1 The Birth of Science - MSRI

4.1 Mechanical Engineering 87
ability to design and build a great many machines. At least two important
novelties arose in early Hellenistic times: the use of a series of new foundational
technological elements, such as screws and cogwheels, and the
appearance of composite machines of high mechanical advantage, whose
design and construction were stimulated by the possibility of computing
advantages theoretically.
Forerunners of the screw, such as augers for drilling wood, certainly go
back long before that, but the use of cylindrical bolts with nuts is not attested
before the Hellenistic period. 8 Heron describes two manufacturing
methods. The simpler one consists in wrapping around a cylinder a right
triangle made of metal foil, one short side being parallel to the axis of
the cylinder; the hypotenuse thus coils into a cylindrical helix that serves
as a guide for the grooving. 9 The second method employed an automatic
groover, but its description, as given in the extant Arabic texts, is unfortunately
too obscure to be useful. 10 Both methods are based on scientific
design, without which precision screws cannot be made.
Cylindrical objects having a helical groove were used for different purposes,
as we shall see. The theoretical properties of cylindrical helices were
studied in a lost work of Apollonius of Perga, On the cylindrical helix 11
( ; the curve’s Greek name means “snail”). According to
Proclus, Apollonius proved, among other things, that the cylindrical helix
is homeomeric; that is, given any two points P and Q on it, there exists a
rigid motion that leaves the curve invariant and moves P to Q. Thus the page 124
curve can slide along itself without changing shape; this is precisely the
property that makes it useful in the construction of bolts and nuts.
It seems that cogwheels, too, were made for the first time in the early
Hellenistic period. 12 They opened to engineers many novel possibilities,
ranging from the transferral of rotational motion from one axis to a perpendicular
one, to the construction of reduction gears having several uses,
such as the creation of machines with high mechanical advantage. 13 The
reduction gears that we still use in many devices, from bicycle derailleurs
to timepieces, are direct descendants of the Alexandrian inventions, recovered
through the study of ancient works — particularly those of Heron of
8
Cylindrical bolts with nuts are then attested in presses; see Section 5.3 for the question of dates.
9
Heron, Mechanica, II, i, 5.
10
Heron, Mechanica, III, ii, 21.
11
[Proclus/Friedlein], 105, 1–6.
12
Our earliest documentation about gears is from the first half of the third century B.C. See
[Drachmann: MTGRA], pp. 200–203; [Price: Gears]; [Sleeswyk]. As we shall see, gears were used
in Hellenistic times in water mills and in machines for lifting water, among others.
13
Reduction gears and their mechanical advantages are examined in Heron, Mechanica, II, iii,
21–28.
Revision: 1.14 Date: 2002/10/24 04:25:47