The following section identifies issues of construction, assembly, and setting up that arose during the engine build.
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.
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.
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.)
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.
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
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].
Checking the engagement of the locking lugs on the carry lever.
Checking Restoration to "Unwarned"
Checking Carry Action
The Drawings 14710 177 inclusive
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.
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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