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The Wikipedia entry for Milling (machining) is recommended as a good source on the history of the development of milling machines. There is no point in duplicating the information presented, so this entry will be limited to some lesser-known aspects of the milling of metals.
A milling process had been in use from the 17th century to machine gears for clocks and watches. Such machines became very sophisticated, but were intended for light cutting. Larger, more substantial versions were developed in the late 18th century for cutting gears for textile machinery,
It is certain that milling, or at least flycutting, would have been undertaken on ordinary lathes prior to the introduction of purpose-built milling machines. This would no doubt have led to modifications of lathes to make them more suitable for milling, and also to purpose-built milling machines.
Milling processes were used from c.1790 to produce the locks invented by Joseph Bramah. From 1789 to 1798 he employed Henry Maudslay to mechanise production. We do not know the relative contribution of the two engineers to the design of the machines. Part of one of the machines is preserved in the London Science Museum (see first photo). It is described as a 'quick grip vice', but this does not do justice to its role. It is part of a milling machine which incorporates an ingenious vice. It would have been clamped to the bed of a lathe or lathe-type machine having a milling cutter between centres. A dovetail slide operated by a hand-cranked leadscrew provided movement at right angles to the axis of the cutter. The height of the vice was adjusted by screws. The depth of the cut was probably determined by lifting a handle (missing in photo), with the depth limited by the vertical thumbscrew (nearest camera). The machine's role was probably to cut the slot in the top of the lock's cylinder which engaged with the drive peg on the key. Another special-purpose horizontal milling machine, known as the 'nibbling machine', was used to cut the narrow slots in the key, whose width and depth were critical. The machine was saved, but its fate is uncertain. From a photograph  we can determine that the cutter, presumably an end mill, was held in a lathe-type spindle. The key was held in an indexing head fixed to a large spring-loaded cross-slide moved by a long handle. A dovetailed cross-slide is located at the end of the machine remote from the headstock. Its role appears to be to determine the travel of the handle, and hence the depth of each milled slot.
In the USA, the earliest 19th C milling machines were very similar to lathes, with the workpiece being fixed to the equivalent of the cross slide. In the absence of dependable information about the early machines, we are left with individuals' recollections and with others' speculation. An interesting article by Edward G. Parkhurst appeared in the American Machinist in 1900, in which he described and illustrated a primitive milling machine shown to him by Robert Johnson in 1851. Johnson was one of a number of British gunmakers who established an armoury in Middletown, Connecticut, in 1814. Johnson said that the machine, which he did not claim to have introduced, was put to work in 1818. Its capability was very limited, the workpiece being clamped at a fixed height. If a second cut was required, the workpiece had to be packed up with strips of metal or paper. The V-edged cross slide was guided by four pegs having V notches. See illustration. The machine used a lathe headstock bolted to a wooden bench. Mr Parkhurst emphasised that the drawings showed the principle rather than the exact pattern.
Various claims have been made about 'interchangeable manufacture' and the associated use of milling machines in the second decade of the 19th century. However, the production of accurate work with a satisfactory finish is far from straightforward. Considerable demands are imposed on the rigidity of the machines and on the quality, detail design, and method of holding the cutters. To address and overcome these challenges in the early part of the 20th century would have been an impressive achievement. It is easier to envisage milling being used in the early days for roughing out components, using semi-skilled labour, leaving any critical finishing to be done by filing.
However, John H. Hall designed a breech-loading rifle in 1811 and went on to supervise production of this rifle at Harpers Ferry Armory. It is stated that he devised and built milling machines with guides and stops such that truly interchangeable parts were produced on machines operated by boys. Hall's ideas spread to Springfield Armory and the private armouries. When Simeon North began building Hall rifles in Connecticut, the Hall's gauging system ensured that parts were interchangeable between rifles from the two armories.. Discussions of 'interchangeable manufacture' rarely go into the all-important question of as-machined tolerances, or about which specific components could be used straight from the machine, and which items needed to be individually dressed to satisfy the gauging requirements.
The challenges of machine rigidity, bearing clearances, and the limitations of cutter design, manufacture and retention may have been addressed by simplicity: by having individual machines designed to do one specific job with one type of cutter and with the minimum number of moving parts (to reduce the scope for chatter due to looseness and lack of rigidity). An early example of such a machine was included in the Marc Brunel/Henry Maudslay blockmaking machinery at Portsmouth. The machinery included a form of vertical milling machine built in 1803, although it machined lignum vitae rather than metal. It was by no means a versatile machine, having only one purpose, namely the milling of recesses in sheaves.
The next stage of development involved providing a third axis of movement for the workpiece. This was not straightforward, given the difficulties of providing accurate guidance and adequate resistance to vibration.
Another early type of versatile milling machine with Y-axis movement came to be known as the 'Lincoln Miller'. It resembled a lathe, but was transformed by introducing a simple arrangement for elevating the spindle by raising each of the two headstock bearings by screws. Various names have been associated with its development: Thomas Warner, Frederick W. Howe, Elisha Root, and Francis A. Pratt.. The first examples were made at the Phoenix Iron Works, Hartford of George S. Lincoln and Co in the early to mid 1850s.. The arrangement for elevating the bearings was inconvenient, and it seems likely to impair the rigidity of the machine, and hence its acccuracy, productivity, and and ability to produce a good finish. Nevertheless, Lincoln millers were produced in vast numbers and remained in production for decades. On some, an outboard bearing was added, corresponding to the tailstock of a lathe. A number of types of early Lincoln Miller were illustrated in the American Machinist in 1900 
The next type of milling machine from the Phoenix Iron Works was the Lincoln Index milling machine, also designed by Pratt and built by Whitney. The spindle bearings were fixed in the headstock (i.e. non-elevating). The headstock could be moved relative to the workpiece in the X and Y planes. The workpiece was held in a vice or other fixture on top of a vertical cylindrical column which could be elevated (Y plane movement). The column could also be rotated, and was supplied with an indexing (division) plate. Starting in 1861, numerous examples were supplied to the armoury of Samuel Colt.
The Lincoln machines were not particularly versatile, but the introduction of 'universal' milling machines would revolutionise aspects of engineering production. In addition to machining flat surfaces, grooves, etc., they were available with accessories to allow the machining of gears, twist drills, splines, etc. The demand for a method of machining the helical flutes in twist drills led Frederick W. Howe, in consultation Joseph R. Brown of Brown and Sharpe to develop the universal milling machine. The first example was sold to the Providence Tool Co on 14 March 1862. B&S patented the type in 1865.
Frederick W. Howe introduced a profile milling machine with vertical spindles c.1848 .
A barrier to the acceptance of milling machines would have been the quality, availability, expense and ability to sharpen the milling cutters. These aspects were addressed with great success by Brown & Sharpe.
A further problem area to be addressed was the method of holding the cutters, especially end mills, so that they run truly and are held securely.
Some British Developments
It has been mentioned that milling-type operations would have been undertaken on lathes before the introduction of milling machines. One recorded example concerns a treadle lathe adapted by Joseph Clement for Charles Babbage. A description and photograph appeared in 'Machinery' in 1909, and the photograph is reproduced here . It shows an auxiliary bed with a compound slide mounted on the main bed. It could be driven by gears from the spindle. Components were added by Clement between 1824 and 1830 which made the lathe very versatile, including the ability to do milling work. Flycutters and a facing mill with inserted cutters can be seen on the table in the photo.
Milling machines were more widely used in Britain than is generally recognised, although the term 'milling' was initially avoided. 'Cutting' or 'drilling' was typical applied to the machines.
James Nasmyth wrote about a machine he built c.1830, while working for Henry Maudslay, to mill the faces of small hexagon nuts. He developed self-acting industrial versions of the machine for sale, and Nasmyth, Gaskell and Co were selling them by 1837. They were described as 'nut cutting machines', although they were by no means confined to nut cutting. They could machine polygons using an indexing head, or could do simple facing work by clamping the workpiece to the table. Writing to a customer in 1838, Nasmyth advised that the cutter should never exceed 55 rpm, to avoid damaging the cutter. By 1839 Nasmyth, Gaskell and Co had sold over 50 machines.. See photo.
Richard Roberts produced self-acting machines on a commercial basis to machine hexagonal and other multi-faceted components, and these were sometimes described as 'polygon machines'. They were made by firms in which Roberts was involved, namely Sharp, Roberts and Co (early 1840s), Sharp Brothers and Co (early 1850s): see Directory of Manchester and Salford, 1853. p33-37, Roberts and Dobinson (early 1850s).
Richard Roberts was undertaking milling on a larger scale by 1839, when American visitor William C. Davol described Roberts's ' Cutting Engine for cutting locomotive Engine cranks, the cutter was made by having a cast Iron wheel about 18 inches in Diameter 3 1/2 to 4 In wide with cavitys cut in the edge about 3 In deep to 5/8 wide set 3 In apart round the face of the wheel to receive the steel cutters which was ruther wider than the wheel and ground sharp on three sides. '
A later machine for milling the cranks on locomotive axles, designed by Robert Willis, was featured in an 1848 article . See illustration. The cutter was an 18" cast iron disc with inserted cutters. Cutting speed 28 ft/min.
A number of British firms produced machines for cutting keyways and slots for cotters using rotating cutters. These were commonly called slot drilling machines. James Nasmyth stated that he produced such a machine in 1847. It was self-acting, and Nasmyth stated that two machines could be overseen by an intelligent lad or labourer. However, it appears that Nasmyth, Gaskell and Co only started making such machines for sale c.1853. They were called 'patent grooving machines', although they were not patented by Nasmyth. Sharp, Stewart and Co started making such machines in the mid 1850s to Sharp and Furnival's patent of 1855. An accurate large scale model dated 1857 is on display at the Musee des Arts et Metiers in Paris, along with a sample workpiece produced on one of these machines. The Science Museum also have a similar sample workpiece. Photo here.
Kendall and Gent made a nut and bolt head cutting machine with three milling heads, allowing rapid production using cheap labour.
Another Manchester maker was J. and J. Kershaw. Their 'Drilling & Recessing Machine' was described and illustrated in The Engineer in 1856. It was a small vertical 2-axis milling machine, limited to cutting keyways in shafts.
These slot drilling machines were effectively vertical milling machines, but at that time their makers did not develop these or other milling machines to increase their versatility, unlike the situation in the USA, where universal milling machines found a ready market.
It seems that by the turn of the century, British and Continental firms were devoting much attention to the development of vertical milling machines, whereas in the USA horizontal machines continued to be favoured.
Despite the developments in Europe, there is no doubt that the USA led the way with small versatile milling machines. These found a ready market with makers of armaments, sewing machines, typewriters, etc. In turn, the use of milling machines encouraged the development of precision grinding machines, abrasives wheels, milling cutters, twist drills, micrometers, etc.
'Some Early Milling Machines'
An interesting article with this title appeared in the American magazine 'Machinery' in 1896.
The oldest machine found by the author was the machine referred to above at the works of Gay, Silver and Co. The exact age was not known, but Gay, Silver and Co sold their first example in March 1841 to the Amoskeag Land & Water Co.
A horizontal planer type mill was featured, its early date being indicated by its wooden bed.
Perhaps surprisingly, a British Smith and Coventry horizontal overarm-type milling machine was featured, at work at the Pettee Machine Co in Newton, Upper Falls, Mass., which the author described as the 'The earliest machine of the well-known "Knee" type which I have found' and dated it at 'about 1860', which does seem rather early for this type of machine. It was still doing fairly heavy work.
A horizontal milling machine by William Sellers and Co had a peculiar arrangement for altering the height of the cutter spindle relative to the table, the spindle being mounted eccentrically in a rotatable cylindrical housing.