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Circular Motions


The calculating cycle requires intermittent circular motions of the figure wheel axes, the sector axes, the warning and cany axes. The circular motions are smooth (i.e. have no sudden discontinuities), intermittent and reciprocating. The circular motions are executed in turn by the odd and even axes in a phased sequence as specified in the timing diagram. The circular motions of the carry axes which drive the helical arrangement of carry amns are not derived from the circular motion cams but from an intermittent drive mechanism coupled to the main drive socket This is described in the Drive section: this section describes the circular motions of the figure wheel, sector and warning axes.

Figure wheel circular motions occur during giving-off and during restoration by the sectors of the number given off. During giving off the figure wheel axes rotate the figure wheels to the zero stops by driving the giving-off arms against the internal lugs of the figure wheels (171). After giving off, the vertical rnotion mechanism raises the figure wheel axis. This disengages the arms from the internal lugs by lifting thern clear. In the raised position the figure wheel axes return the giving-off arms to the home position until lowered to reengage at the start of the next calculating cycle. The circular motion therefore consists of two separate sweeps, one a drive stroke and one a return stroke, separated by timing gaps and phased with the vertical motions.

The sectors store the number given off and, after a timing interval, restore it to the figure wheels. During giving off the sectors are driven by the figure wheels. When restoring, the sectors are driven by restoring arms which are keyed to the axis and drive against the internal lugs of the sectors. The sector axes and the sectors are lifted clear of the lugs by the vertical rnotion mechanism and the restoring arms return to the home position ready to be lowered for the next cycle. The circular motion of the sector axes therefor consist of a drive stroke which restores the number to the figure wheel and a return stroke, separated again by timing gaps and phased with the vertical motions.

The circular motions of the warning axes reset the carry warning rnechanisrns by a forward sweep followed irnrnediately by a return sweep which restores the rnechanisrn to the unwarned position.

The circular motions are derived frorn the six pairs of conjugate cams located on the upper section of the cam stack (163). The twelve cams drive earn followers which rock on pivot shafts (159). The arrangement converts the continuous circular motion of the earns to reciprocating motion of the follower cams. The six sets of follower cams drive links to six long backing bars each of which carries four toothed racks which slide in straight machined channels. The backing bars join the racks but do not themselves slide in guide channels. The original design calls for six sets of four inline racks, one set for each of the four odd figure, odd sector and odd warning axes, and set each for the three sets of even axes (see 'Modern implementation for modification of racks for the warning axes). The arrangement translates the reciprocating circular locus of the follower arm extensions into linear reciprocating motion of the racks. The racks mesh with sector gears which convert the linear motions back into the required intermittent reciprocating circular motions for the axes ( 171, lower right).


Drawing References

Main drawings are 159 left and 170, also 160 and 163 for the vertical cam layout; 161 extreme right shows a partial detail of a sector wheel circular motion follower arm; 169 left is a printing cam and its significance is unknown. Modern drawings: the B-series.

The general layout is given in plan in 159 left which shows a set of three follower arms and partial cam profiles. The pivot for the sector follower is shown at ten-to-twelve, the warning follower pivot at five past twelve, and the figure wheel follower pivot at twenty-five to. Except for a rotational offset of the earns the layout is identical for odd and even motions and 159 shows only one set cams and followers i.e. the arrangement is duplicated for the alternate set but is not shown and the followers for the unshown use the same pivot shafts. 170 is a clearer version showing the full cam profiles for the even difference earn pair and follower in one view, with the arrangement for the other two motions shown separately on the left. The view on the right corresponds to the plan view of the uppermost two cams in the stack.

It is not immediately clear whether the layout shown on 159 left is intended to represent the odd or even cams or whether this view is intended to serve for both. One way of resolving this would be to establish the top-to-bottom sequence of cams. However, the convention of using dotted lines to indicate hidden edges is not strictly adhered to and differentiating the planes of the followers to establish how they are layered is not obvious. The sector and figure wheel followers in 159 (left), for example, are in different planes but are both drawn with unbroken lines and superimposed; the same is true for the two rollers at five-to-twelve. There are other signs of draughting inconsistencies: the two arms of the same figure wheel followers are shown in the same plane in 159 lower left, and in different planes in 170.

Unlike the vertical motion cam followers which have sliding contacts (sector followers are an exception, see Vertical Motion section) the circular motion followers use rollers throughout. In the case of the sector and figure wheel followers the links are driven by a simple extension of the follower arms. In the case of the warning followers the links are driven by an additional arm, integral with the follower arms. Unlike the vertical motion followers, where the arms for a cam pair and the associated bar lever are vertically staggered on the pivot shaft, the arms for the circular motion followers and the drive to the link are all in the same horizontal plane. For both types of circular motion followers the two rollers of a follower set are pivoted on either side of the arm so as to span the distance separating the two cams (160 shows this though identifying parts of the same assembly from this crowded drawing takes some hard peering). The drive extension arms have slotted forked ends which take pivots for the links to the rack assemblies.

The three lowermost cam pairs of the upper twelve cams in the stack generate the odd axes motions in the order bottom to top, sector axes, figure wheel axes, and warning axes. The uppermost three cam pairs generate the even motions in the order top to bottom, sector, figure and warning axes. So the upper and lowermost circular motion cam pairs generate the even and odd sector motions respectively, and the two cam pairs generating the odd and even warning axes motions are adjacent to each other in the centre.

The spacing between two cams of a conjugate pair of circular motion cams is wider than for the vertical motion cams. The figure and warning earns are a standard 1.25" apart; the separation of the sector earns is 0.75" (160, 163). So the two outermost pairs of circular motion cams (odd and even sector cams) are closely spaced and these sandwich the four more widely spaced cams between them. The wider spacing of the figure and warning axes earns allows the forked ends of the extension arms to pass between the cams. This is shown clearly on 170 left where the follower arm is shown on the inside of the roller. In the case of the sector arms, the forked ends are outside the largest cam diameter which allows the smaller spacing (170 right). The rollers on the figure and warning follower arms have longer bosses to span the separation of the of the more widely spaced figure and warning cams (160).

Description of Motions

Each figure wheel has four decades of numeral 0-9 i.e. 40 teeth with each decade occupying one 90o quadrant of a full circle. The maximum rotation of a figure wheel is 81o i.e. 9 increments of 9o representing a ten-digit interval (171). The internal lug occupies the remaining 9o sector. The circular motion of the figure wheel giving-off arms is therefore a fixed sweep from the home position to the zero stop position during giving off. This is followed by a vertical lift to disengage from the internal lug, and return to horne while the number given off is restored by the sectors. The width of the internal lugs is kept sufficiently small to prevent the giving off arm interfering with the lugs when the arm is next lowered after the return-to-home stroke.

The sector restoring arms execute a similar pattern of circular sweeps. In the fully lowered position the sector wheels engage the two adjacent figure wheel columns and giving-off right to left takes place. The maximum angular displacement of a sector wheel occurs if a '9' is given off. In this case the sector is moved through 81o from the zero stop position. However, the rest position of the restoring arm is shown 84o from the zero stop position (171). The 3o margin prevents the lug and the arm interfering by ensuring that the arm is well clear of the worst-case angular displacement of the internal lug. The '81o' inscribed in the circle representing the sector axis in 171 refers to the maximum displacement of a sector wheel and not the total angular sweep of the restoring arm.

This 3o clearance for the restoring arm accounts for the slight difference in length of the sector and figure wheel follower arms on 159 though the cam throws are identical. The distance from the pivot to the forked end of the figure wheel follower arm is 9.0". This is extended to 9.3125" for the sector follower arm. This gives a 0.1" longer stroke to the sector rack which corresponds to about 3" safety clearance for the sector restoring home position.


The numbering convention adopted for the vertical motion cams was extended to the circular motion cams. The vertical motion cams are numbered 1 through to 16 starting from the bottom of the stack. The circular motion cams continue the series from 17 through to 28, this last being the topmost cam of the stack. The circular motion cams and their functions are as follows:

  • 28 even sector arm restore
  • 27 even sector arm return
  • 26 even figure wheel arm give off
  • 25 even figure wheel arm return
  • 24 even warning detent restore
  • 23 even warning axis return
  • 22 odd warning axis return
  • 21 odd warning detent restore
  • 20 odd figure wheel arrn return
  • 19 odd figure wheel arm give off
  • 18 odd sector anm return
  • 17 odd sector arrn restore


The omission of the carry and warning axes for the 7th difference column removes the need for a rack for the warning axis circular motions. The rack for the first odd warning axis was omitted and the backing bar for the odd warning axes therefore has three racks instead of the four originally specified.

Because of the introduction of mirroring of alternate columns the direction of the active strokes and return strokes are reversed for the odd and even axes. For example, even sector restore stroke (170 left) occurs when the link pivot drives from right to left. In the duplicated arrangement for the odd sector axes (not shown) the odd sector restore stroke is from left to right.

Cam profiles

The cam profiles were generated from the known requirements for the circular motions. The overall shapes were confirmed on 159 and 170 by visual inspection rather than exact tracing and matching. The timing windows for the circular motions of the figure wheel, sector and warning axes were all shortened slightly to accommodate the locking action (see Vertical Motion section) and the detail of the original shapes was therefore in any event subject to minor alteration.

The even sector cams (Cams 28 and 27) illustrate the general relationship between cam shape and cycle timing. 170 right shows the position of the cams at the end of the even sector axes return stroke i.e. with the link at the right hand extremity of travel and the roller of Cam 27 at the top of the rise. This corresponds to 66o into the cycle (337B31). The even sectors do not rotate for the next 294o as indicated by the long sections of constant radius on both even sector cams. During this period the sectors undergo various vertical motions: they are lowered from their fully raised positions into full engagement for giving off odd-to-even and then lifted into half-engagement ready for the restore stroke.. Cam 28 then becomes the active cam and drives the sectors to the zero stops so completing the stroke which restores the number given off to the figure wheels. The end of the stroke occurs 354o into the cycle (timing diagram and 337B31). In the case of the circular motion cams the timing diagram and the angular distribution of events round the cam correspond exactly; in the case of the vertical motion cams, there were occasionally slight deviations. A short dwell of 12o follows during which the sector axis is fully raised. This corresponds to the sections of the cams where the profiles coincide (170 right view, bottom centre). The dwell occupies the interval 354o to 6o The return stroke follows which occupies the interval 6o to 66o During this period Cam 27 is active.

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