Introduction

A CURTA model II mechanical calculator is simulated in all its visible operations.

In the drawings above you see the machine in a front view at the left and a top view at the top right.  For ease of understanding a synoptic view of the registers is added at the bottom right.

Operation

At the start all registers show zero, the crank is in the adding position (down), the counter inversion switch is up (counts positively) and the register clear handle is at the right.

(click the "Show Legends" button to show the names of the parts)

To operate the calculator:

• Slide the red and black sliders up or down on the input register to set an input number.
• Click the crank handle in either the top or front view to make it perform a single revolution, this will add the number of the input register to the result register, and will add one to the counter register.  The crank only turns in clockwise sense.
• Click the cap in the front view at the left or the right to make the cap turn by one position or drag it to another position.  This is used for multiplication and division.
• Click the crank in its axle on either view to make it go up or down. When it is up a red ring shows to warn you that the machine now subtracts the input number from the result (it actually still adds, but adds the ten's complement).
• In the top view, click one side of the clearing handle to clear the register on the side you clicked.  The handle will then rest at the other position between the result and the counter registers.  There is no way to clear the input register except by sliding all sliders up to their zero position
• Slide the counter inversion switch to its down position to make the counter subtract one at each revolution.  This is used when dividing.

About

A CURTA model II is used for this simulator:  11 input digits, 15 result digits, 8 counter digits and 8 shift positions.  Parts shown are:

This simulator of the CURTA mechanical calculator is written in SVG and JavaScript.  We don't try to do better than Jan Meyer's flash simulator from 2008.

The simulator only shows how to operate the machine.  It does not show how the carry mechanism is implemented, how the clearing of registers works internally, how the ten's complement is computed.  I.e. it lets you operate it but it does not tell you how it actually works.

Limitations

There is no attempt at 3D visuals:  the model is "flattened" on purpose because the number of digits is too high for them all to be visible at once from the front. The impact on operation is minimal.  The most significant deviations from a real view are:  (1) all sliders of the input digits are visible and the space between them is more than halved, (2) the counter inversion switch has been moved very close to the right of the first input slider whereas in reality it would be out of sight.  The resulting image looks "flat" but still has the same silhouette as the real machine.  The top view displays the machine as accurately as necessary.

The commas/thousands separators are not shown.  On the real machine there are three in the bottom groove and six in the top cover groove.  Their presence is not necessary for understanding how to operate the machine.

Parts

Parts shown are:

• a flattened input register with the cursors for the 11 input digits and the counter inversion switch
• a top view of the cap with the crank, the result and counter registers and the clearing handle,
• the three registers in linear form.

Interactions

• the cursors of the input register and the inversor switch can be dragged to desired positions,
• the crank handle can be clicked to turn one full turn,
• the crank can be clicked to change between the pulled-up to the pushed-down position,
• the cap can be shifted left or right one position at a time,
• the clearing handle can be clicked to clear either of the result or counter registers.

Thus, for the cap:

• the crank always rests in the same position and does not rotate with the cap,
• the clearing handle rotates with the cap,
• the clearing handle always rests in one of the positions between the result and counter registers.

The SVG object hierarchy is:

• MachineFromTop turns if the machine is turned
  • Cap with registers and clearing handle, turn together
  • Crank turns with the machine but is independent of the cap.

Objects:

register I of 11 input cursors I01 to I11

register R of 15 result digits R01 to R15

register C of 8 counter digits C01 to C08

crank or drum handle H

counting direction switch D

clearing handle E

cover: the painted cylinders covering the inner mechanism, usually painted grey, green or blue. Top part slides over bottom part.  Bottom part has the input register.

Values:

register R shift position S

clearing handle position P

How the simulator was made

To work with whole numbers, the dimensions of the actual machine are expressed in tenths of a mm, thus what in reality would be 3.4mm would here be expressed as 34. Angles are in degrees and to avoid dealing with negative angles they may be greater than 360.

Objects are generated around 0,0 as their object centre, then transformed as needed.

There are 15+8+11 = 34 digit wheels.  Each digit wheel on the cap is represented as a black background rectangle with a white digit.  Since the digits need to change, each digit is a clone of one of ten digit glyphs.

Dimensions and Coordinate Systems

Top circle: (in 0.1mm)

inner diameter: 510

digit width: 25, inter-digit space: 42 inter register space: 72

angle between digits: 15º

15x(14+7)=315, leaves 360-315=45, or 22.5º on each side between the registers.

Let 0º pass through the centre of the result register's first digit.  Let angles increase clockwise (they do so in SVG anyway). Then:

• Input register digits are at 0, 15, 30, …, 150 degrees,
• Result register digits are at 0, 15, 30, …, 210 degrees,
• Counter register digits are at 210+22.5=232.5, 247.5, …, 337.5 degrees.

This helps in deciding when to set a digit to 0 as the reset handle passes over it.

Clearing Registers

In the real machine there is something sophisticated going on:  when the clearing handle turns clockwise, digits are cleard slightly ahead of the handle, if it turns counterclockwise they are cleard slightly after the handle passes over them.  But this happens only at the start of the clearing operation, towards the end (before the handle reaches its resting position) digits closer to the handle and finally under the handle are cleard. This is very difficult to simulate, decide to do it under the handle so that we don't even have to simulate the rotation of the digit wheels.

The handle has two resting positions:  one in each of the centres of the register separation spaces (which themselves are -22.5/2 = -11.25º away from a digit's centre).  These positions are at 337.5º (resting position 1) and 232.5º (resting position 2).  However:

• When clearing the counter starting from position 1, we rotate counterclockwise, the angle decrements from 337.5 to 232.5 and remains positive throughout.
• When clearing the counter starting from position 2, we rotate clockwise, the angle increments from 232.5 to 337.5 and remains positive throughout.
• When clearing the result starting from position 1, we rotate clockwise, the angle increments from 337.5 and goes over 360. We can then either subtract 360, i.e. start from -11.25 and go to 232.5, or we can add 360, i.e. go to 232.5+360.
• When clearing the result starting from position 2, we rotate counterclockwise, the angle decrements from 232.5 and should stop at -11.25 but is being compared to 337.5.  We can again subtract 360 in one sense or add 360 in the other.

The problem with clearing the result could also be solved by using two different values for resting position 1:  337.5 for the counter and -11.5 for the result.  This solution is effectively used by comparing with cRegisterDivide1-360 in the result procedures.

To make it easier to decide when to clear a digit as the clearhandle passes over it, we move the clear handle in increments of 5º but because it starts at either -11.25º or 221.25º we begin by putting it at a whole multiple of 5º:  -10 or 220º .  Then, as its angle modulo 15 is zero, we clear the digit corresponding to its position.

Both resting positions are taken to be at positive angles.  After clearing the handle has to be in the other resting position.  This makes a more general mechanism so difficult that it is easier to use four unfortunately very similar routines rather than trying to fold them up into one.

Programming

All graphics are fairly simple SVG objects.  There are no images, only vector graphics.

The operations are performed in JavaScript (arguably the programming language with the worst ever syntax).  Because there are only three objects (the top view, the front view and the linear registers) I did not use an object oriented approach.  Everything is done with a few global variables and event listener procedures.

Trick for those who want to play with the code:  option-clicking (alt key) on the Show Legends button displays a grid of 100x100 units and a circle around the path of the clear handle.  This aids in positioning elements.

Using stroke-dashoffset to simulate rotating the cap in front view works well but is of course a trick.  It avoids having to clip.

All graphic objects that are referred to by id have their handle stored during the setup phase, so there should not be uses of document.getElementById after setup.  During setup (i.e. inside the Setup() function) there are a few local references, used only to position graphic elements.

A few numbers remain in the code:  they are small offsets to make things look slightly prettier and it was deemed not worth the trouble to define them as parameters:  they would have needed very long names and are used only once and only during seetup.  An example is the distance from the top cover of the CURTA name.  These numbers are marked in the code with the word tweak.

Graphics

At first the digits were taken from Helvetica, no font was found to be closer to the Curta's digits.  A possible solution would be to use a path for each digit instead of a font glyph, and this was ultimately adopted.  There is no noticeable increase of processing time.

SVG filters were used to show some 3D and lighting effects.  These do introduce a noticeable delay when clearing registers because the clearing handle has to be redrawn with a different lighting at each position, and furthermore the two little buttons have to be separate with a separate filter.  Finally, the filters do not turn with the objects, it is impossible to make them rotate, they do not work in Firefox and there is no way to modify their attributes satisfactorily.  In the end I abandoned them infavour of simple flat fills.

The real machine in front (side) view is a cylinder. On the model II not all input digits are then visible and the counter inversion switch is most of the time out of view. I rolled the cylinder out flat, but then the cap's 15 digit positions become very wide and the counter switch is far away to the right. To cope with that I took a few liberties: only show 11 positions of the cap at a time and put the counter switch adjacent to the first input slider.

Making the interslot step 1.8mm instead of 4.8mm makes the flat front image look much better and the sliders then all fit into a space that corresponds to the width of the actual machine when seen from the front.  I decided to leave it flat, despite the relative ease of introducing a round look to some parts.

Issues:

On my machine the crank is the only element made from plastic.  There is a triangle on top of its axle centre, it points to the counter digit that is currently incremented or decremented.  The paint of this arrow is yellowish, probably because of age (I bought my Curta in 1969).  I reproduced this yellowish colour but should perhaps use plain white.

Most of the machine is black.  To distinguish parts levels of grey are used as fill colours:

• #000 for stroke, fill background of digits (wheels)
• #222 for the cap, bottom
• #333 for surfaces that are inclined 9usually 45º or close to that)
• #444 for surfaces that are horizontal (mainly for the top view) or are the bottom of the grooves

Symmetric paths have their origin in the centre.  Rectangles have their origin at top left;  Digits (unfortunately?) have their origin at bottom left instead of centre.