Ancient Astronomical Instruments

21
With the developments of ancient astronomy, ancient astronomical mechani-
cal instruments were extensively used for measurements, computation, and dem-
onstration. These instruments represented the combinational achievements of
astronomy and mechanical engineering technology at the subjects’ eras. The
investigations of the recorded ancient astronomical instruments not only give us
a glimpse of their historical developments, but also provide overall concepts and
knowledge about the mechanical characteristics for some designated functions
and applications. Furthermore, the relevant craftsmanship is realized. This chapter
presents a study of the ancient astronomical mechanical instruments and classifies
them in accordance with their display functions. Some representative artifacts such
as sundials, astrolabes, calendrical device and relevant compound instruments,
astronomical (mechanical) clocks, and orreries are introduced. Focusing on a spe-
cific display function, the designs among different astronomical instruments are
compared. In addition, the manufacturing technology and craftsmanship for gener-
ating some particular functions are analyzed.
2.1 Classifications Based on Functions
Designs of mechanical devices are advanced with the historical developments of
diverse cultures, sciences, and manufacturing techniques along with numerous
applications. Astronomy is one area much affected in ancient cultures. The char-
acteristic of constrained motions of mechanical devices is widely used for the
astronomical applications to produce complicated calculations, precise measure-
ments, and ingenious exhibition. The development of ancient astronomy attaches
to several ancient astronomical instruments with sophisticated designs and special
applications. For examples, sundials, astrariums, astrolabes, planetariums, and
Chapter 2
Ancient Astronomical Instruments
© Springer-Verlag Berlin Heidelberg 2016
J.-L. Lin and H.-S. Yan, Decoding the Mechanisms of Antikythera
Astronomical Device, DOI 10.1007/978-3-662-48447-0_2

22 2 Ancient Astronomical Instruments
astronomical mechanical clocks are well-known devices with various knowledge
of mechanisms and astronomy.
In what follows, the available ancient astronomical mechanical instruments,
based on their functions, are classified into the applications of measuring time,
measuring position, observation, computing, and demonstration [1–9].
2.1.1 Observation Application
These refer to the mechanical instruments used to assist in observing the phenom-
enon of celestial bodies in yonder universe. Observational astronomy is a division
of modern astronomy. It is the practice of observing celestial objects by using
telescopes and other astronomical apparatus. The observation of astronomical
phenomenon is the leading work of ancient astronomy for recording and under-
standing what happened in the sky and their cycles by simple mechanical devices.
The changes of seasons are conscious natural phenomenon; however, it is
closely constrained by the areas and climates the observers live in. Once the cli-
mate change of area is not obvious, the time cycle is not defined. Therefore, the
revolutions of phenomenon of celestial bodies are regarded as the most popular
and steady units of time. According to this requirement, the historical records
about the astronomical observations existed in many ancient civilizations. Also, it
is related to the developments of mechanical instruments for astronomical obser-
vation. Telescope is the representative work of observational astronomy. The first
one was made in Holland around 1608 [5, 6]. In ancient Western civilizations,
cross-staffs and astrolabes could be regarded as the instruments to assist the obser-
vation of astronomical phenomenon and events.
2.1.2 Measuring Position and Distance Application
These refer to the mechanical instruments for identifying positions of celestial
bodies in the sky and the angles between each other, even to estimate the distances
between these objects and the observers. Depending on the contribution of geo-
metrical mathematics, the distance between measured objects could be estimated.
In general, the application of measuring position or angle can be regarded as a part
of astronomical observation work in ancient times.
The developments of measuring devices start with the study of geometry. For
measuring distance, the measuring devices were usually used in the building of
towers, temples, and towns [2, 6]. In addition, they can measure the distance with
a wide range that was difficult to cross over such as a river, a mountain valley, or
a sea inlet. For navigation, navigators used them to measure the elevation angle
of the noontime Sun above the horizon, which allowed them to estimate their lati-
tude. For astronomers, they were used to measure the angle between the directions

23
of two celestial bodies or position heavenly bodies in the sky before the invention
of telescopes. The aspiration was to estimate the distance between the Earth and
stars. Cross-staffs and astrolabes are two popular ancient astronomical mechanical
instruments not only for observation, but also for measuring.
2.1.3 Measuring Time Application
These refer to the mechanical instruments for counting or indicating some time
standards, which did not have obvious phenomenon (such as sunrise, sunset, and
moon phase) to distinguish their time intervals.
Measuring position (angle or distance), measuring time, and observation can
represent the first step in developing the combination of astronomy, mechanical
design, and science and technology [2]. The work of measuring time starts with
the definitions of a day, a month, a year, and other time cycles. These time defi-
nitions were based on the long-term observational records of cyclic astronomical
phenomenon. Sunrises and sunsets are the basic standards to distinguish a day.
For Egyptian and Romans, they further divided their day into 24 h, like we do
today. Among these 24 time intervals, 12 h are for the day and another 12 h are for
the night [1, 3, 5, 6]. Even though this definition resulted that an hour of the day
is not the same as an hour of the night in some seasons, an hour was contributed
to distinguishing and indicating the time much clearly in ancient times. Hence, the
mechanical devices for measuring time were designed to distinguish the hours of
a day.
In ancient times, the hours of a day were identified based on the position of the
Sun in the sky. For instance, sundial is the ancient measuring device that used the
shadow of object, gnomon, to reflect the position of the Sun. In addition, the users
could understand the time according to the time graduation that the shadow indi-
cated. Nevertheless, the operation of the device is determined on the appearance of
the Sun. It was useless on days when there was no Sun, and it could not measure
the nighttime. The appearance of clocks overcomes the above constraints of the
sundials.
Clocks were an important invention for measuring time. The precursor of
clocks was the water clock [1, 3]. It depended on the flow of water from a tank
to indicate the hours, as shown in Fig. 2.1 [10]. Because of the different duration
of hours of the day and the night, the tank could be designed to coincide with the
duration of the day by varying the quantity of a scale. Afterward, the mechanical
clock was invented based on the redefinition of hours, and its service depended on
the accurate motions by gearing. Many early mechanical clocks were not a sepa-
rate instrument for measuring time. They were astronomical clocks for measur-
ing time, displaying astronomical motions, and showing astronomical information.
Such a sophisticated device was regarded as a combination of outstanding manu-
facturing technique and advanced astronomical achievement. It could continuously
demonstrate the cyclic astronomical motions according to the clockwork.

2.1.4 Computing Application
The astronomical mechanical instruments for computing applications refer to the
devices with mathematical gearings for calculating the astronomical cycles. For
mechanical devices, the power output or transmission was not the only required
application. This type of instruments focused on using the kinematic characteris-
tics of mechanisms to generate specific rate of transformations. Generally, such
an output function was achieved by gear mechanisms. The resulting mechanical
instruments could calculate some astronomical cycles or calendars based on the
known mechanism characteristics. In addition, these astronomical mechanical
devices seemed to be the precursor of computation devices [4].
In fact, the ancient astronomical mechanical devices with computing applica-
tions were used for calendrical devices. According to available historical records,
they were mostly not formed as independent instruments, but usually associated
with other astronomical instruments, such as sundials or astrolabes.
2.1.5 Demonstration Application
The astronomical mechanical instruments for demonstration application are
defined as the devices used to simulate relevant academic and science theories by
mechanical designs, such as planetariums, armillary spheres (concentric spheres),
and orreries. Simultaneously, their displays could be regarded as the computation
results to show the attitude, latitude, and/or longitude of designated positions.
As mentioned in Chap. 1, it is understood that the ancient astronomy had
developed the hypothesized geometrical models of the universe and the orbits for
describing the motions of heavenly bodies based on the observational records.
Fig. 2.1 Virtual imitation of
ancient Egyptian water clock

25
These geometrical models in writing form were applied on the physical mechani-
cal devices that generated the motions satisfied their corresponding astronomical
geometrical models, owing to the development of manufacturing technique and the
advanced understanding of mechanism characteristics. Some complete mechanical
devices referred to the embryo of the universe that was opinioned at that time. Like
the astronomical computing devices, they sufficiently applied the kinematic char-
acteristics of mechanisms for generating appropriate rate ratios and built by gear
mechanisms. Furthermore, they were the essence of astronomy in their eras.
2.2 Jacob’s Staff
Jacob’s staff was a widely used ancient measuring device. It, also called baculum,
cross-staff, or radius, consists of a main staff with a perpendicular crosspiece,
which was attached to the staff at its middle and was able to slide up and down
along the staff, as shown in Fig. 2.2 [2, 5, 8, 9, 11–13].
In navigation, this apparatus was used to determine angles or distances: The
angle between the horizon and Polaris (or the Sun) can be determined to estimate
the latitude at which a vessel is located. The angle between the top and bottom
of an object can be measured to determine the distance to the object, based on
geometric mathematics, if its height is known, or to determine the height if its dis-
tance is known. Furthermore, the horizontal angle between two positions can be
measured to determine the other position on a map [2, 9, 11, 12].
When Jacob’s staff was used for astronomical observation, it was referred to as
a radius astronomicus. Figure 2.3 shows a schematic introduction of application
method of a staff. In order to measure the angle between two stars or the altitude
of a star, astronomers would place the staff below one of his eyes. Since the cross-
piece would have a pair of open sights (sticking out perpendicular to the scheme)
Fig. 2.2 Virtual imitation of
Jacob’s staff

at symmetric locations such as P and P′, they slide the crosspiece up and down
until sight P covered one of the stars and sight P′ the other. Moreover, Jacob’s staff
was workable at night because of the convenient slits on the sights [9, 11, 12].
2.3 Astrolabe
An astrolabe is an astronomical instrument used for measuring altitudes of celes-
tial bodies, displaying the positions of stars, and finding the time of a day and the
time of celestial events, such as sunrise and sunset [14]. Its origin was in the clas-
sical Greece (lasting from the fifth through the fourth century BC). The astrolabe
was introduced to the Islamic world until the mid-eighth century and was highly
developed and extensively spread during the early centuries of Islam. With the
popularization of Islam, it moved through North Africa into northern Spain and
was introduced into Europe in around eleventh century [15–19].
The stereographic projection is the most important theory for building an astro-
labe. It was as if Apollonius had studied the theory. Afterward, Hipparchus refined
the structure of the theory. He redefined and formalized the concept of projection to
build a method for solving complex astronomical problems. Hipparchus is regarded
as the most influential individual in the discovery of the stereographic projection
theory, but he did not invent the astrolabe [11, 16]. The earliest evidence for apply-
ing the stereographic projection theory in a mechanical device was an anaphoric
clock in around the first century. Nevertheless, exactly when the stereographic pro-
jection theory was turned into the astrolabe, we known today remains a mystery.
A traditional astrolabe was composed of several members, as shown in Fig. 2.4
[15]. Its major members were rete, mater, and plate. A rete is a skeletal plate that
Fig. 2.3 Application
illustration of Jacob’s staff
[11]
Sun or Star
Horizon
P
P
Measured Altitude

27
fits into an astrolabe on top of the selected latitude plate and is freely rotatable
over it. The rete is the stereographic projection of celestial sphere. It had star
pointers and the stereographic projection of the ecliptic. The star pointers were
placed at the positions of their stereographic projection to mark visible and bright
stars [14, 15, 18, 19]. The form of the pointers could be simple indicators or pat-
terns of vines and animals. The retia of the astrolabes are various. For early astro-
labes, the number of star pointers varied from 10 or 12, and they increased to as
many as 50 or 60 on later ones. They were regarded as the representative symbol
of a family. Besides, a mater is the disk of an astrolabe which usually had a hollow
section. A plate for representing the local latitude engraved with circles of altitude
and azimuth for a certain latitude was inserted into the hollow section of the mater.
It is the stereographic projection of the local sky based on the latitudes of build-
ers’ positions. Sometimes, the ancient astrolabes included several plates engraved
on both sides, so the instrument could be used in various latitudes. For the astro-
labe, the projection of the celestial sphere and the projection of the local sky are
overlaid with a common point, the north celestial pole. Thus, the projection of the
celestial sphere can be rotated with respect to the projection of the local sky to dis-
play a view of the sky for any combination of date or time [15, 19].
Whenever an astrolabe was used, the moveable members were adjusted to
a specific date and time. After appropriately setting, much of the sky was repre-
sented on the instrument. The two faces of the astrolabe had their own functions.
Most problems were solved by the front of the astrolabe which has fixed and rotat-
able parts. The fixed parts represent timescales and the stereographic projection of
the sky. The rotatable parts were adjusted to simulate the daily rotation of the sky.
As to the back of the astrolabe, it usually had scales for finding the longitude and
the altitude of the Sun or a star for a specific date.
Fig. 2.4 Members of astrolabes; reprinted from Ref. [15]
2.3 Astrolabe

2.4 Sundial
A sundial is a device for measuring the hour of a day existed in many civilizations
in the ancient world. The oldest sundials appeared around 3500 BC and were rep-
resented by obelisks and solar clocks by Egyptians and Babylonians [3]. In gen-
eral, a sundial consists of the gnomon that is also called the style and the surface
engraved with the timescale for indicating the time of a day, as shown in Fig. 2.5.
The shadow of the gnomon is projected on the surface. When the Sun moves in the
sky, the corresponding gnomon’s shadow moves in the surface. According to the
position of the gnomon’s shadow, the hour of a day is identified.
The shape of gnomon might be that of a road or an edge, which was not con-
strained, and the styles of the surface were diverse. Ancient sundials could be
Spring/Autumn equinox
declination line
Summer solstice
declination line
Winter solstice
declination line
Hour lines
Dial plate
Gnomon
To the celestial pole
Gnomom
Dial plate with
time scale
Summer
solstice
Equinoxes
Winter
solstice
The position of the sun at the noon
Nodus
= latitude
(a)
(b)
Fig. 2.5 Illustration of the sundial. a Members. Reprinted from Ref. [40], copyright 2015, with
permission from Carl Sabanski. b Projection [41]

29
classified into two types: fixed sundials and mobile portable sundials. Fixed sundi-
als refer to sundials that are mounted in a fixed structure. According to the styles
of the sundials’ surface, fixed sundials can be further divided into equatorial sun-
dials, horizontal sundials, vertical sundials, and non-planar sundials, as shown in
Fig. 2.6. The surface of equatorial sundials is an incline parallel to the equator, and
its gnomon is parallel to the axis of the Earth. The surface of horizontal sundials
is parallel to the ground, and the gnomon is parallel to the axis of the Earth. These
Fig. 2.6 Fixed sundials. a Equatorial sundial [42]. b Horizontal sundial. c Vertical sundial,
reprinted from Ref. [43], copyright 2015, with permission from the Web site. d Non-planar sun-
dial [44, 45]
2.4 Sundial

two types of sundials were much popular in the excavated sundials. The surface of
vertical sundials must be vertical to the ground, and their gnomon is still aligned
with the axis of the Earth. As a result, this type of sundials was usually built on the
wall. The final type is non-planar sundials with curved surface, like a part of inter-
surface of a cylinder, a cone, or a sphere, to receive the shadow of the gnomon [3].
There were many styles of portable sundials developed in ancient times. The
excavated fragment of an Egyptian portable sundial for example [19], in general,
this type of sundials still had a gnomon that was a perpendicular block rising at
the foot of the sloping face, as shown in Fig. 2.7. The height and width of the
gnomon and the sloping object were the same. Whenever the instrument was to be
used, it must be put down on a flat surface and be turned so that it faced the Sun
directly [20, 21]. Thus, the shadow of the gnomon could fall upon the sloping face
for showing the time. Furthermore, there were two special types of portable sundi-
als, except for the surviving Egyptian portable sundial. One is a diptych sundial,
as shown in Fig. 2.8. This type of portable sundials had two leaves. For a simple
Fig. 2.7 Virtual imitation
of Egyptian portable sundial
[21]
Fig. 2.8 A simple diptych
(portable) sundials [40]

31
diptych dial, the inter-face of one leaf was a vertical sundial and the inter-face of
the other leaf was a horizontal sundial. Such a sundial can be adjusted accord-
ing to users’ latitude, by inclining it until its gnomon is parallel to the axis of the
Earth. Actually, most portable sundials included a compass contained for orienta-
tion and are served completely in museums at present [19]. The other is the ring
sundial, as shown in Fig. 2.9. Its main body was a ring held by a cord and had a
hole through which lights could pass. Thus, the resulting light point could project
on the ring with a timescale to indicate the hour of a day.
2.5 Calendrical Device
It is well known that one of the characteristics of gear mechanisms is to trans-
mit motions with designated gear ratios. According to finding of archaeology, such
a technique was used widely in the building of calendrical devices [22–28]. As
mentioned above, all known ancient calendrical devices were associated with other
astronomical mechanical devices to form multifunction astronomical mechanical
devices until now. In what follows, some of these special mechanical devices are
introduced.
2.5.1 Astrolabe with Calendrical Gearing
The astrolabe with calendrical gearing is the combination of the calendrical device
and the astrolabe. It is an ancient astronomical mechanical device with compound
functions. Except for the fundamental function to understand the night sky at some
Fig. 2.9 Ring sundial [43]
2.4 Sundial

observation position, this device can also operate the calculations of calendars
through the application of mathematical gearing.
A complete historical record of mathematical gearing, as shown in Fig. 2.10a,
illustrated the calendrical device by Al-Bı
-rūnı
- (973–1047), who is regarded as
one of the greatest scholars of the medieval Islamic era and was versed in phys-
ics, mathematics, astronomy, and natural sciences [22–26]. Since relevant histor-
ical records did not definitely describe what mechanical devices contained such
a calendrical gearing, the definition of the calendrical gearing is uncertain. It is
mainly believed that the gearing could be associated with an Islamic astrolabe
based on the investigation of other similar mechanical devices. But, it is believed
that the gearing was a separate mechanical device and was a rare ancient astro-
nomical device. This gearing is described completely in the manuscript of the
Islamic treatise in 1000. And it functions to model the cyclic variation of moon
phases and the calendars. Figure 2.10b illustrates Al-Bı
-rūnı
-’s relevant astronomi-
cal work for explaining various moon phases. Furthermore, Fig. 2.10c is the
mechanical scheme of this mathematical gearing in the manuscript. It was clearly
indicated that the mechanism was an ordinary gear train consisting of 8 gears and
5 separate arbors. Through the analysis of gear ratios, the gearing is known as
using axis B as the input, that rotates once every 7 days; axis A rotates once every
28 days to display the position of the Moon; axis C rotates once every 59 days to
reveal the age of the Moon; and axis E rotates once every 366.42 days.
Another example is the Persian astrolabe with calendrical gearing that dated
back to AD 1221–22 and has been preserved in the Museum of the History of
Science of Oxford [23, 24, 29], as shown in Fig. 2.11a. The front plate is for astro-
labe, and two lugs on the rete serve as sights. The back plate is for the calendar
without the use of a normal alidade. This device was operated by turning the cen-
tral pivot, probably by hands or by using the astrolabe rete as a handle. The cor-
responding calendar and the lunar phase are moved accordingly. This compound
mechanical device is found to consist of the gearing with the same purpose as that
in Islamic treatise but with different gear ratios. Figure 2.11b shows the mechani-
cal scheme of the calendrical gearing of this device. This gear train consists of 7
gears and 5 separate arbors. According to the analysis of gear ratios, the functions
of this calendrical gearing are known as using axis B as the input, that rotates once
every 7.375 days; axis A rotates once every 27.23 days to display the position of
the Moon; axis C rotates once every 59 days to reveal the age of the Moon; and
axis E rotates once every 354 days.
2.5.2 Sundial with Calendrical Gearing
This type of mechanical devices is the combination of the sundial and the
calendrical device. A known example is the Byzantine sundial with calendrical
gearing dated from late-fifth century of the Christian era or the first half of the

33
B (Input) E
A C D
Moon in Zodiac:
28 days
Age of Moon:
59 days
Sun in Zodiac:
366.42 days
40 10
7 59
19 59
24 48
Input (1 rotation):
7 days
Fixed plate
Fixed plate
(a)
(b)
(c)
Fig. 2.10 Calendrical device by Al-Bı
-rūnı
-. a Historical picture, reprinted from Ref. [24]. b Illus-
tration of moon phase, reprinted from Ref. [43]. c Mechanical drawing [23]
2.5 Calendrical Device

sixth century [23–29]. It was much earlier than the Islamic calendrical device.
The excavation of this mechanical device survives as fragments including 2 vis-
ible arbors [23, 30]. In 1984, a reconstructed model of the Byzantine sundial
with calendrical gearing was presented by J.V. Field and M.T. Wright, as shown
in Fig. 2.12[23, 30]. The calendrical gearing of the reconstructed model adopted
similar design with the historical record of Islamic treatise and the Byzantine
sundial with calendrical gearing to display the positions of the Sun and the
Moon.
B (Input) E
A C D
Moon in Zodiac:
27.23 days
Age of Moon:
59 days
Sun in Zodiac:
354 days
48 13
8 60
Input (1 rotation):
7.375 days
60
10
60
Fixed plate
Fixed plate
(a)
(b)
Fig. 2.11 Persian astrolabe with calendrical gearing. a Antiquity, reprinted from Refs. [14, 19, 24],
copyright 2015, with permission from Museum of History Science. b Mechanical drawing [23]

35
2.6 Planetarium, Astrarium, and Astronomical Clock
Planetariums are diverse with ages. In early times, the planetarium was referred
to as a mechanical device that could demonstrate the cyclic motions of heavenly
bodies based on the universe model proposed at that time. This mechanical device
was driven by gear mechanisms. However, in modern times, a planetarium usually
refers to a theater built primarily for presenting educational and entertaining shows
about astronomy and the night sky, or for training in celestial navigation.
An astrarium was also defined as a mechanical device for displaying the
motions of the celestial bodies. It was generally for the astronomical clock [23].
According to historical literatures, this type of astronomical instruments is an
outstanding achievement in the fourteenth century. The earliest astronomical
clock was devised by Richard of Wallingford (1292–1336) between 1327 and
1330, but no historical descriptions or schemes about this earliest one exists [23].
Until now, the most famous example is the 7-sided brass astronomical clock, as
shown in Fig. 2.13, designed and created by Giovanni de’ Dondi, a professor in
the University of Padua and a clock maker between 1348 and 1364 [18, 24, 29,
31–33]. Seven dials of the upper section of this astronomical clock, respectively,
demonstrate the primum mobile, Venus, Mercury, Moon, Saturn, Jupiter, and
Mars. Figure 2.14 shows all of the reconstructed dials of de’ Dondi’s astrarium.
The mechanism contained in each dial of the astronomical clock was an epicy-
clic gear train with pin-in-slot joints [34, 35]. This special design was common
in the ancient astronomical mechanical devices and was essential for the anomaly
motion.
Fig. 2.12 Reconstruction model of the Byzantine sundial [23, 30]

In the fifteenth century, an unclear schematic drawing appeared in the manu-
script of Leonardo da Vinci (1452–1519), as shown in Fig. 2.15a [29, 36]. The
gear mechanism seemed to be a part of an astrarium and was supposed to serve
the purpose of demonstrating the cyclic motion of Mars. Figure 2.15b shows the
corresponding schematic drawing. There are 8 gears in this mechanism. Three of
them (members 2, 6, and 9) are regarded as the carrier, and three of them (mem-
bers 3, 7, and 10) are regarded as the input members for providing the input power.
Therefore, this mechanism required three input sources to generate a controllable
and constrained motion. By the viewpoint of modern mechanism, this mechanical
device was a 9-bar mechanism with 14 joints and 2 degrees of freedom. The pro-
fessional knowledge of mechanism is represented in Chap. 3. The chief concept of
design should be satisfied with the Ptolemaic epicycle system. Certainly, it is obvi-
ous that the design of gear mechanism with pin-in-slot joints was applied again.
Besides, the demonstration function of planetarium was used for combining
with other astronomical mechanical devices. For example, a French Gothic astro-
labe, dated about 1300 and preserved in the Science Museum of London, has a
similar purpose for displaying the relative positions of the Sun and the Moon in
Fig. 2.13 Manuscript of astrarium by Giovanni de’ Dondi [43]

37
the zodiac by the corresponding pointers driven by an arrangement of gears, as
shown in Fig. 2.16 [24]. The gear mechanism was built over the front plate of
the astrolabe. The existing situation of the Gothic astrolabe is quite complete, but
lacking the Moon pointer. Therefore, its operation and functions are understood
clearly.
In fact, the names “planetarium” and “astrarium” are frequently used to
call the same device. In the manuscripts and treatises by de’ Dondi, these two
names appeared successively several times to mean his own astronomical clock.
Therefore, in the study of astronomical mechanical devices in early times, the
roles of planetarium and astrarium shall be regarded as the same.
2.7 Orrery
An orrery is a modern astronomical mechanical device that is designed based on
heliocentric model. It displays the relative positions and motions of the planets
and the Moon in the solar system [37–39]. The design and function of the orrery
is very similar to the ones of planetarium or astrarium. Nevertheless, the orrery
only refers to a display device whose motions of celestial bodies are around the
Sun, i.e., the center of device is the Sun. The orrery was invented by clock makers
Fig. 2.14 Reconstructed dials of de’ Dondi’s astrarium [35]

George Graham (1673–1751) and Thomas Tompion (1639–1731) before 1719 and
then gradually developed to be one of the achievements in the eighteenth century
[37]. Such a device is typically driven by a gear mechanism, like a clock, and has
a globe representing the Sun at the center as well as a planet at the end of each
arm. The solar system is clearly represented in three-dimensional pointer system.
The most important is that the revolution and the rotation of each planet can be
understood easily.
2.8 Comparisons of Astronomical Instruments
A mechanical device is defined based on its functions and purposes. From the
viewpoint of mechanical design, it is reasonable to believe that a common design
for the specific purpose can be applied to various mechanical devices. A thorough
Fig. 2.15 The planetarium
by Leonardo da Vinci.
a Schematic drawing of
historical manuscript [29,
36]. b Modern schematic
drawing
1
2
3
4
5
6
7
8
10
9
1
2
3
4
5
6 7
8
9
10
(a)
(b)

39
investigation of the ancient astronomical mechanical apparatus is indispensable for
understanding the historical development of mechanism designs for some specific
output functions, such as computing, demonstration, and measuring.
According to available ancient astronomical mechanical devices (the Islamic
calendrical device, the Byzantine sundial with calendrical gearing, and the Persian
astrolabe with calendrical gearing), ancient mechanical design for the application
of computing was ordinary gear trains. The excavation of some devices reveals
that the design of gear mechanisms was workable and precise, even though the
shapes of the teeth could be slightly different. In order to satisfy the calculations of
different calendars, these astronomical apparatus with calendrical calculation had
different teeth and numbers of gears to construct their gear trains.
The variation of moon phase is a cyclic astronomical phenomenon. It seemed
to be regarded as one of the calendars. The function for displaying the variation
of moon phase was usually attached to the calendrical device. The manners for
showing the moon phase were particular and diverse. They depended on the rela-
tive motion of the Moon disk and the fixed plate for showing the moon phase. They
could have a rotatable moon disk with full-black circles that were regarded as the
moon shadow. Depending on the corresponding gearing, the moon disk was driven
Fig. 2.16 French Gothic
astrolabe, reprinted from Ref.
[24], copyright 2015, with
permission from Science
Museum of London
2.8 Comparisons of Astronomical Instruments

to gradually show the shadow in a hole of fixed case. Or, a Moon disk that was white
and had a hole rotated over a fixed full-black plate for moon shadow. The fixed case
still had a hole. And, the new moon appeared when the hole of Moon disk coincided
with the hole of the fixed case. Furthermore, a Moon disk could be replaced by a
Moon ball. This manner was rare, but existed in ancient astronomical apparatus.
For the function to demonstrate the motions of celestial bodies, the study of
ancient astronomical apparatus concludes two different designs. One design is
the ordinary gear train used in the Islamic astrolabe with calendrical gearing, the
Byzantine sundial with calendrical gearing, the Persian astrolabe with calendrical
gearing, the French Gothic astrolabe, and the orrery. Such a mechanical design
represents the mean motions of heavenly bodies. Since these motions are almost
anomaly, there are errors between the prediction positions of these apparatus and
the actual observation positions in the night sky.
Another design is a planetary gear train with pin-in-slot joints. This design was
applied in all dials of the Dondi’s astronomical clock and the scheme of the manu-
script by Leonardo da Vinci to generate the variable rate of output so as to satisfy
the anomaly motions of the celestial bodies. The difference between the applica-
tion examples is the numbers of the pin-in-slot joints. For these designs, the num-
ber of applied pin-in-slot joints is determined by their demonstrated planets and the
universe model that the planets applied. According to the historical development
of astronomy, both Dondi’s astronomical clocks and the planetarium by Leonardo
da Vinci were invented after the publication of the Ptolemaic system. Thus, it is
confirmed that the demonstrations of planetary motions of these apparatus should
adopt the Ptolemaic system. The numbers of pin-in-slot joints used made the
designs satisfy the geometrical models of the astronomical theory at that time.
Such a design concept was believed to have spread into Western scientific culture.
Except for the investigations of functions and mechanisms, the manufacture
technique is also a point. For the ancient astronomical mechanical apparatus, gears
were regarded as the soul of mechanisms. The difficulty of manufacturing was
related to teeth shape, size, and teeth number of gears. The teeth shape of most
early gears approximated to equilateral triangles, and the gear of Olbia is a par-
ticular example. Their shape and the required shape cutter were obviously simpler
than modern gears. These early gears could be manufactured much easily, but the
triangular shape made impact and vibration stronger during the engagement pro-
cess of gears. In general, the size of the gears used in astronomical apparatus was
so fine that they could be installed in a constrained case. As to the choosing of
teeth number, it was absolutely related to the precision of scale division of a circle.
Thus, all teeth could averagely surround the gear without deforming the shape.
Furthermore, coaxial arbors of gears were much popular in the ancient astro-
nomical mechanical apparatus and clockwork. This design must consist of a hollow
outer arbor, and the inner arbor could pass through it. The outer arbor and the inner
arbor rotated, respectively. The manner for mounting a gear and an arbor was not
constrained. Sometimes, some of the gears had squared holes by which they were
fitted to their arbors. The relevant traditional technique was persisted generation by
generation. At least, the design is used widely in the later content of this book.

41
2.9 Remarks
The research of ancient astronomical mechanical apparatus contributes to the
understanding of the historical developments of their applications, mechanical
designs, and relevant manufacturing techniques. It is essential that such an investi-
gation provides the fundamental bases for constructing an astronomical mechani-
cal apparatus with some specific functions.
Ancient astronomical mechanical apparatus, based on their functions, were
classified into applications for observation, measuring time, measuring distance,
computing, and demonstration. Except for separate ancient astronomical appara-
tuses, some of them are compound apparatus with multifunctions. For calendrical
calculation and demonstration of celestial bodies’ motions, several design exam-
ples are introduced and the relevant types of mechanisms and manufacturing tech-
nologies are analyzed.
In summary, it is believed that the design concepts to operate the motions with
variable rates and the calendrical calculation were spread out in the Western world.
And, the manufacture technique for these clock mechanisms had been preserved
as a tradition.
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