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The following section identifies issues of construction, assembly, and setting up that arose during the engine build.

Base Rails

Cast base rails were delivered dog-legged at the printer end i.e splayed outwards. We were contractually entitled to replacements but pressure to complete discouraged recourse to remaking. The alignment deficiencies in the castings were not corrected by machining prior to supply. The fixing holes for the upright framing members and for the legs supporting the bearings (which straddle the rails) are drilled into the machined palms on the rails. These were not aligned along the length of the rails. It appears that they were marked out by reference to two inconsistent datums possibly resulting from two separate stages of planing. The problem was solved by elongating the fixing holes in the legs straddling the rails and in the base of the uprights.

Cam Profiles

The cam profiles are determined for the ideal case in which the locus of the follower is a rectilinear path along the radial line of the cam i.e. the path that would occur with follower arms of theoretically infinite length. However, conjugate cam pairs have finite cam follower arms (of equal length) which rotate on the same pivot i.e. the locus of the followers is an arc, not a line, with a radius equal to the length of the follower arm For the idealised case, the rises on one cam would be mirrored as symmetrical inversions for the falls on the conjugate cam. In the actual case of short pivoted follower arms, cams designed for ideal follower trajectories could result in clearance gaps between the followers and the cams, or interference.

For example, an anti-clockwise rotating cam with a rise on the main cam drives the follower outwards (170 helps to visualise this case). If the arm is trailing then the sweep of the arc has the effect of lagging the follower behind the position it would take were the locus a linear radial one. At a given point in the rise the outward displacement will be slightly less than ideal with the worst case deviation from the radial line occurring at mid-rise. The effect of the trailing follower on the conjugate follower is to displace it towards the fall by less than would be the case for an ideal follower arm of infinite length. In this case the effect of the lag of the main follower on the conjugate follower is to create a clearance between the conjugate follower and the fall. However, there is a self-cancelling effect The follower arm on the conjugate cam is a leading arm. Because of the finite radius of the follower arm, the arc of the follower locus reaches forward, as it were, into the fall i.e. the follower leads the position is would occupy were the geometry ideal. The leads and lags so produced are self-cancelling.

In the example cited, the rise of the main cam is taken as the drive. However, in the general case of the cam design it cannot be assumed that all rises, whether on the main cam its conjugate, provide active drive: in the case of vertical motions the fall could be active in lowering the weight of an axis under gravity and/or controlling a return motion biassed from the neutral position by a counterbalancing spring. So, similarly, if a trailing follower was faced with a fall it would lag and therefore not clear the fall as quickly as an ideal follower. The conjugate leading follower would reach into the rise and be displaced outwards earlier than the ideal. Again the tendency of the lag and lead to create either clearance or interference respectively is self-cancelling. The general direction of deviation from ideal is as follows: if the main cam is leading then the non-ideal locus will act to produce interference; on the conjugate cam the deviation from ideal on trailing follower will act to produce a clearance; a leading follower on the main cam in the face of a fall will produce clearance: and the conjugate trailing follower on the rise, interference.

Since the effects of the non-ideal follower trajectories appear to be self-cancelling no account was taken of deviations from ideal loci when the cam profiles were specified i.e. the cam pairs were specified with symmetrical rises and falls. Since the vertical motions of the axes are comparatively small the undulations in the profiles of the corresponding cams are proportionately modest In contrast, the circular motions cams show more extreme variation. The effect of the non-ideal behaviour of the followers was therefore ignored in the case of the vertical motion cams and these were cut, finished and hardened without correction. However, in the case of the circular motion cams, there remained some uncertainty as to the correctness of the reasoning that the effects were self-cancelling. Since the cam profiles are critical to the correct functioning of the engine the circular motion cams were finalised in a two-stage process during the build.

All the rises on the six circular motion cams were cut but none of the falls i.e excess material was left in the sector corresponding to the falls. The pair was assembled on the stack and an inked roller substituted for the roller follower on the partially cut cam. When driven, the follower of the fully finished cam tracked normally, and the inked roller, driven by the rises of the conjugate cam, traced out the required profiles of the falls on the unfinished cam. The traced profile was then compared with the profile based on idealised rises and falls. The process was carried out on all the circular motion cam pairs. In each case the difference between the inked profile and ideal profile was negligible, and the conjugate cams were cut, finished and hardened with no modification. This two-stage process specifying the cams served to confirm the reasoning indicating that the effects of non-ideal follower trajectories were self-cancelling. Comparing the profiles generated in situ by the rises with those specified on the drawing board served also to verify the correctness of the specification before the commitment to final manufacture.

In the design of the cams the start and stop positions of the rises and falls are critical to the timing of the cycle. The effect of the non-ideal loci of the followers does not affect this timing: each circular motion follower describes a single motion which starts and finishes at either the minimum or maximum displacement, and it is clear from the geometry of the original design that the minimum and maximum follower displacements both occur on the radial line through the cam centre i.e. follower is tangential at the mean diameter. Geometrically this corresponds to the pivot point of the follower arms being chosen such that the line bisecting the sector of motion of a follower arm is at right angle to the radial line through the cam centre. The effect of the non-ideal loci of the followers is therefore to slightly alter the internal timing of the excursions of the followers within a rise or fall but not to alter the cam angle or the timing widow within which the excursion is completed. Since the rises and falls are arcs of circles i.e. monotone increasing or decreasing curves with no inflection points within a single excursion, there are no internal events within the timing window that might be affected by the deviation from ideal of the follower loci.

Speed of Operation

When the machine was first assembled the manual drive was relatively stiff and for reasons of caution the operating speeds were kept low. After several thousand cycles the manual drive was found to be noticeably freer and the run-in speed of operation is 10 complete engine cycles per minute i.e. one "tabular calculation every six seconds (equivalent to 40 turns of the handle per minute with the 4:1 reduction gear operative). If the machine is run faster than this the detent wheel of the intermittent circular motion drive of the carry axes tends to overshoot and cause jamming of the drive. If the motion is erratic or slower the sectors when lowered tend not to mesh cleanly with the figure wheels and jams occur. This is thought to be related to the effects the bell-cranks flexing under load at slow speeds and producing timing lags. With sufficient uniform momentum the meshing is unproblematic in normal operation.


Since the lead-in and lead-out timings are critical and the relative phasing of the cams can only be verified during the build, the keyways in cams and the main cam drive shaft were cut narrower than indicated in the drawings. This was to allow for fine timing adjustments during the build should this prove necessary. This measure allowed some leeway to fine tune the phasing between cam pairs as well as between one cam and its conjugate. In the event no adjustment was needed and the keyways were opened out to the specified size.

Figure Wheel Drive Arms

The figure wheel drive arms for the Trial Piece were manufactured as indicated in the original drawings i.e. with no chamfers on the undersides to provide lead-in to the internal nibs when lowered. On the Trial Piece the drive arms did not foul the internal nibs and there was therefore no advance warning that fouling might be a problem. However, with multiple stacks on the engine, lowering the figure wheel axes produced consistent jamming especially with figure wheels set at '0' or '9' at which points the clearances are small. The solution was to chamfer the undersides of the drive arms to make the engagement less critical.

Checking Carries after Assembly (Red Book, page 106-7)

Setting Up Initial Values

The setting up procedure consists of a series of operations that allow the figure wheels to be set manually with the initial values of differences and the tabular value from which the calculation is to commence. The design of the calculating section features several measures to protect the integrity of the calculation: the figure wheel and sector wheel locks as well as the lugs on the carry levers restrict size of the time windows in which the figure and sector wheels are free to move as well as restricting the origin of their motions to legitimate sources only. These measures are intended to prevent derangement of the wheels during normal operation i.e. movement imparted by extraneous sources including deliberate or inadvertent manual input These security measures act against readily inputting initial values by manually altering figure wheel settings, and the security devices need to be disabled or bypassed to allow setting up. The setting up procedure specifies the sequence of operations to be followed to allow the initial values to be set on the figure wheels.

The original design drawings are not accompanied by any contemporary explanatory text or discussion. In a very rare exception a brief textual account is given for the setting up procedure as a preface to the timing diagram (BAB [F] 385/1a) dated March 1848. The setting up sequence described takes the engine through two complete calculating cycles. The first cycle leaves the sectors disengaged, the figure wheels zeroised and residual carries cleared; the initial values are entered during the second full cycle of the set up sequence.

The procedure described by Babbage has a major flaw (see Paragraph 2 below) which became evident when the procedure was attempted in practice. The italicised sections below are transcriptions of the original text Paragraph numbers are not original and have been added for ease of reference.

  1. The Engine is to be stopped at the end of a cycle of 50 when both sets of sectors S will be at zero, the bars 23E 24E which give them vertical motion ungeared by means of the axis 2F (see drawing 159) and oil those sectors raised to their highest position by the handles 5E drawing 163.
The first instruction is to disengage the sector wheels from the figure wheels. The timing diagram which follows the manuscript description (385 1/a) confirms that both odd and even sectors are at zero at the end of the second half-cycle. This is to prevent the new values set on the odd axes being given off to the even axes when the engine is advanced during the set up procedure. Both sets of sector wheels are therefore fully disengaged (raised to their highest point) for the duration of the set up procedure. The sectors are disengaged by operating the two lifting handles (163 E, E [Notation Refs?], detail 177). The left hand handle lifts the odd sector axes to the fully raised position; the right hand handle raises the even sector axes.

At the end of the second half-cycle ('the end of a cycle of50') the odd sectors are already disengaged (fully raised) and the left hand lifting handle can be locked in place with the pull-out plunger. However, to raise the even sectors, the horizontal sector bars (23E, 24E) need to be uncoupled from the horizontal drive at the cam stack end. This is achieved by lifting the release lever (2F, 159 centre and 168 top right) which lifts both the odd and even bar levers out of their drive slots in the sector bars. This frees the lifting handle to move the sector bar. The lifting handle is locked in the raised position as before with the pull-out plunger. Disengaging the sector bars prevents the vertical motion drive from conflicting with the now immobilised sector axes when the engine is cycled through the set up procedure. (The lifting handles waggle slightly during normal operation.)

  1. Reduce all the fig. wheels ' [Delta] to zero by moving the driving axis 'A once round.
This step contains a major flaw evidently overlooked in the original procedure which leads to the setting up process being self-corrupting. This arises through a process in which the figure wheels tend to be dragged back from their zero positions by residual friction with the figure wheel axes during the return stroke of the axes while the figure wheels are neither locked, nor meshed with the sector wheels. To expand: reference to the timing diagram shows that at the start of the cycle the odd figure wheel locks disengage, the odd the figure wheel axes at the same time lower to bring the drive arms into the plane of the internal nibs, and the odd figure wheels are then driven to zero and then locked. The odd figure wheel axes then lift to disengage the drive arms. During this process the odd figure wheels remain engaged with the sectors which then restore the figure wheel number just given off. So during the first half cycle of normal operation the odd figure wheels are being driven by the drive arms, are locked, or being restored by the sectors. However, the first step of the set up procedure was to disengage the sectors. So during the set up procedure (as distinct from normal operation) when the locks free the figure wheels for restoration by the sectors after giving off, the figure wheels are not secured and it was found that the return of the figure wheel axes, after zeroising dragged back some of the figure wheels a varying amount depending on the differing amounts of friction. The intended zeroising action is thus subverted. Moreover, when the locks attempt to reengage at the end of the first half-cycle jams occurred on the wheels that were deranged by other than a full digit interval. In normal operation any drag of this kind would be unlikely to derange a figure wheel meshed with a sector wheel because of the additional load. But even if it did, the direction of motion simply anticipates the action of the sector wheels to restore the figure wheel values and any drag-induced motion is non-corrupting. (During normal operation the restoration of the figure wheel values occurs during the same period as the return stroke of the figure wheel axes). The process of zeroising the even figure wheels during the second half cycle will be similarly thwarted by variable derangement. Whether or not figure wheels are deranged so as to foul the locks is unpredictable. Even if jamming the locks was not a problem the same dragging action of the figure wheel axes would corrupt the initial settings during the second cycle of the setting up procedure. This flaw renders the original set up procedure ineffective and could not be left unremedied.

The solution was to provide manual locks for each of the axes. These consist of vertical lengths of steel fixed to the front-most figure wheel supports of each of the axes. The eight setting locks are fixed to the vertical supports by knuried screws passing through slotted holes in the locks. In normal operation the locks are retracted and play no part. During setting up each lock is freed by partially unscrewing the fixings by hand. The lock is slid forward to engage with the column of figure wheel teeth and secured in the locked position by retightening the fixings. The locks come into play twice during setting up: they secure the figure wheels in the zero position during the first set up cycle and they secure the figure wheel initial settings during the second cycle (see below). The odd axes setting locks are engaged at the 10-unit point i.e. immediately after the odds axes values are given off by driving the figure wheels to zero. Engaging the locks at the 10-unit point ensures that the figure wheels can be zeroised by the figure wheel axes drive arms without obstruction. The even setting locks are engaged at the 35-unit point for the same reason. The revised set up sequence which includes the operation of the setting locks is given after step 5 below.

  1. Move the axis 1A 20 units more . and set the Odd Difference Figure wheels '.
This is the start of the second full cycle in the set up procedure. The 20-unit point occurs during the period of normal operation in which the figure wheels would be restored by the sectors. However, the sectors have been manually disengaged and the locks withdrawn, so the figure wheels can be turned freely by hand to the required initial values. The reason for advancing the engine to the 20-unit point is that this is the point in the cycle at which the carry mechanism is inactive i.e. the odd carry levers have been driven against the reset stop by the sweeping motion of the detent support arm. The figure wheels can be turned in either direction without regard for producing spurious warnings i.e. the wheel can be turned to any of the four decades with the confidence of knowing that the carry mechanism will not engage. The choice of this point in the cycle is an elegance. Warnings set by manual set up prior to the 17-unit point would be cleared automatically; those set after the 20-unit point would remain as residual warnings and would have to be cleared by hand. The elegance of performing manual settings at the 20-unit point is twofold. Firstly, the there are no spurious warnings to reset and therefore no danger of residual warnings from the setting up procedure corrupting the calculation. Secondly, the figure wheels can be rotated in either direction: if the carry mechanism was operative the curved warning limb of the carry lever would foul the cany finger on the figure wheel if rotated in the wrong direction.

  1. Move the axis 1A 25 units more, that is o the end of the 45th unit, and set the even Diff. Fig. wheels '.
The 45-unit point is the even-axis equivalent of the 20-unit point for the odds axis and the same considerations (see 3 above) apply with respect to the elegance of choosing this part of the cycle for setting initial values.

  1. Move 5 units more, that is to the end of the Cycle of 50, gear the sectors by means of the handles 5E and axis 2F and all is ready for commencing the calculations.
This step reengages the sectors by releasing the lifting handles and reengages the drive arms with the sector bars to restore the drive from the cam followers.

Revised Setup Procedure

The revised sequence of operations for setting up taking account of the setting up locks introduced to overcome the self-corrupting effect of the unmodified procedure is given below. Reference to units of the cycle refer to Babbage's 50-unit cycle which corresponds to one complete rotation of the main drive shaft and one complete calculation. The 50-units of the cycle are engraved on the chapter wheel which rotates with the main drive shaft and the position in the cycle is indicated by the pointer fixed to the vertical framing member in full view of the operator turning the handle. Setting up Procedure

  1. Cycle the engine to the zero point i.e. the end of a cycle.

  2. Lift the release lever at the cam stack to disengage the drive to the sector bars.

  3. Rotate in turn each of the two lifting handles anti-clockwise to fully disengage the sectors (the movement is only a few degrees).

    When each of the handles reaches the end of its travel, lock it in the raised position pulling the locking plunger fully out so as to secure it with the bayonet locking device. (It is important that the sectors are raised to the highest point to avoid fouling the figure wheels during setting up. The way to ensure this is to check that the locking plungers are slid fully home towards the operator standing in front of the engine).

  4. Advance the engine to the 10-unit point.

  5. Engage the odd setting locks. (Unscrew the knuried fixing screws, slide the locks into engagement, petighten the fixings).

  6. Advance the engine to the 35-unit point

  7. Engage the even setting locks (see step 5).

  8. Complete the first cycle and advance the engine to the 20-unit point ('SET ODD' on the chapter wheel).

  9. Disengage the odd setting lock on the axis being set up, (Unlocking only the axis being set up avoids inadvertent derangement of axes already set up).

  10. Enter the odd difference values on the figure wheels by rotating each figure wheel by hand to read the required value. The figure wheel value is indicated by a cursor/arrow engraved on the figure wheel supports above each figure wheel. The least significant digit position is at the bottom, the most significant digit position is at the top.

    Automatic cycle counting

    If a section of the tabular column (last even axis) is to be used as a cycle counter then when the first difference column is set up a '1' should be placed on the figure wheel opposite the least significant position of the counter. Each time a calculation cycle is performed the counter will be incremented by 1 and the counter will register the cumulative total number of calculations performed. An additional elegance is to enter the start value of the independent variable in the section of the tabular column reserved for the cycle counter and enter a '1' in the first difference column in the counter's least significant digit position. The value of the variable will be incremented by '1' each calculation cycle and the counter will directly keep track of the value of the variable.

  11. Reengage the odd setting lock.

  12. Repeat steps 9, 10 and 11 for each odd axis required for the calculation.

  13. Advance the cycle to the 45-unit point ('SET EVEN' on the chapter wheel).

  14. Disengage the even setting lock on the axis being set up.

  15. Enter the even difference values on the figure wheels by rotating each figure wheel by hand to read the required value. The figure wheel value is indicated by a cursor/arrow engraved on the figure wheel supports above each figure wheel. The least significant digit position is at the bottom, the most significant digit position is at the top.

  16. Reengage the even setting lock.

  17. Repeat steps 14, 15 and 16 for each even axis required for the calculation.

  18. Advance the cycle to the zero-unit point i.e. the end of cycle.

  19. Retract the locking plungers to release the two sector lifting levers and reengage the sectors. Ensure that the locking plungers are fully retracted and locked in this position by the bayonet fixing.

  20. Reengage the sector drive by lowering the release lever at the cam stack. The drive levers may require jiggling to allow them to drop into the slots in the sector bars.

  21. Disengage all the setting locks and re-tighten the knurled fixing screws.

It is imperative not to deviate from the fixed recommended sequence of the procedure and any temptation to take short cuts by omitting any of the steps should be resisted. It is especially important to strictly observe the sequence for engaging and disengaging the setting locks. If a setting lock is left engaged and a residual warnings left uncleared by omitting part of the procedure then the figure wheels are immobilised and the steel carry arms will snap the bronze carry levers during the carry cycle.

Babbage's rare and welcome lapse into text [385/1a] in which he describes the setting up initial values calls for two complete cycles for the procedure. It is not evident that the first cycle is indeed indispensable to the process. The first cycle leaves all figure wheels zeroised and spotting non-zero values is a convenient visual check of the correct operation of giving off and carry clearance. Apart from this there is no evident reason why the cycle cannot be omitted. There may in fact be some advantage in dispensing with it when the odd axes are set up (20-unit point) these will be at zero while the even axes will retain their residual values. In progressing along the machine from odd axis to odd axis, the odd axes are more easily identifiable by their fully zeroed values and there it is less likely that an even axl's will mistakenly be altered. This is a marginal psychological benefit that might assist in avoiding operator confusion but one which is perhaps outweighed by the value of the first cycle as a verification of the giving off and cany clearance function.

Checking Carry Operation

The checking procedure described should be used as part of the commissioning process after first assembly and to check a column after reassembly following removal for repair or inspection. Moreover, it serves to verify a suspect column after the machine has been in service.

The warning and carry axes are assembled on the bench and then offered up to the machine. The reset stops (the comb-columns) are fixed after the warning axes are in place. If the procedure is being used after the first assembly then the reset stops should be left off the machine until the appropriate step below. A warning axis and its corresponding carry axis are checked as each pair is installed i.e. the commissioning and verification process is progressive: each of the seven difference positions are checked in turn. The procedure described allows the verification of the operation of one difference position consisting of a thirty-one digit figure wheel column, a carry axis and warning axis. [Ref: Red Book, page 106].


  1. Uncouple the sector wheels by raising them to their upper-most position. This is done using te sector uncoupling levers (front lower right horizontal framing member). Advance the engine to or 2-unit point on the chapter wheel if column being checked is even, or to the 27-unit point if column being checked is odd. This ensures that the warning axis is in the raised position which is necessary for the first phase of checks i.e verifying the warning mechanism, and unlocks the figure wheels.

Warning Check

  1. By hand set all bronze carry levers in the column to the "unwarned" position (first notch on the detent lever).

  2. Check that each of the four outer nibs on a given figure wheel advances the carry detent limb one notch from the "unwarned" to the "warned" position. This is best done with two operators, one at the front of the engine and one behind. Each time the mechanism is warned by the front operator rotating the figure wheel, it is restored by the rear operator to the unwarned position by hand. The direction of rotation here is critical: if the column being checked is an even figure wheel column then the figure wheel should be rotated anti-clockwise; if the column is an odd one, rotate clockwise.

  3. If the carry detent limb overshoots (the v-shaped insert ends up resting on the shoulder past the detent notch) or undershoots (fails to reach the notch) then adjust the bend of the warning limb using the special tool, to eliminate any over- or under- shoot of the cany detent lever.

  4. Repeat the procedure described in the previous step for each of the figure wheels in the column.

  5. Restore each carry lever to the "unwarned" position.

Carry Check

Checking the engagement of the locking lugs on the carry lever.

  1. Swing the lowermost carry lever (this has the long arm removed) out of the way i.e. so that the locking lugs are clear of the figure wheel.

  2. Cycle the engine slowly to lower the warning axis: if the column is odd, advance to the 36-unit point on the chapter wheel; if the column is even then advance to the 11-unit point While the axis lowers check that the locking lugs on the carry lever all mesh smoothly and do not derange the figure wheels. If any figure wheel motion is detected go back to the previous step and investigate. The engine may need to be cycled several times while different sections are observed.

  3. Position the lowermost carry lever so that the lugs on the carry lever correctly mesh with the lowermost figure wheel and fix using grub screws.

Checking Restoration to "Unwarned"

  1. Fix the reset stops to the figure wheel supports. This is best done with the engine at the zero unit point on the chapter wheel i.e. when the carry levers are reset to the "unwarned" position.

  2. By hand set all the carry levers to the "carried" position. Check each carry lever to confirm that the carry limbs do not foul the stops and that there is a small clearance between the lever and the stop.

  3. Cycle the engine at normal speed.

  4. Check that all carries are returned to the "unwarned" position. If the carry levers do of return to the "unwarned" position then the warning rack will need adjustment.

Checking Carry Action

  1. Set carry levers numbers one and sixteen to the "warned" position. (Lever number one is the first lever to be engaged by a steel carry arm).

  2. Cycle the engine very slowly. While one operator cycles the machine the other checks that the figure wheel locks withdraw in time to allow the figurewheel to receive the carry from the decade immediately below i.e. this checks that there is sufficient clearance for the locks to accommodate a carry. This check is vital: the clearance is small when correctly adjusted and if the lock does not clear then the steel carry arm will snap the bronze carry lever. If there is insufficient clearance then the phasing of the carry axis circular motion needs to be retarded. This is done by adjusting the bevel gears on the shaft from the intermittent drive.

  3. By hand set all the carry levers to the "warned" position.

  4. Cycle the engine and check that all positions carry. If carries malfunction adjust the warning rack.

  5. Check that having carried, all carry levers reset to "unwarned" at the end of the appropriate part of the cycle.
[Transcript [F] 385/1a]

Notation of Units for Difference Engine No.2
The Drawings 14710 177 inclusive
March 1848

The Engine is to be stopped at the end of a cycle of 50 when both sets of sectors S will be at zero, the bars 23E 24E Which give them vertical motion ungeared by means of the axis 2F (see drawing 159) and all those sectors ro/sed to their highest position by the handles 5E. drawing 163.

Reduce all the Fig. wheels ' to zero by moving the driving axis 1A once round.
Move the axis 1A 20 units more , and set the Odd Difference Figure wheels '.
Move the axis 1A 25 units more, that is o the end of the 45th unit, and set the even Diff. Fig. wheels '.

Move 5 units more, that is to the end of the Cycle of 50, gear the sectors by means of the handles 5E and axis 2F and all is ready for commencing the calculations.

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