Sliders

The classic example of this type are Addiators, i.e. Troncet adders, such as the Pocket Adding Machine. The sliders that you push up or down also act as the register display.

Pocket Adding Machine

Wheels

On this type of machine the register consists of a set of wheels next to each other on the same axle. The Addimat / Schnellrechner is the obvious example. I consider the Golden Gem to be a direct drive adder with wheels, because its chains are essentially just extensions of the number wheels. A chain acts like a large flattened wheel that you manipulate.

​Addimat ​Golden Gem

Dials

Dials are wheels on an axis that is pointed towards you, so you have to do a circular motion to turn them. There are many dial adders such as the Calcumeter, Dial-A-Matic, Stephenson's adder, and the Kes-add. I would also include the Lightning Adding Machine, because its number wheels are directly and constantly connected to the dials. The dials do not have to be the same size, see for example the Webb Adder, and can be concentric, like in the BriCal.

​British Calculator ​Calcumeter ​Checkbook Balancer ​Sterling Dial-A-Matic ​Kes-Add ​Lightning Adding Machine ​Stephenson Adding Machine ​Webb Adder

Sliders

The best known example of a machine with semi-direct drive and input through sliders is the Comptator / Rapid Computer, but there is also the SuN, and the Stima.

​Peter Pan Adding Machine ​Rapid Computer ​The SuN Adder ​Stima

Wheels

The Resulta E7 is a good example of this type. Its predecessor, called the Minerva was still an adder with direct drive as it did not have a separate input register. The Triumphator KA also falls into this category, because its input levers are just a way of turning the wheels of the input register.

​The Resulta E7 ​The Triumphator KA

Dials

The only example of a semi-direct adding machine that uses dials is the Conto. Note that it adjusts the main register when the input dials are cleared rather than when the input is performed.

​Conto C

Buttons/Keys

Key-driven adding machines fall into this category. The register is updated during either the downstroke or the upstroke of a key. Examples of this type are the Burroughs Calculator, the Comptometer, Sumlock and Plus Adders, the Direct II and the Contex A/B. There are also small counting machines with buttons, such as the Aderes, the Alexe, the Benton Tally Register, the Denominator, and the Pocket Counter.

​Aderes ​The Alexe Mini Calculator ​Benton Tally Register ​Burroughs Calculator ​Baby Burroughs Calculator ​Comptometer E ​Comptometer ST ​Contex B ​The Denominator ​Direct II ​Plus Adder ​The Pocket Counter ​Sumlock 906

Stepped Drum

The stepped drum was first successfully used in a calculator by Leibniz, but it wasn't until Thomas de Colmar's Arithmometer that stepped drum machines were produced in larger numbers. Consider one gear, driving another gear of the same size. One revolution of the first gear causes one revolution of the second. If you were to remove the teeth from one half of the first gear, then a full revolution would only cause half a revolution of the second gear.

Now imagine that you have an axle on which there are ten gears, each with a different number of teeth, ranging from zero to nine. So you have one "gear" with no teeth, one gear with only one tooth, one with two teeth, and so on until the one with nine teeth. All of these are next to each other on a shared axle. On a parallel axle you have another gear, but you can slide it so that it can interact with any one of the ten gears on the first axle. In this way you can use a sliding motion to select how much the second axle is to be turned by the first axle. A stepped drum is essentially the set of ten gears on the first axle, but fused together into a single object. In its simplest form it is a cylinder with ridges of different lengths, but parts of the cylinder where there are no ridges can be cut away to reduce weight.

In the Thomas Arithmometer and its descendants such as the Unitas and the Archimedes, there is one stepped drum for each digit of the input. The input is through a slider or keyboard, and it sets the position of the gear that is driven by the stepped drum. It is of course also possible to move the stepped drum relative to a fixed gear. This even allows the stepped drum to be made of two halves, one half whose number of teeth range from 0 to 4, and the other half which is set to supply either 0 or 5 extra teeth. This is done in the Monroe calculators.

Stepped drums tend to be bulky, causing the register digits to be spaced far apart. The Rheinmetall avoids this by having two digits share a single stepped drum. An entirely different stepped drum design is used in the Curta. This drum is shared by all the input digits, which are arranged at regular intervals around the drum. Instead of ridges, the Curta's drum has small pins, similar to what you would see on a cylinder of a music box. The drum has 20 different tracks, alternating between adding and subtracting, one pair of tracks for each digit. Pulling the crank up for subtraction mode simply shifts the drum by one step, shifting from the additive tracks to the subtractive ones.

​Rheinmetall D II a ​Curta Type I ​Monroe Model K ​Unitas

Pinwheel

The pinwheel first became commercially successful with the machine designed by Wilgott Odhner. Although there were previous attempts to use the mechanism going back almost two centuries, only a few machines had been constructed using the principle.

A pinwheel is a gear with teeth that are retractable or extendable. Usually it has a lever attached to it that the user can move to select how many teeth the pinwheel gear has, ranging from 0 to 9 teeth.

The pinwheel has the disadvantage that when the pinwheel is turned, the setting lever turns with it. This means that there should be some kind of locking system to ensure the setting lever does not get moved inappropriately when the wheel turns. But more than that, the setting lever usually is short and thin because it has to go inside the body of the machine. Examples of these are the Brunsviga, Minerva, Original-Odhner, and Walther.

Some machines were made that had setting levers that disconnected from the pinwheels when the crank was turned, for example the Melitta. There are also machines that use an external keyboard to set the pins of the pinwheel, and Facit machines are a good example of this.

​Brunsviga Nova II ​The Facit C1-13 ​Melitta VII/16 calculator ​Minerva ​Original-Odhner ​Walther RMKZ

Other wheel mechanisms

The pinwheel allows you to select the number of teeth that are present on the gear, and once set this then remains constant while the crank or motor turns. There are other mechanisms in which pins are set during the rotation.

One way is to have a fixed camwheel with a setting lever with which the profile of the cam wheel can be changed. The rotating gear wheel next to it has a cam follower that changes the behaviour of the gear wheel as it goes through the rotation. The Hamann Manus has wheels in which the teeth are on a ring that becomes connected or disconnected as the axle rotates ("switching latch" or "latched gear" mechanism). The Marchant XL has wheels in which a toothed section is retractable during part of the rotation ("adapting segment" mechanism). The Numeria and the Kuhrt both use pins that can move sideways by a cam, though their implementation is very different.

​The Hamann Manus F ​Kuhrt A2 ​Marchant XL ​Numeria 7101

Toothed rack mechanisms

Instead of a wheel in which we select the number of teeth, it is also possible to have a linear rack with a variable number of teeth. That is what happens in the Thales KA - each key column is a rack, and the state of each key adds or removes one tooth. Pressing the lever pulls the number wheels along the racks, turning them appropriately. On the return journey the wheels travel at a lower height along a second set of racks which handle carries between the wheels.

One could also have a rack with a fixed number of teeth, but simply vary the distance that the rack moves to get the amount of rotation corresponding to each digit. The Brunsviga 90 KA has toothed racks that are pulled until they are blocked by barriers that were set up by pressing input keys on the keyboard. The Corema uses something similar. The Contex 10 uses a curved rack at one end of a lever, and the other end of the lever travels until it hits a pin that was set up by pressing a digit key.

Lastly, the Mercedes-Euklid has 10 parallel racks that move different amounts as a replacement for a stepped drum. It uses axles with gears that can slide along the axle and in this way select which toothed rack to engage with.

​Brunsviga 90 TA ​Contex 10 ​Corema Portative MC 15 ​Mercedes Euklid ​Thales KA

Other mechanisms

The only mechanism I know of that does not fall into any of the above categories is the one used in the later Marchant calculators, such as the Silent Speed and Figurematic models. Instead of a stepped drum for each digit, there is a 10-speed gearbox. Unlike all other calculators, this makes the number wheels turn at different speeds, but for the same length of time. Combining this with a carry mechanism that is a simple 10:1 gear ratio, the number wheels turn directly to the answer in one smooth motion instead of the start-stop motion of other machines.

​Marchant ACT-10M