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Carry Detection and Propagation

(Eight of each assembly are required)

Addition in the difference engine proceeds in two phases. In the first phase, numbers are added digit by digit, and then in the second phase, any carries that were generated in the first phase are added to the result. The pictures below show the assemblies needed to accomplish the detection and subsequent propagation of carries. The axes which carry the digit wheels rotate four revolutions per cycle of the machine. During the phase where digit by digit addition is taking place, if the output digit wheel passes from 9 to 0 then a carry must occur to the next higher digit in the same column.
Carry detector
Detection of the carry is very simple. A 2½" gear wheel mounted freely on the bolting axis engages with the upper 2½" gear of the digit assembly. This gear carries an angle bracket mounted by its slotted hole to one of the outer round holes of the gear. Be careful when positioning this to make sure that the teeth of the gear fully project beyond the angle bracket.

When the digit wheel advances from 9 to 0, the angle bracket trips a pawl which releases a spring loaded carry assembly. In the subsequent carry phase of the cycle this assembly will be reset, resulting in the addition of one more count to the next higher digit wheel.
To the right is the simple assembly which mounts on the rod carrying the trip pawl. The tension spring is attached by a 3/8" bolt. After assembly, the other end of the spring fits over a rod in the rearmost row of holes in the flanged plates of the framework and provides the tension to hold the carry trip pawl in place. A stop is provided by a short threaded pin also mounted in the flanged plate of the frame.
Carry pawl retainer
The components of a carry assembly are shown below. A face plate with boss down carries a 1½" narrow strip, an angle bracket, and a tension spring, held on a 3/8" bolt. The angle bracket should be held at the end of the slotted hole and aligned such that the vertical end is flush with the edge of the face plate and shown in the picture to the right. The other end of the tension spring will be slipped over the rod of the carry axis and provides the force required to set the carry once the pawl is tripped by the digit wheel advancing from 9 to 0. Shown on the left, on the underside of the face plate, a ratchet wheel is connected by a socket coupling. This assembly must be free to turn on a rod so select and adjust parts carefully to make sure there is no binding. The assembly is completed by a short threaded pin which carries a ½" pulley without boss held in place by a collar.
 Carry assembly
Carry assembly  
The ratchet wheel will engage with a pawl mounted on a 2½" gear wheel by a pivot bolt. A small spring to hold the pawl in engagement is formed from about ½" of spring cord and two hooks for spring cord. In operation, when a carry is detected the spring loaded carry assembly is released and rotates until the narrow strip hits a stop, allowing the pawl to pass over two teeth on the ratchet wheel. In the carry propagation phase when the assembly is reset, the gear will be carried through 1/10th of a rotation. The gear engages with the 2½" gear of the digit wheel, thus advancing it by one count.
Carry wheel
carry actuator arm
The carry assembly is reset by an arm rotating on the rearmost axis, the carry axis. The arm is simply a 2" rod mounted in a coupling. The length of the rod protruding needs to be carefully adjusted for correct operation of the carry mechanism. as it rotates the rod will engage with the pulley on the carry assembly if set, bringing it back to the reset position and advancing the digit wheel one count.

A single grub screw in the coupling is insufficient to ensure no slipping under the load of operation. To overcome this problem, the coupling is sandwiched between two bush wheels with a 1" rod locking all three components together. Now the load can be carried by the set screws in the bosses of the bush wheels. The bush wheels are bolted together by a 3/4" bolt with a short coupling as spacer in the hole opposite the 1" rod.

A total of eight of each of the items described above will be required. The pictures below show two views from the rear of the machine of the components assembled together. Note that between the carry assembly at the bottom and the carry detector gear at the top is the bolting assembly. The bolting assembly is the only item rigidly attached to the rod, the other components are all free to turn on the rod, held in place by collars.
carry assembly
carry assembly
The view to the right shows a somewhat clearer view of the carry trip pawl and associated mechanism.  A compound rod runs from top to bottom.  The coupling is fixed only to the lower segment at each joint and the upper rod is free to rotate in the coupling. The picture is actually showing the lower half of one trip assembly (at the top of the picture), and the top half of another trip assembly (in the lower part of the picture). At the top the position of the trip pawl can be seen relative to the angle bracket on the trip gear. In the lower half, a second pawl can be seen. This one retains the carry assembly against the pull of the tension spring. When the trip pawl (on the rank below this one) is pushed by the turn of the trip gear, the carry assembly is released and rotates till the narrow strip contacts the vertical rod seen to the right of the picture. The pawls are returned to the idle position by the lower spring attached to the double arm crank. Not visible in the picture is the threaded pin mounted in the hole right behind the rod carrying the crank which provides the stop to position the pawls in the idle condition.

As  the carry axis subsequently rotates, the 2" rod pushes against the pulley returning the assembly to the idle position and carrying the 2½" gear with it. Since this gear is in mesh with the gear on the digit wheel, the digit wheel is advanced one unit. If in advancing, the digit wheel passes from 9 to 0, the carry assembly on the rank above will be tripped to propagate a carry to the next more significant digit.
carry release pawl
Although in any given column, carries are only propagated every fourth rotation of the main crank, the carry axes actually rotate at half the rate of main crank, though only every second turn actually results in carries propagating. The reason for this is that carries must ripple up from the bottom of a column to the top. That is, when a carry adds one to a digit wheel it is possible that that wheel will, as a result, move form 9 to 0, generating another carry to the digit above. Thus the carries
must be propagated sequentially from digit to digit up the column. To achieve this the carry arms are arranged spirally on the carry axes. In order to get the carry operation completed in one turn of the main crank, the carry axes must revolve more quickly than they would if only making one turn per full cycle of the machine. On every other rotation of the carry axis, since no addition has preceded it, there naturally are no carries to propagate and the carry axis rotates with no action resulting.
This is in fact one aspect of the machine that would not scale up directly to numbers of arbitrary numbers of digits. Babbage recognized this in his original plans and to accommodate the time required for the carry propagation he also staggered the digit by digit addition up the columns, which had the desirable side effect that the load on the drive is more uniform. However, for this very small scale model which does not handle large enough numbers for this to be an issue, I preferred the simplicity of having all the digits be added simultaneously, which makes setup and alignment of the machine much simpler.

    Arrangement of axes and drive system
    Decimal digit storage

    Digit readout and addition
 > Carry detection and propagation
    Setup and adjustment
    Parts list

Last modified:  16 July 2004

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