might in itself generate a further carry if added into a "9". This implies that the arithmetic has to be carried out sequentially, one digit at a time.
First, the units have to be added and any carry generated added to the tens. Then the tens have to be added in on top of the carry and any carry generated from this has to be added to the hundreds and so on...
This can be done. All we need to start with is space on the cylinder for the nine "units" pins, then we need a small gap. Then we need space further round the cylinder for the nine "hundreds" pins, then we need a small gap. Then we need ... hang on, we've gone right round the cylinder. We need a bigger cylinder.
In practice, this method would either require an unreasonably large diameter cylinder or a calculator limited to three or four digits.
Try something else
An alternative would be to arrange the pinwheels so that they did not revolve as one unit. The first turn of the crank would move the units pinwheel, advance the tens figure wheel and attend to any carry. The second turn of the crank would then move the tens pinwheel and so on. For a ten digit calculator made in this way, the addition of two numbers would require twenty turns of the crank. This seems excessive.
Is there a better way?
The method that is generally adopted is to separate the carry procedure from the main process of arithmetic. This means that the arithmetic can occur simultaneously on all columns of figures and only a small diameter cylinder is required. (In practice, the various pin arrays are staggered very slightly, just to avoid the mechanical strains involved if many gear trains had to be started simultaneously.) During the arithmetic process, any carries necessary are "flagged". Once the arithmetic is complete, any carries that have been flagged can be processed sequentially, from right to left one digit at a time. Since the maximum possible value for a carry is 1, a staggered array of individual carry pins can also be accommodated on the small diameter cylinder.
How is this achieved?
Each pinwheel has a carry pin permanently protruding from its rear surface. This carry pin is mounted so that it can move slightly sideways and it is spring loaded to one side. In its normal position, as the pinwheel cylinder rotates, the carry pin misses the transfer gear and has no effect. If, however, the carry pin is made to move sideways, against its spring, it will be able to mesh with the transfer gear and advance this by one position.
So far so good. What is needed now is some means of setting the carry pin into its active position when a carry is required.
In order to do this, each transfer gear / figure wheel pair is fitted with a carry warning cam, which can be set or cleared. In the cleared position, the carry pin misses the cam as the cylinder revolves and the cam has no effect. When it is in the set position, the cam lies in the path of the carry pin and the moving pin hits the surface of the cam. The carry pin is pushed sideways by the cam so that it meshes with the transfer gear whence further rotation of the cylinder advances the gear by one position.
The carry cam becomes set when a figure wheel in the output register revolves through nine to zero. It is cleared automatically once the carry had been added.
Now we are nearly there, but there is still the problem of a carry generating a further carry. (For the sake of the description that follows, the far right pinwheel is called number 1, its neighbour to the left, number 2 and so on.)
The movable (arithmetic) pins lie in a narrow zone on the front face of the pinwheel cylinder. As the cylinder is revolved, the number set up on the individual pinwheels is transferred via the transfer gears to the figure wheels of the output register. If any figure wheel in the output register has revolved past 9, then its carry warning cam is set.
The carry pins are arranged in a staggered array across the rear face of the pinwheel cylinder, so that they come into operation sequentially. The first to take effect is on pinwheel 2. Now, if the carry cam for figure wheel 1 is set, then the carry pin on pinwheel 2 is pushed sideways, meshes with transfer gear 2 and advances it and figure wheel 2. So the carry from figure wheel 1 is added to figure wheel 2.
If figure wheel 2 has just moved from 9 to 0 then carry cam 2 becomes set.
As the crank handle continues to turn, the carry pin on pinwheel 3 comes into position and in striking carry cam 2 gets pushed sideways into transfer gear 3 etc, etc.
In this way, any required carries are passed along the output register from right to left, one digit at a time.
The
image shows the carry mechanism of the Marchant calculator. The
upper half shows the pinwheel cylinder with five staggered carry
pins descending diagonally from the top left. As the cylinder
rotates, the carry pins will move downwards. In the centre, just
above the figure wheels, there is the horizontal array of
transfer gears and carry cams. The rightmost carry cam has been
set and the corresponding carry pin is just about to engage with
the curved surface of the cam which will push it sideways to the
left so that it will engage with the transfer gear and increment
its figure wheel in the foreground.
NOTE: The calculator is in the process of adding 1 to 9. The rightmost (units) figure wheel has just advanced from 9 to 0. The zero would show through a window in the front panel of the calculator. As the pinwheel cylinder continues to rotate the carry pin, in moving downwards, will advance the transfer gear and the (tens) figure wheel, which would then show a 3 in the top line and the 1 would move down to be visible in the display window.
The Marchant
calculator is a variant on the pinwheel system. In this case the
cylinder is fitted with a gear segments whose 9 teeth all move as
a single unit. The position of the setting lever determines the
position at which the teeth retract into the cylinder. If, for
instance the setting lever is at position 2, then the gear
segment retracts suddenly after the transfer gear has been
advanced two positions and before it can be advanced further.