How Pinwheel Calculators Work

How Pinwheel Calculators Work

The modern pinwheel calculator was invented
in the 1870’s in America by Frank Baldwin and in Europe by Wilgott Odhner. Pinwheel
calculators were very popular in Europe, where tens of thousands were in use until the 1970’s.
Calculators based on Ohdner’s design were manufactured by many companies, including
Brunsviga and Facit. The design shown in this video is a Triumphator Model K, manufactured
in Germany around 1915. All “pinwheel” calculators feature metal
wheels containing pins that extend radially and engage with a gear-driven accumulator
register when the wheels are rotated. The number of pins that are extended can be set
by rotating a slotted ring mounted to the pinwheel. Typically, eight or more pinwheels
and setting rings are assembled into a cylindrical “rotor” that is rotated by turning a handle.
To perform an arithmetic operation, the user enters a number – for example, 27 — using
the levers on the setting rings. Rotating the handle clockwise causes the number encoded
by the setting rings to be added to the accumulator, while rotating counter-clockwise results in
subtracting the number from the accumulator. Each column of the accumulator register contains
an intermediate gear, a numeral wheel, a detent lever, and a detent spring. As the pinwheel
is turned, each extended pin engages the intermediate gear and advances the numeral wheel by one
digit. The detent spring and the arms of the detent lever act as an escapement mechanism
to prevent the numeral wheel for over-rotating. Carry operations are accomplished through
the coordinated actions of the carry sensing lever and the carry finger. The carry sensing
lever contains a small, spring-loaded pin that presses against the side of the intermediate
gear shaft, forcing the lever to be in either a forward or rearward position. At the start
of an addition, the carry sensing lever is set to its “forward” position. If the
numeral wheel passes between 9 and 0 during an addition, a pointer on the numeral wheel
pushes against the tip of the carry sensing lever and forces the lever into its “rearward”
position. A ramped surface at the back of the lever
is now positioned so as to deflect a spring-loaded carry finger on the next higher rotor disc,
pushing the finger sideways into the path of the next higher intermediate gear, causing
the gear to advance the next higher numeral wheel by one digit. After the carry operation is completed, a
shoulder located near the back of the rotor disc pushes the carry sensing lever back into
its forward position. When the carry sensing lever is in its forward
position, the carry finger of the next higher rotor disc passes by uninterrupted and nothing
happens. The location of the carry finger on each rotor
disc is staggered to allow carry operations to ripple across the accumulator columns as
needed. A second set of carry fingers is arranged
symmetrically on the opposite side of the rotor to implement borrowing during subtraction
operations. The Triumphater Model K supplements its nine
complete rotors with four partial rotors that only perform carry operations, allowing a
wider operating range of numbers while reducing the cost of the calculator. The accumulator register is contained in a
carriage that can be shifted to the left or right, allowing multiplication and division
to be accomplished through a combination of repeated additions or subtractions and carriage
shifts. The carriage movement is controlled by the shift lever, which fits into a set
of slots in the base of the calculator that are aligned with the rotors. The carriage also contains a counting register
that records the number of rotor turns during multiplication and division. The intermediate
gears of the counter are driven by a single large tooth geared to the rotor shaft, which
advances the current column by one digit each turn of the rotor. The design of the counter register differs
from that of the accumulator in several ways. First, there is no carry mechanism, because
it is never necessary to turn the rotor more than nine times for any column. Second, the
counter wheels are numbered in a special way to avoid displaying 9’s complement values
when the rotor is turned counter-clockwise during subtraction. White numerals 0 through
8 are displayed for addition and red numerals 1 through 9 are displayed for subtraction.
The 0 and 9 are shared by both operations. Finally, because the number wheel has 18 teeth,
the intermediate gear has only nine teeth and is geared to the number wheel with a 2:1
reduction. The accumulator reset mechanism works as follows.
The center part of each numeral wheel is hollow, except for a small tab on the right side of
the wheel, located between the 9 and 0 digits. The accumulator shaft contains metal teeth
that are normally located on the left side of the hollow wheel, allowing the wheels to
turn freely. When the accumulator reset lever is twisted, a cam on the face of the shaft
bushing pushes the shaft outwards slightly, causing the teeth to move to the right side
of the numeral wheels, where they will engage the tabs and turn the wheels towards zero.
After a full revolution, the shaft returns to its original location and the keys disengage
the tabs. A similar mechanism is used to clear the counter register. When it’s not turning, the rotor can be
locked in a resting position by inserting a spring-loaded pin inside the handle into
a matching hole in the lower handle bushing. Locking the rotor causes three safety interlock
mechanisms to disengage. The first interlock prevents users from changing
the setting rings while the rotor is turning. This is implemented by a rotor locking bar,
which has a series of notches that can allow or block movement of the setting rings. A
spring pressing against the locking bar keeps it in the blocking position while the rotor
is turning. When the rotor is locked in its rest position, the handle’s locking pin
pushes against a rod attached to an arm that presses the locking bar into the open position,
allowing the setting rings to rotate. The second interlock prevents users from shifting
the carriage while the rotor is turning. This interlock consists of a slotted disc and an
arm that is lifted by the carriage shift lever while a shift is in progress. The arm has
a protrusion that must be aligned with the slot in the disc in order to allow the carriage
shift lever to be depressed. The arm is aligned with the disc only when the rotor is locked. The third interlock prevents users from clearing
the registers while the rotor is turning. The third interlock actually utilizes the
mechanisms of the second interlock. Two arms extend from the back of the carriage shift
lever and fit into a depression on the faces of the center bushings of the registers. When
a register reset lever is twisted, the bushing turns and pushes on the arms, forcing the
carriage shift lever downward. If the rotor is turning, the carriage shift lever is locked
in the up position, which prevents the arms from moving, the bushing from turning, and
the reset lever from twisting.

15 thoughts on “How Pinwheel Calculators Work

  1. Excellent question! The description of how to perform division is rather lengthy, so I have added a link to a web page with a good explanation of how to perform division in the video description above.

  2. I get the feeling computers was much easier to make than this machine lol. The power of the brain, yet man still say there is no god?

  3. Hello, I have a calculator similar to this, but I do not know the multiplication operation. I would like to know the procedure for this operation.
    Thank You, Mario

  4. Very nice. Thanks for doing ALL of these.

    You got a mention in the CRAV Computing (Classic/Retro/Antique/Vintage) Yahoo Group and Facebook pages:

  5. This is an excellent video – well done!!! For those who want to try using one, there is a pinwheel calculator simulator (Windows executable) available at and I have written instructions for using it at 

Leave a Reply

Your email address will not be published. Required fields are marked *