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Vertical Motions


The calculating cycle requires intermittent vertical motions for the figure wheel axes, sector wheel axes, locks and warning axes. These vertical motions are derived from the eight pairs of conjugate cams located in the lower section of the cam stack. Cam followers operate three pairs of horizontal bars slung on the underside of the engine and one pair midway up the cam stack. The arrangement of cams and cam followers converts the continuous rotational motion of the cams into intermittent reciprocating motion of the horizontal bars. The reciprocating motion of the horizontal bars is converted to vertical motion by bell crank levers (163, detail on 160). These lift and lower the axes and locks. The overall arrangement produces four sets of intermittent vertical motions phased according to the timing diagram.

The 'vertical motion' section covers the vertical drive for the locks, figure wheel axes, sector wheel axes, warning axes, as well as the cams, horizontal bars, bell crank levers, and additional framing support members.


Drawing References:

Main drawings are 159, 160 and 177. Also 161, 163, 167, 168, and 169.

Action of the Cams and Followers

The vertical motion cams are the eight pairs of closely spaced cams in the lower section of the cam stack (160 and 163). Eight pairs of cam followers rock on eight separate pivots and are driven by the irregular shapes of the cams (159 shows all 16 cam followers and the pivot layout; 168 and 169 show clearer partial views). Bar levers, which are integral with the cam follower bosses, slot into the horizontal bars. Six of the follower pivots project through the lower framing plate of the cam stack to enable the bar levers to engage with the drive slots of the horizontal bars. The arrangement of cams, cam followers and bar levers, convert the continuous rotational motion of the cams into intermittent reciprocating motion of the bars.

The levers operating each of the eight horizontal bars is driven by two cam followers on the same boss. Each of the cam follower arms is driven by a separate cam. Cams therefore occur in conjugate or complementary pairs with one pair of cams associated with each of the eight vertical motions. The purpose of the complementary cam arrangement is to provide positive bidirectional drive for the vertical motions. The motion of a cam follower boss is determined by the outside surface of the active cam of the pair and the rises acting on the leading and trailing arms dictate these motions. The leading arm provides drive in one direction and the trailing arm, driven by the mating cam, provides the return motion. The naming convention adopted is that the leading arms point in the clockwise direction as viewed from above (the cams rotate anticlockwise so viewed). The leading arm does not necessarily make contact with the active cam first. At any given time only one of the pair of cam followers is in direct contact with the cam. The other follower is provided with a clearance from the cam surface.

The overall layout of the vertical motion cams and followers is shown in plan on 159 with additional partial views on 168 (left) and (right). 159 gives partial cam profiles with ail significant rises shown in local relation to active portion of the cam follower. The eight follower pivots are shown distributed around the cam stack on a fixed diameter pitch circle. The cams are shown with standard outside diameters. The shape of the cams deviates inwards from the standard outside diameter.

In six of the eight cases the contact between the cam follower and the cam circumference is shown as a sliding contact (159). Only in the remaining two cases are the cam followers shown with a roller on one of the two arms and a sliding follower as the other. Roller-cum-slider followers are provided for odd and even sector motions only. This is shown on 159; the spaghetti junction of intersecting followers with rollers is clarified in 168. In all cases (i.e. sliders and rollers) leading arm rises are shown as straight and trailing arm rises as are shown curved on a 2.5" radius. The straight plane surfaces of the leading sliding arms are shown near-parallel to the rises on the cams (see for example the even warning follower on 159 top); in the case of the trailing arm rises, the shape of the inside of the arm roughly matches the curve of the rise (see even figure wheel follower on 159 lower right). It seems that Babbage was concerned to avoid point loading by distributing the load over a contact surface. The trailing arm rises are radiused to avoid fouling: if the trailing rise was straight, the top comer of the rise would foul the inner surface of the arm with the worst case occurring about half way through the rise.

In all cases of sliding followers the distance from the centre of the cam follower pivot to the line of contact on the sliding arm is shown as 3.50". In the case of the roller followers the 3.5" is taken from the pivot centre to the centre of the roller rather than to the line of contact In the case of sliding contacts, the line through the pivot centre and the point of contact is in each case tangential to the outside diameter of the cam i.e. with the follower at the top of a rise. The effective angle between the follower arms on the same boss is therefore constant. In the case of the two roller-curn-slider followers the line through the point of contact of the roller and the pivot centre is tangential. Here the effective angle between the follower arms differs from that of arms with sliders only.

It is not immediately obvious why rollers were preferred for the sector vertical motions. The sector wheels represent the largest deadweight to be lifted, while the locks, though lighter, represent the largest shock load to the drive. It is possible that Babbage sought to reduce wear by using a roller on what he considered to be the most demanding load. This view is supported by the fact that in the case of the circular motions, rollers are preferred on all the cam followers, and sliding contact is avoided entirely. Though the loads for the circular motions are lighter, the duration of the actions tend to be more sustained. The rises on the cams are therefore longer and the period of active sliding contact, and therefore of wear, is correspondingly greater. It is possible that Babbage preferred rollers to sliders wherever possible. However, rollers are less space efficient they require greater separation between the cams than do sliders and a lower stacking density of the cams would be required to accommodate them. The compressed space of the lower cam stack assembly as drawn prohibits the general use of rollers. However, the tight pitch of the cam spacing is relaxed in the case of the sector cam followers because they require a free vertical motion to disengage during setting up. It is likely that Babbage exploited this additional space to provide rollers where he could i.e. one for each of the sector followers. An alternative to the general use of sliders would have been to reduce the overall stacking density of the vertical motion cams and expand the lower section of the cam stack. Without an additional stage of lining this would increase the overall height of the machine and the knock-on effect would be to put the upper figure wheels out of normal reach. It seems that Babbage preferred sliders to an overall increase in cam stack height

Lifting and Lowering

The lifting and lowering action for the figure wheel axes, warning axes, and the locks is provided by bell crank levers which are slotted into the horizontal bars below. The bell cranks for the sector axes are operated from above (160) (163 shows the even sector bar but not the bell cranks).

The bell cranks for the figure wheel axes, warning axis and sector axes have forked ends which fit into bobbins pinned to the lower end of the axes (160). The fork and bobbin arrangement allows independent vertical and circular motion to be imparted to the axes without conflict the axes are lifted by the forked crank in the bobbin and rotated in the fork by the racked drive (see section on Circular Notion). The basic action of the bell crank and horizontal bar is cleariy shown for the figure wheel axis bearing the tabular result (extreme left hand axis on 163 with detail on 160). The lower end of the axis projects below the bobbin through a bearing hole in a plate fixed across the underside of the front and rear framing members (160 lower left). The arrangement for the locks is slightly different. Unlike the axes, the locks do not rotate so a bobbin drive is not called for. Instead the lifting and lowering action is transmitted by a connecting rod pivoted at each end to the lock and at the other end to the bell crank (160). The connection between the sector bars and the sector bell cranks is shown as a mix of pivots and slots. 163 shows the even sector bar with pivots for the first and last bell cranks, and with slots for the two intermediate cranks. 160 confirms pivots for the last odd and last even crank drives.

The layout of the bell cranks is shown on 177. The bell cranks for a figure wheel axis, sector axis, and warning axis share a single shaft for each of the eight colurnn positions (160 and 177). The lock cranks each have a separate shaft. The bell crank shafts are located at each end in bearing holes in the horizontal framing members. The longer of the forked bell crank levers drive the sector axes; the shorter ones drive the figure wheel axes (middle) and warning axes (rear) (177).

The figure wheels are set to their initial values manually. To free the figure wheels for setting up they must be disengaged from the sector wheels. Two lifting handles are provided for this purpose. The arrangement is shown on 163 and 177. Lifting the left hand handle operates shaft to which the bell crank lever for the first odd sectors is pinned (pinning shown on 161 ). This bell crank lever drives the odd sector bar to lift the remaining odd sector axes. The right hand handle lifts the even sector axes in the same way.

As well as disengaging the sector wheels from the figure wheels when setting up, it is also necessary to disengage the sector bars from the horizontal drive. This prevents the drive for the vertical motions conflicting with the now immobilised sector axes when the engine is turned over during the setting up cycle. Details of the mechanism for disengagement are given on 159 centre, and 168 top right (163 shows only the support bracket on the cam stack side of the right upright). The sleeve, cam follower and bar lever for each of the odd and even sector bars are an integral assembly which is free to slide upwards on the cam follower pivot Operating the release lever raises the two sleeves and lifts the bar levers out of their drive slots. Two detents for the release lever spring hold the lever in the released and unreleased positions.


Support for Horizontal Bars

The six lower horizontal bars, which provide the vertical motions for the figure wheel axes, warning axes and locks, span the full length of the frame. The bars are supported at each end by slotted supports fixed front to rear to the main frame uprights. Five of the bars pass under the cam stack and are and these have an additional support on the underside of the right hand side of the cam stack. This slotted support, fixed to the right hand print shaft bearing mounting, is shown in 167, 163 and on 159 (faint dotted). The five longer bars are associated with the vertical motions for the odd warning, odd and even figure wheel axes, and the odd and even locks (159).

There is very little separation between the horizontal bars for the even figure wheel motions and the odd lock motions (159) and 167 shows the bar support with a thin tongue separating the two bars. This was considered a weakness and, given the material (phosphor bronze), difficult to manufacture. The thin tongue was omitted in all four bar supports and single broader slots provided for the two bars. Separation was instead provided by five spigotted phosphor bronze spacers. These are located in equally pitched holes along the length of the odd lock bar. The original separation remains unchanged. The spacers are 5/8" diameter and 0.082" thick (E323).

During assembly it was found that the full 62" span between the main uprights was too long to avoid downward bowing of the horizontal bars. An additional intermediate support was added for the six bars at the approximate midpoint of the span between the main uprights. The extra support is identical to the two fixed across the uprights.

Counterbalancing the Locks

During assembly it was found that even with a four-to-one reduction in the drive the engine could not be turned past the points in the cycle where the locks are released. The weight of the locks, friction in the angled slot-bearings, sideways pressure from the figure wheels, and the suddenness of the motion, make releasing the locks the most demanding load in the cycle. The 45o pressure angle on the lock cam presents a shock load to the drive which was too great to overcome with the original arrangement.

The solution adopted was to counterbalance the weight of the locks using springs. The original design (163) shows a single figure wheel axis projecting above the upper bearing plates and passing through a spring to counterbalance its weight. This single feature was assumed to be generic and the technique was used to counterbalance all figure wheel, sector wheel and warning axes. However, counterbalancing the locks from above in the same way poses difficulties. The locks are not shown projecting above the upper bearing plates and the shock load problem was encountered after manufacture i.e. during the build. Extending the locks would have meant remaking the locks and modifying the bearing plates. An additional difficulty is presented by the fact that the motion of the locks has a sideways as well as vertical component: the locks are lifted by the bell crank levers and slide in angled bearing slots which give a sideways motion so as to withdraw from the figure wheels (160,161). In addition, the locking mechanism for the first column (seventh difference, extreme right) was modified to immobilise the first column during a part of the cycle in which it is unsecured (see below, pg. 6). The correct operation of this mechanism relies on the weight of the lock. If each lock was counterbalanced individually, this additional lock would need to be excepted.

These difficulties weighed against counterbalancing the locks using individual springs acting on the upper bearing plates. Instead, a single spring-loaded assembly was devised to act on the horizontal drive bars to counterbalance the locks via the bell cranks. This relatively small assembly is visually discrete and for the most part passes unnoticed.

The counterbalancing mechanism consists of a set of three springs placed end to end. The springs are in compression and kept in axial alignment by a forked tie rod (E411) threaded along its length and a threaded sleeve (E419) passing through the centre of the springs. The tie rod acts on a lever which is trapped in a recessed block (E414) screwed to the side of the horizontal lock bar. The effect is to bias the bar to the left i.e. in the direction of lift.

The compression force is adjusted by turning the threaded sleeve and shortening or lengthening the effective length of the composite spring. There are two identical mechanisms housed in the one assembly - one for the odd axis locks and one for the even axis locks. The six springs are of the same type used on the upper bearing plates to the counterbalance the figure wheel, sector wheel and warning axes.

Modification to the Sector Bars

The bar driving the sector bell cranks is shown supported only by the bell crank levers (160 and 163). The cranks for the first and last even axes have pivot fixings and the two intermediate cranks are shown with slot drives. The arrangement is assumed to be repeated for the odd sector axes (in 163 the odd sector bar is masked by the even sector bar). As drawn, the sector bars would ride in a slight arc determined by the length of the bell crank arm, and the intention seems to be that the intermediate cranks would lose the vertical component of motion in the slots. This arrangement gave rise to two concerns. The effective length of the crank with the slotted drives is shorter than that of the pivoted cranks, and the vertical motions imparted to the first and last sector axes would therefore differ slightly from those imparted to the intermediate sector axes. Deepening the slots to equalise the lever lengths would weaken the bar to an unacceptable extent and would risk fouling the slots at the extremities of the travel. A further concern was the risk of vertical bowing due to the upthrust from the bell cranks.

The sector bars and associated bell cranks were modified to take account of these concerns. The extreme left hand pivot connection between the bell crank and the bar was retained as shown in the original. All other slot drives, including the two closest to the cam stack (odd and even sector bars), were replaced with pivots and slightly elongated holes in the bars. With this arrangement, the vertical component of motion imparted by the arc of the bell crank lever tends to diminish over the length of the bar. Elongating the holes in the bars avoids any contention that might arise from small differences in the lengths of the levers, and the use of pivots in preference to slots avoids the risk of disengagement from upward bowing.

An additional mechanism was provided to control the operation of the lock for the first odd figure wheel axis (see below 'Modified Seventh Difference Lock'). A further advantage of replacing the right hand fixed pivots with elongated pivots is that the downward motion imparted to the even sector bar by the additional first odd lock mechanism (E22) does not conflict with the upward arc that would otherwise be imparted by the bell crank.

An additional slotted support was fixed to the right hand uprights to provide front-to-rear support for the sector bar close to the cam follower. The purpose of this modification was to spare the bell cranks taking any side thrust from the cam follower lever acting in the profiled slot at the end of the sector bar, and also to reduce the risk of disengagement during normal operation.

Modification to the Drive for the Warning Axis

The modification of the axes layout for mirroring [see Calculation section] only affects the position of the carry axes so the layout of 177 is unaffected with the exception of the bell crank for the first odd warning axis (seventh difference, top right on 177) which was omitted. The drive slot for the horizontal bar for the axis was also omitted.

Cross-over Bar Levers

There are three instances in which the bar levers which drive horizontal bars need to cross over bars in the same plane. These are the bar levers for the odd locks, even warnings and even figure wheels (159). The bars for these three motions have raised projections with slots for the bar levers as shown for the even sector bar on 163. Raising the drive slots allows the bar levers to clear the intervening bars and provide drive to the otherwise obstructed bars.

The lower cam stack framing plate is drawn 1/2" thick ( 160) with just sufficient clearance for the vertical projections on the three bars. The annotation on 160 indicates that the framing plate should be thickened from 1/2" as drawn, to 1". If the upper surface of the framing plate is taken as the reference and the plate thickened downwards, there would be insufficient space for the slotted projections on the horizontal bars (E324, E342, E334). This was resolved by following the vertical layout arrangement on 163 which is drawn with the plate thickened and with sufficient clearance for the bars.

Disengaging the Sectors for Setting Up

Babbage's annotated instructions for setting up BAB[F]385 suggest that the sectors should be 'lifted to their highest point' during the setting up procedure i.e. the sectors should be taken out of engagement. The sectors are disengaged during setting up by operating the two sector lifting handles (163, 177). No provision is made on the original drawings for locking these in place to hold the sector axes in their raised (disengaged) positions so as to relieve the operator of the load during setting up. Two pull-out plungers were added to the front horizontal framing members (F361A). During normal operation the plungers are locked in their home positions by bayonet locks. During setting up they are pulled out by hand after the levers have been lifted and provide fixed resting support for the levers. Babbage would perhaps have simply jammed the levers in their raised positions.

There appears to be a dimensioning error on 177. A small section of shaft is shown projecting from the framing member to the lifting handle. The diameter of this shaft is drawn the same as the diameter of the bell crank boss. A bearing hole in the framing of that size would present a structural weakness. In addition, the outsized diameter of the boss for the lifting handle is shown smaller on 163 and on 161. It was assumed therefore that the shaft diameter on 177 shown projecting from the framing member is an error. The final dimensions are shown on E394.

Modified Seventh Difference Lock

The original design goes to some lengths to ensure that the figure wheels do not derange. Locks immobilise the figure wheels at appropriate stages in the cycle. During the carry portion of the cycle the figure wheels need to be free to receive carries and even here antideranging provision is made. Figure wheels are prevented from deranging during the carry cycle by horns on the carry levers which hold the figure wheels stationary in unwarned digit positions or advance the figure wheels one position in warned positions. So the figure wheels are secured at different times by locks and carry lever horns, or by engagement with the sector wheels during giving off.

However, the seventh difference axis has no even sector column alongside to the right Consequently, during giving off even-to-odd, the locks are released and the first odd axis is unsecured. In addition, because the warning axis for the seventh difference column was omitted, the seventh difference column is unsecured during the carry cycle. The drive to the seventh difference lock was modified to secure the figure wheels during the parts of the cycle in which it is vulnerable to derangement.

The modification to the lock is based on the operation of a collapsible link shown in E22 and E31. The unlocking lever is pivoted on a bracket fixed to the right hand front upright. The unlocking lever, which is integral with the operating lever, is driven from the even sector bar. The even sectors are disengaged (even sector bar to the right) during giving off odd-to-even. In this position the slotted link holds the hinge member firm and the seventh difference lock is released, with the rest of the locks, by the odd lock bar lifting the lock acting through the twinarmed bell crank lever, the hinge member and the connecting rod. In the unmodified arrangement (i.e. with the bell crank driving the connecting rod directly) the odd lock bar would release the seventh difference lock and leave the column unsecured. During giving off even-to-odd and during the odd carry which follows, the even sectors are engaged and the even sector bar is to the left. With the additional mechanism, the slotted link releases the hinge member and when the odd lock bar moves left to lift the lock, the hinge member turns on the connecting rod pivot and fails to transmit the motion. This leaves the seventh difference figure wheel lock engaged as required, and held in place by its own weight

Vertical Motion Cams

Drawings References: 159 (right), 160 (cam stack), 163, 168, 169.

Specifying the cam detail was the most taxing task in the overall specification of the engine and comparable in difficulty only to aspects of the printer design. Unlike the circular motions, which are intermittent but smooth, vertical motions are stepped i.e. lifting and lowering by fixed distances. The figure wheel axes, warning axes and locks are lifted and lowered by single fixed distances; the sector axes have a two step motion with separate steps for partial and full engagement

The following features of the vertical motion cams require specification: the height of the rises and falls to provide the required travel of the induced motions; the outside diameter of the cam blanks from which to manufacture the cams; the profile or shape of the rises and falls; the dwell to sustain the motion for the appropriate duration; the timing of each motion - firstly to produce the correct start, duration and succession of the motions for a given cam pair, and secondly, to ensure that the motions from the cam pairs are correctly phased in relation to each other.

Cam Follower Pivots

The eight follower pivots are shown distributed around the circumference of a fixed pitch circle in 159. The exact size of the pitch circle is not explicitly given though it was assumed that Babbage would have chosen a convenient round dimension. Measuring the distance between the centre of the cam shaft and the centres of the cam follower pivots on 159 was not exact enough to recover the pitch circle radius with sufficient precision for manufacture and this radius was found through a combination of scaling and calculation. The X-Y co-ordinates of each of the pivot centres was measured referenced to the right-angled axes through the cam shaft centre. The radial distance from the cam shaft centre was then calculated as the hypotenuse of the triangle in each case and the list was inspected for a convenient round number. The X-Y coordinates of the even warning pivot, for example, were measured at 4.50" and 5 and 13/16th inches which gives 7.35086" for the radial distance. The figure of 7.35" was the number closest to a round number for the eight calculations and this was adopted as the pitch circle radius. Each of the pivot centres was then specified as the intersection of two loci -the pitch circle radius, and a coordinate referred to either of the right angled lines through the cam shaft centre.

Modification to Pivot Positions

A small change was made to the position of the even figure wheel cam follower pivot (159 lower right). As drawn, the cam follower boss fouls the horizontal bar for the even lock, and also fouls the end bar support (shown dotted). To avoid fouling, the position of this pivot was moved forward (down on the drawing) and slightly left to provide clearance. The slight alteration to the pivot entails lengthening the corresponding bar lever. As originally drawn there are only two different lengths for the eight bar levers. The two lower bar levers (even figure wheel and odd lock) are one length, and the remaining six bar levers, another. To maintain only two standard lengths of bar lever, the pivot for the odd lock cam follower was also moved to equalise the lengths of the two lower bar levers. The new positions were located on the same pitch circle. The cams themselves were modified slightly to compensate for the slightly extended lever lengths so as to ensure the correct final travel of the bars.

Identifying the Cams

For ease and consistency of reference the cams were numbered. The sequence starts with 1 at the bottom and runs through to 16 at the top (E21). The rotation of the cams viewed from above is anticlockwise. With the numbering indicated, the odd-numbered cams engage trailing levers and the even-numbered cams engage leading levers. The trailing levers are therefore below the leading levers on the follower pivots. The relationship between the numbered cams and vertical motions is as follows:

   1  odd figure wheel lift
   2  odd figure wheel lower
   3  even figure wheel lower
   4  even figure wheel lift
   5  even unlock
   6  even lock
   7  odd lock
   8  odd unlock
   9  odd sector lower
   10 odd sector lift
   11 even sector lower
   12 even sector lift
   13 odd warning lift
   14 odd warning lower
   15 even warning lift
   16 even warning lower

Height of the Cam Rises

The heights ofthe cam rises are specified by working back from the required vertical motions via the drive train to the cams. The travel of the vertical motions ofthe warning axes, figure wheel axes and sector axes are given on 171 where the length of travel is inscribed inside the circles representing the shafts: the vertical motion of the figure wheel axes is given as 0.3", that of the warning axes as 0.34", and that of the sector axes as 0.68" (for full engagement with odd and even figure wheels) and 0.34" for partial engagement when the figure wheels are restored. The significance of these figures is confirmed by the timing diagram (F385/la) where these figures are reproduced alongside the arrows indicating the vertical motions.

The vertical travel required was multiplied by the ratio of the length of the arms of the bell crank levers to give the translational travel of the horizontal bars. The bar motion was then multiplied by the ratio of the length of the bar lever to the length of the follower arms to give the height of the rise (E327A, E371A for example). These calculated rises were then checked against the rises shown on 159 and 168. There were no significant corrections required.

Where the size of the required vertical motions is given explicitly as for the warning, figure wheel and sector wheel axes, this information was taken as the starting point of the calculation working back through the drive train to determine the cam rises. However, the vertical travel of the locks is not specified in the original drawings. The length of travel of the locks was derived from the depth of the figure wheel teeth and the gradient of the angled sliding bearing in the upper and lower bearing plates which support the locks. As before this figure was worked back through the drive train to determine the cam rise and then checked against the cam profiles shown on 169 (right) and the less clear view on 159 (bottom centre). Again there were no significant corrections required to the height of the lock rises though small adjustments were required to the dwell (see 'Timing' below).

Cam Diameter

The cams are shown with a standard outside diameter from which the outer shape deviates inwards by the height of the rises and falls (159, 169). The outer radius of the cams was taken as 6.46". This figure was calculated by triangulation and confirmed by scaling from 159. The pitch circle radius of the cam pivots is 7.35" and the length of the cam follower arms is 3.50" (see above). In the case of the sliding followers the follower arms are shown tangential to the outer cam circumference i.e at the top of the rise. The odd warning follower in 159 (top centre) provides one of the less cluttered examples. Here, as for the other sliding followers, the line joining the point of contact and the centre of the pivot is at right angles to the cam radius through the point of contact In the case of the roller-cum-slider followers the same holds true i.e. the line through the point of contact of the roller and pivot centre is tangential to the outer cam circumference. The cam outer radius of 6.46" is thus calculated as the third side of the nght-angled triangle formed by the radius of the pivot pitch circle (7.35"), the follower arm (3.50") and the cam radius. Scaling from 159 confirms that this figure was taken as standard for all the vertical motion cams. The figure of 6.46" was thus used to specify the maximum outer diameter of the vertical motion cam blanks (E391C).

Design Alternatives

Questions arise as to the implications of alternatives. The locus of the point of contact is an arc with radius equal to the effective length of the follower arm. In the case of non-conjugate cam pairs it is usual to specify the rises as bilateral deviations from a mean circumference rather than inward deviations from a standard outside dimension as Babbage has done. Using bilateral deviations from a mean circumference has the advantage of minimising the amount by which the arc needs to be taken into account in determining the actual angular position of the point of contact at the extremities of travel (i.e. the bottom and top of the rises). However, using deviations from a mean has the disadvantage of greatly complicating the specification. If mean circumferences were used in the case of conjugate pairs, the outside diameters of the cam pairs would differ. While there is no great penalty in this as regards manufacture, the loss of standardisation has a knock-on effect that introduces variations each of which would need to be catered for separately. For example, if the pivot centres are retained on a fixed diameter pitch circle, as Babbage shows, and the cam diameters varied, then the cam followers cease to be standard components: the lengths and angles of contact will vary from cam to cam and each cam pair would require additional calculation to specify its followers and ensure correct timing. Non-standard followers have the additional drawback of more expensive and troublesome manufacture. Another possibility would have been to abandon the fixed pitch circle for the pivot centres. In this case the radial distance of the pivot centres from the cam shaft centre would differ. To retain tangential contact would again require non-standard follower arms. To disregard tangential contact would entail having to again take into account, in each individual case, the effects on timing of the arc traversed by the swing of the follower arms.

Babbage appears to have standardised the layout to simplify an already complex arrangement. Adopting a standard outside diameter for the cams, fixed pitch circle for the follower pivots, fixed follower arm lengths and tangential contact to the outer circumference, eliminated the need to cater for variant combinations of pivot position, contact angle, and arm length. The arrangement preferred by Babbage significantly reduces calculation and simplifies layout, manufacture and, moreover, reduces the risk of drafting and layout errors in attempting to keep account of variations. One example of the benefits of a standardised geometry arises in the determination of the cam keyways the positions of which are critical in ensuring the correct phasing of the various motions derived from the eight pairs of mating cams. With a fixed pivot pitch circle, standard follower arm lengths and standard outside cam diameters, the angular offset between contact points of leading and training arms can be taken as a standard 56o. This fixed offset between mating cams substantially simplifies the specification of the keyway positions for the full set of cams (see worked example below).


Timing Diagram

The basic timing data is derived from the original timing diagram F385/1 a which provides the main source of information on the sequence and phasing of the motions in the calculating cycle. However, the original timing diagram lacks a level of fine detail and in some instances is in the nature of a guide rather than an exact specification. There appear to be a number of inconsistencies in notation (see separate section on 'Timing Diagram') though the most serious omissions concern the timing of the locks. Unlike the motions of the calculating axes and wheels, the action of the locks does not specified in a separate column of phased actions indexed against the cycle divisions. The locked and unlocked condition of the axes and wheels is indicated by an 'L' (locked) and a reversed 'F (presumably 'free") though no detail is given for the lapping or phasing of the actions of the locks. For example, the circular motion of the odd figure wheel axis is shown commencing immediately the axis is lowered by 0.3" with 'L and 'F' notations alongside the arrows indicating locked and unlocked conditions. The timing of the withdrawal or entry of the locks as an event with afinite duration is not indicated on the diagram and the avoidance of contention is simply implied.

In the case of the even figure wheels we find that the wheels are locked briefly between the end of the counter-clockwise motion giving off odd-to-even and the start of the carry cycle. Here, a unit interval of one Babbage-division (7.2o) is allowed for locking and unlocking. There is no horizontal grid on the diagram and the level of precision in the drafstmanship discourages exact scaling. The practice of allowing a single Babbage timing unit as the standard nominal interval for actions that are not specifically detailed is characteristic of the diagram. Nonspecific timing gaps are not confined to locking action.

A new timing diagram was drawn (X21) which supplements the original diagram by providing the detailed lapping and phasing information otherwise lacking. As in the original diagram the redrawn version shows the timing of an event specified as the number of degrees of a 360o cycle starting from Babbage's original zero datum. Babbage's 50-division cycle is for convenience of reference but was not used in the modern specification.

Timing: Lapping and Clearance

In the case of leading lever rises the point in the cycle at which the motion commences coincides with the point of contact of the follower with the start of the rise. In these instances the start of the rise is taken as the critical reference. In other instances it is necessary to sustain a motion to overlap another motion. Here the start of the fall is taken as the starting reference and is used, making allowance for clearance, as the reference for the rise on the mating cam which initiates the return motion. For example, the odd figure wheel axis is raised and lowered once during each calculating cycle. Cam I lifts and Cam 2 lowers the axis. The lifting action on the cam occurs between 67o and 75o which gives the start of the leading rise and the duration. The corresponding falling rise on Cam 2 is given a few degrees clearance and is specified between 64o to 73o (E373A). The few degrees timing clearance correspond to a clearance of about 0.003" between the passive follower and the cam [check]. The action to lower the axis is determined by the rise on Cam 2. This action occurs between 357o and 5o and a corresponding clearance is allowed on the falling rise on Cam I (E374A). The timings given in this example are taken from the cam specification. These are not always identical to the timings on the redrawn timing diagram. For example, the timing diagram (X21) shows the lifting action commencing at 68o though the start of the rise on the cam is shown at 67o. The foot of the follower is slightly angled and as the foot starts to mount the rise the actual point of contact leads the point of contact otherwise operative on the plateaus. A 1o lag in the cam rise is introduced to compensate.

Allowance was made for the roller followers used for the sectors. The active surface leads the centre of the roller by a few degrees and this was taken into account when specifying the take-off point of the rise.

Timing: Locks

The cams for the locks presented special difficulties. A single calculating cycle requires four separate episodes of engagement of the locks. Three short engagements are specified for correction of minor derangements and to secure the figure wheels during momentary otherwise unsecured intervals. The longer locking period is to secure the figure wheels after giving off while the sectors disengage and the alternate axes carry. The figure wheels that have just given off remain locked until the sectors commence restoration.

Where allowance is made for the entry and withdrawal of the locks on the original timing diagram (F385/la), a nominal single Babbage timing unit is allocated i.e. an interval of 7.2o is allowed for locking and unlocking. However, working back from the rises on the locking cams shown on 169 the actual period locking and unlocking would occupy is 10o (4o for entry, 2o for dwell, and 4o for withdrawal). It is clear from the cam details on 169 and 159 which specify the height of the rise, pressure angle, dwell and fall that Babbage did consider in detail how the operation of the locks should be phased. However, the detailed mapping from timing to cam specification is omitted in the original drawings. In the modern implementation a minimum allowed was 11o to ease the pressure angle (4o plus 3o plus 4o). The difficulty was then to fit these slightly stretched locking actions (particularly the three short engagements) into the already crowded and therefore tight timing cycle. The solution in the case of the figure wheel axes was to shorten the duration of the circular motions (without reducing the total rotation) to allow for the locking action - in particular for the withdrawal of the locks so as to avoid contention between the lock and the circular motion that follows. The dwell of the locks was extended slightly in some instances to cater for the arc of the point of contact of the follower.

Phasing the Vertical Motions

The cams are keyed to the central cam drive shaft (Cam I is the sole exception, see previous section). The position of the keys is the critical determinant in ensuring the correct phasing of the motions separately created by the eight cam pairs. The original drawings do not indicate a datum for the keyways nor any keyway positions. An arbitrary datum was chosen: the single keyway running the length of the cam drive shaft is positioned at the front of the engine when the cycle is at 0o. For drafting convenience cams are drawn with the 0o-position of leading lever cams at 12-o'dock.

If the active point of contact on each of the follower arms was at the front of the engine then all the keyways would be in line and at zero. However, the pivots are distributed around the cams and the cam keyways need to be offset relative to the front of the engine to compensate i.e. each cam needs to be rotated from the zero datum until the event on the cam that is to occur at zero is at the point of contact of the appropriate follower. The position of the cam keyway is then fixed at the front of the engine. Because of the standardised geometry of the pivots, follower arms and standard outside cam diameter, once the offset calculation is done for one cam of the pair, the keyway of the mating cam is found by adding or subtracting a fixed offset of 56 depending on whether the mating cam is leading or lagging.

The offset for each of the 16 cams needed to be calculated separately. The keyway calculation for the even warning cams (Cams 15 and 16) is shown in the example (see Fig. 1).

Keyway Offset -- Example

Figure la. Keyway Offset Calculation for Odd and Even Warnings
Figure 1b. Locus of Point of Contact

The first step is to calculate the angular displacement (Theta) of the pivot centre. The coordinates of the even warning pivot (Fig. la) are given by the pitch circle radius (7.35") and the distance from the horizontal axis (4.50" scaled from 159) (see 'Cam Follower Pivots: Position', above). The displacement of the pivot centre is simply given by arcsine 4.5/7.35.

The next step is to determine the angular displacement of the point of contact of the follower arm. Since the cams rotate anticlockwise, the leading arm is the one to the right of the pivot and the trailing arm is to the left. With the leading arm tangential to the outside diameter of the cam (i.e. at the top of the 0.50" rise) the angle subtended at the cam shaft centre by a 3.50" follower arm is 28o26'. It would be convenient if this could be rounded down to 28o to save carrying the 26' through each calculation. For practical purposes the error introduced by this rounding down was ignored on the following considerations. The height of the rises in the case of the warning cams is 0.5" (see Fig. 1b). The foot of the active rise determines the start of the motion for both leading and trailing arms. The locus of the point of contact is a circular arc of radius equal to the effective length of the follower arm. Taking this into account Fig. 1b shows that a 3.50" arm at the foot of the 0.50" rise subtends and angle of28o5' i.e. only 5' of arc off the rounded figure. Working backwards it emerges that a 3.45" arm at the top of the rise subtends and angle of exactly 28o. If for purposes of calculation the distance to the point of contact is taken as 3.45" (the physical distance remains unchanged at 3.50") then the difference on the outer circumference of the cam amounts to 0.050" which corresponds to a worst case timing error of 26' of arc in the start of the falls and the end of the rises.

Using a 3.45" arm in the calculation to represent a physical arm of 3.50" ("it is emphasised that the physical arm remains 3.50") introduces timing error of 5' of arc for a 3.50" arm at the foot of the rise (a 3.45" arm tangential at the top or a rise has the same timing relationship as a 3.50" arm at the foot of a 0.59" rise). A worst case error of 0.050" on the circumference of a 13" cam was considered to be acceptable and a worst case timing error of 26' was considered to be an acceptable price to pay for substantial simplification of both calculation and manufacturing specification given that the resolution of the timing had already been increased from Babbage's 50-division per cycle scale to a more conventional 360o scale (a factor of 7.2). The errors introduced by using 3.45" as the arm length for purposes of calculation, and taking both follower arms tangential to the outer circumference at the same time (physically this never occurs as one follower is at the foot of a rise when the other is at the top), were therefore regarded as negligible for practical purposes in all cases except the lock timing for which the timing cycle is particularly tight and for which special provision was made for the circular locus of the point of contact.

With the follower arms represented by a 3.45" tangential to the outer circumference we are now in a position to determine the angular displacement of the points of contact i.e. Theta+- 28o. The cams rotate anticlockwise viewed from above. The even warning pivot thus lags the zero position by 270o-Theta and the leading point of contact lags by 270o-Theta-28o. The later the event in the timing cycle the further clockwise on the cam the corresponding rise or fall i.e. lag corresponds to clockwise displacement of the keyway. The keyway offset for the leading even warning cam (Cam 16) is therefore 270o-Theta-28o clockwise from the zero datum (204o15'). Similarly, the displacement of the trailing point of contact lags the leading point of contact by round and convenient 56o. This translates into a clockwise displacement of keyway for the trailing cam (Cam 15) of 260o15'.

Separation of the Cams

All the vertical motion cams were made from identical blanks (E391C) specified with maximum metal and machined to suit differing requirements of outer shape and vertical spacing. Fourteen of the cams (1 through 9, 13 through 16, plus 11) have the bosses machined down for the six closely spaced pairs. The two cam pairs for the sectors which are spaced further apart have the bosses left intact (10 and 12). Cams 1 and 2 (odd figure wheel axes) have the standard close spacing but special provision is made to accommodate the lubricated annular cam shaft bearing set into the lower framing plate. 160 shows the bearing and the cam in the same plane but no details are given for clearance or for securing the lower-most cam (Cam 1). The boss on Cam 1 was removed to clear and the cam shaft bearing and Cam 1 is screwed and dowelled to Cam 2. The lower cam shaft bearing prevents Cam 1 being keyed to the shaft. Cam 1, fixed as an undercarriage to Cam 2, is driven by Cam 2 which is keyed to the cam shaft. Each of the other fourteen cams is each keyed to the cam shaft and each cam is screwed and dowelled to its mating cam. Cam 1 is the only cam not keyed to the shaft.


The cam rises and phasing were verified graphically. Tracings of the cams were overlaid on the mating cam and as though fixed together and the motion and clearances checked using tracings of the follower arms. The standard 56o lag is a significant drafting convenience in ensuring that the dowelling and fixing holes of the mating cams line up as well as aligning the aperture cutouts. (See E383A&B for warning cams (leading); E384A&B for warning cams (trailing).

The cams were manufactured without keyways in the first instance. During assembly each cam was fixed and pinned to its mating cam and turned by hand on the shaft. When the motions of the followers were verified, the keyways were cut with the cams still fixed in mating pairs.

Manufacture and Assembly of the Follower Arms

The original drawings give no details of how the pairs of follower arms are to be fashioned. The two roller-cum-slider arms were made as one piece (E353&4). The twelve twin-slider arms were made in two parts spigotted together so that the two arms could be rotated to alter the angle between them. The paired arms were assembled on the pivot shaft with the position of the arms provisionally fixed with grub screws. Fine adjustment to the arm positions was carried out with the assembly and related cams in situ. The follower assembly was then removed from the cam stack, the arms (still fixed in relation to each other by grub screws) were slid off the pivot shaft, welded together, slid back on and then pinned to the pivot shaft. There was an awareness that this procedure might be judged to be overcautious. It was nonetheless considered preferable to having to scrap out-of-specification follower arm assemblies that might result from fixing the angles without trial.

The contact foot of each slider arm was case hardened prior to adjustment and welding to ensure that any heat distortion from the hardening process did not affect the trial settings.


[Note : Some of this material has been incorporated into separate sections in the Vertical Motion material and is repeated below].

Timing Diagram BAB [F] 385/1 a

This drawing is the main source of information describing the sequence and phasing of the various motions in the calculating cycle. In general single arrows are used to denote circular motion (up arrow clockwise and down arrow counterclockwise); double headed arrows are in general used to denote vertical motions with the length of travel of the motion indicated alongside in inches. However the convention of double and single arrows for vertical and circular motions is not consistent. For example, the lowering of the odd sector axis by 0.68" is indicated by a downward single-headed arrow, the succeeding upward motion of 0.34" is denoted by an upward single-headed arrow, and the final restoration of 0.34" is indicated by a double-headed arrow. There are also evident errors within the convention. For example, the direction of rotation if the odd sectors, figure wheels and carries is incorrect, as well as those indicated for the even warning and carry levers.

Broken lines indicate that the motion is not necessarily sustained for the full duration of the cycle interval allowed. For example, the circular motions of the figure wheels are indicated by broken lines. Here the duration of the motion is data dependent i.e. the proportion of the figure wheel axis rotation that the that the figure wheel is driven depends on the number-value of each figure wheel. Not all the notations were decoded. For example, the significance of the presence or omission of a bar on the tail of an arrow is not clear.

The timing diagram lacks a level of fine detail and in some instances is no more than a guide. The most serious omissions are in respect of the timing of the locking and unlocking actions. Unlike the motions of the calculating axes and wheels, the action of the locks is not represented as a separate set of phased actions indexed against the cycle divisions. The operation of locks, for example, is indicated by a bold 'L to indicate engagement (locked) and by a reversed 'F (presumably to indicate 'free') but no close detail is given for the lapping or phasing of the entry and withdrawal of locks to avoid contention between conflicting motions. Taking the even difference figure wheels as an example we find that at the wheels are locked briefly between the end of the counter-clockwise motion from giving off odd-to-even and the start of the carry cycle. A unit gap of one Babbage-division (50 to the cycle i.e. 1 division corresponds to 7.2o) is allowed for locking and unlocking. Though there is no horizontal grid on the diagram and the precision of the draughtsmanship discourages exact scaling these one-division gaps appear to be the nominal standard interval allowed for motions that are not contiguous in time.

However, working back from the locking cams (169) indicates that the actual period that locking and unlocking would occupy is 10o (4o for entry, 2o for dwell and 4o for withdrawal). In the modern implementation the minimum allowed was 11o (4o plus 3o plus 4o) but the dwell was varied slightly in some instances.

The 'L and 'F notations thus indicate locking status at the start of the specified motion ('locked' or 'free'), and the completion of the locking or unlocking action in time to avoid conflict is implied. It is clear from the cam details on 169 and 159 which specify the height of the rise, pressure angle, dwell and fall that Babbage did consider in detail how the operation of the locks should be phased. As far as fine detail is concerned the timing diagram is evidently representational with the detailed mapping from timing to cam specification omitted. All the cams were specified and verified from scratch. There were no significant deviations from Babbage's specifications.

A new more detailed timing diagram was drawn [Drawing Reference X21 ] to specify more exactly the cycle timing and to include detailed phasing and lapping of the various motions. Babbage's arrow notation was retained and notational inconsistencies in the original were eliminated. New notations were added: two hatched lines on the figure wheel circular motion arrows indicate addition this to distinguish between figure wheel addition and return motions; horizontal arrows that traverse the timing diagram columns indicate causal trains; and diagonal arrows indicate secondary warnings produced by the carry cycle.

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