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CHINESE JOURNAL OF MECHANICAL ·676· Vol. 28,aNo. 4,a2015

DOI: 10.3901/CJME.2015.0414.061, available online at www.springerlink.com; www.cjmenet.com; www.cjme.com.cn

Decoding the Phase Display Device over the Front Dial of the Mechanism

LIN Jian Liang* and YAN Hong Sen

Department of Mechanical Engineering and University Museum, National Cheng Kung University, Tainan 70101,

Received September 22, 2014; revised April 7, 2015; accepted April 14, 2015

Abstract: The is the most famous ancient astronomical calculator. The damaged excavation is a critical constraint for decoding the mechanism completely. By the systematic reconstruction design methodology, all feasible designs of the moon phase display device, which is one of the unclear mechanisms of the Antikythera mechanism, are reconstructed. These designs, including ordinary trains and epicyclic gear trains, are the simplest designs and satisfy the surviving evidence. The Antikythera mechanism and its reconstruction designs presented by LIN and YAN are introduced first. Three pointer types of the Antikythera mechanism are concluded based on their display motions and the orientation of the mechanism. In accordance with the analysis of the available interior reconstruction designs and the surviving evidence, four feasible designs of the moon phase display device are generated. All of them utilize the ball pointer with black and white that rotates around the radial axis to show cyclic moon phase. Two of these four feasible reconstruction designs are driven by one input source, and their bronze disks are fixed and rotatable respectively. Both of the remaining reconstruction designs are driven by two input sources, and their bronze disks are rotatable. Therefore, the four reconstruction designs of the moon phase display device reveal all possible display conditions of the moon phase pointers and the possible purposes of the bronze disk.

Keywords: Antikythera mechanism, moon phase display device, reconstruction design, gear train

discovery of its excavation is a great of , 1 Introduction and the relevant historical background is interesting. The reconstruction research of this ancient mechanical Ingenious mechanical devices are designed to serve device depended on the development of image technology special purposes or perform special functions. By the in the . In 1975, PRICE presented the first combinations of joints and members, the devices can reconstruction design with the concentric front dials and transmit constrained motions by moving upon each other as back dials. The front displayed the and the Moon. The mechanisms, or transmit forces without any relative motion back was suggested to show synodic and lunar , as structures. The characteristics of constrained motions of and the corresponding gear trains were incomplete[2–3]. On mechanical devices are used to proceed complicated the basis of PRICE’s design, EDMUNDS and MORGAN calculations and precise measurements, especially for the added the indications of Mar and [4]. WRIGHT, et al, astronomical applications, such as , , presented a serious research to correct PRICE’s design and , , and mechanical . gradually reconstruct the design[5–15]. The spiral Among these mechanical devices, the pointer design back dials were presented, and the and the regarding how to indicate the required information is one of were indicated by the back upper dials, and the most important mechanism designs. The Persian the moon phase display function was introduced at the first astrolabe with calendrical gearing dated in AD 1221 as [13]. FREETH, et al, almost completely decoded the shown in Fig. 1 is a good example. Its pointers not only inscriptions of back dials to confirm their functions, indicate the positions of astronomical bodies, but also show including the Metonic cycle, Callippic cycle, moon phase[1]. As far as the pointer design is concerned, the cycle, Saros cycle and cycle[16–19]. Further, Antikythera mechanism, which is the astronomical FREETH, et al, reconstructed the epicyclig gear trains for calculator of ancient , is a classical sample. The the planetary motions[20]. KOETSIER made a detail introduction about the historical development of [21] * Corresponding author. E-mail: [email protected] reconstruction research of the mechanism . EVANS, et Supported by National Council, Taiwan, China(Grant No.NSC al, presented a different concept of the front dial and its 99-2221-E-006-253) corresponding design of epicyclic gear trains[22–23]. © Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2015

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·677·

EFSTATHIOU, et al, investigated the characteristic of the excavation of the Antikythera mechanism that was the triangular gear shape and built a latest reconstruction model oldest astronomical calculator. that is preserved in the archaeological museum of [24]. The Antikythera mechanism was identified to survive The complicated calculation and indication systems of the between 150 BC–100 BC. Its interior structure was a Antikythera mechanism contain many different kinds of sophisticated arrangement of bronzed gear trains and each pointers. Among them, the detail design of the moon phase surviving gear has triangular teeth shape. The available display device over the front dial to show the cyclic information including the gear sizes, the teeth depths and variation of moon phase is unclear owing to the damaged the corresponding teeth numbers implied the outstanding and insufficient evidence, even the existing design of the craftsmanship in the of the Antikythera mechanism. device was identified as an epicyclic gear mechanism. Nevertheless, the device was absolutely strange to everyone at the discovery time. The historical records or literatures about such a geared device were not found. And, it was suggested that the unknown device with complex structure could be a geared calculator for making accurate measurements or calculation. Furthermore, none of all known ancient artifacts was the same as this excavated mechanical device, such as the calendrical gear train described in an Islamic treatise in 1000 AD, the Persian astrolabe with calendrical gearing in 1221 AD, the Byzantine with calendrical gearing in 1062 AD and Dondi’s astrarium in the 14th AD. As a result, this strange mechanical device was just named “Antikythera mechanism” in accordance with the excavated position. The Antikythera mechanism was gradually decoded through a long time period of research. It was a bronze geared astronomical calculator encased in a wooden box approximately 315 mm×190 mm×100 mm and driven by hands through a crank attached on one side, as shown in Fig. 2. Both the front and back have the doors, and there are numerous inscriptions on the plates. The following is the introduction of the known exterior appearance and characteristics.

Fig. 1. Persian astrolabe with calendrical gearing in 1221[1]

The purpose of this paper is to conclude all feasible designs of the moon phase display device that can correspond to various reconstruction designs of the interior structure presented by LIN and YAN[25–30]. The Antikythera mechanism and the authors’ efforts on its reconstruction designs by a systematical design methodology are introduced. The mechanism of all pointer designs contained are analyzed. These possible designs are able to perfectly connect to the authors’ previous reconstruction designs of Fig. 2. Reconstruction model by authors[25–30] the interior structure to restore the whole Antikythera [25–30] mechanism . Certainly, all reconstruction works are on 2.1 Front plate the basis of the surviving evidence. The front plate has one metal dial which includes two concentric annuli with different scales, as shown in Fig. 3(a). The inner scale is fixed and divided into 12 divisions. 2 Known Antikythera Mechanism Those groups are marked with names of the signs of the in Greek. The outer scale is movable and divided In 1900, a team of Greek sponge-divers on their home into 365 parts corresponding to the Egyptian . By way sailing from Tunisia to was driven off course by turning the scale forward one every four years, the a storm and was forced to stay in the Antikythera Island. calendar is corrected to be consistent to the true length of This accident resulted in the discovery of the Antikythera the year. Over the front dial, several pointers respectively shipwreck, a great treasure of archaeology, containing the display the , the sun, the moon and the five ,

LIN Jian Liang, et al: Decoding the Moon Phase Display Device over the Front Dial ·678· of the Antikythera Mechanism including Venus, , , and . Furthermore, a bronze disk with a hole is over the center of 3 Reconstruction Work of the Interior the front concentric annuli and the above pointers. And a Structure small ball with black and white rotates inside the hole to display the change of moon phase during one month. That Ever since 1900, some scholars have made their efforts is the so-called moon phase display device in this paper. to reconstruct the interior gear trains of the Antikythera While the date is appointed, the positions of all designated mechanism[2–24]. D. PRICE presented the first systematic celestial bodies and the moon phase at that time are reconstruction design during the late 1950s to early revealed. In addition, there are some Parapegma 1970s[2–3]. M. WRIGHT presented another reconstruction inscriptions that describe the correspondence between the design, which could display the Metonic cycle and the rising and setting of particular and the civil date on the Callippic cycle in 2001 to 2007[5–15]. Since 2002, FREETH front plate. Some inscriptions could be regarded as the focused on decoding the interior structure of the manual to describe the operating this mechanism. mechanical device to define its appropriate role[16–18]. During 2006 to 2008, FREETH, et al(the Antikythera mechanism research project) presented their latest decoding of the inscriptions of the dials and the reconstruction design including the demonstrations of the lunar motion and the Olympiad cycle[19–20]. EVANS, et al, revealed a fresh viewpoint of the front dials. The scale of the Zodiac dial could be uniformly divided to generate the non-uniform divisions. And thus, the sun pointer could display with a uniform rate on the Zodiac dial with non-uniform scale to demonstrate the solar anomaly. In addition, the planetary pointers were demonstrated respectively on five subsidiary dials[21–23]. K. EFSTATHIOU et al. focused on perfectly reappear the sophisticated mechanism that was based on the existing design by Freeth et al in 2008[24]. To conclude all above decoding work, the authors divided the interior structure of the Antikythera mechanism into six subsystems by the concept of mechanism, including the date subsystem, the calendrical subsystem, Fig. 3. Dials of the Antikythera mechanism the lunar subsystem, the prediction subsystem, the solar subsystem and the planetary subsystem, as shown in 2.2 Back plate Fig. 4(a)[23]. The date subsystem and the eclipse prediction The back plate has two parts, as shown in Fig. 3(b). The subsystem are identified from the excavation and upper part, including one large dial and two subsidiary dials, reconstructed absolutely. The lunar subsystem and the is to express the calculations between different calendar calendrical subsystem are incomplete in the surviving systems and the records of celebrations in . evidence. A strange pentagon pattern in the surviving The large dial has five spiral turns to show the 235 synodic fragment of the lunar subsystem could not be explained of 19-year Metonic cycle. Furthermore, there are logically. The calendrical subsystem lacks the still two subsidiary dials respectively divided into corresponding evidence, and only two are detected quadrants. One shows the 4-year cycle of the Olympiad is from the excavation. The solar subsystem and the planetary included. The other subsidiary dial is suggested to follow subsystem are completely lost in the excavation. And, the the 76-year Callippic cycle. The lower part of the back existence of these two subsystems is supposed by the plate for predicting the occurrence time of the solar and the decoding of the exterior dials, pointers and inscriptions. lunar contains one large spiral dial and one Although modern image technology is contributed to detect subsidiary dial. The large dial has four spiral turns to show the surviving fragments to decode this ancient mechanical the 223 months of 18-year Saros cycle. The subsidiary dial, device, it has no idea for the lost and incomplete structure divided into three parts, shows the 54-year Exeligmos cycle. of the device. Once the daily input is given, these pointers can reveal the In fact, knowledge of mechanical engineering could be accurate calculation results on the dials. used to restore the lost and incomplete ancient machinery. In summary, each plate of the Antikythera mechanism Concepts and theories of mechanisms are consistent so that includes different types of dials and the corresponding the knowledge of modern mechanism can be applied for the pointers. Except for the Olympiad cycle dial and the designs of ancient machinery. By the above viewpoint, a Callippic cycle dial, the remaining dials should display design methodology of the lost ancient machinery is clockwise. presented[31–33]. This design methodology is contributed to

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·679· systematically generate all feasible reconstruction designs feasible designs obtained by this design methodology of the lost ancient machinery, subject to the technique include not only new designs but also existing designs by standard of the time period, based on the research of various scholars. available historical archives. The methodology has been used to successfully reconstruct several lost ancient Chinese machinery[33].

Fig. 5. Reconstruction design procedure

4 Analysis of Display Types of Pointers

In order to clearly introduce these pointer types, the mechanism has to be orientated firstly. The orientation vertical to the dials of the front plate(or the dials of the back plate) is the axial direction, and the one parallel to the dials of the front plate(or the dials of the back plate) is the Fig. 4. Two reconstruction designs of the interior structure radial direction. Thus, these three pointer types of the Antikythera mechanism are analyzed based on the styles According to such a design methodology, the and the motion directions. reconstruction procedure of the Antikythera mechanism is concluded, as shown in Fig. 5. Building historical archives 4.1 Axial rotation is very important for the reconstruction designs of the Based on the orientation of mechanism, the pointers with Antikythera mechanism. This stage varies with the topics of axial rotation contain the most pointers of the Antikythera reconstruction work. The historical archives of mechanism. These pointers include the date pointer, the reconstructing the Antikythera mechanism contain the sun pointer, the moon pointer, the Mercury pointer, the study of related historical literatures, ancient , Venus pointer, the Mars pointer, the Jupiter pointer and the ancient astronomical instruments, and mechanical analysis. Saturn pointer in the front dials; the Olympiad pointer and Previously, the incomplete subsystems(calendrical the Callippic pointer in the back upper subsidiary dials; and subsystem and lunar subsystem) and the lost subsystems the Exeligmos cycle pointer in the back lower subsidiary (solar subsystem and planetary subsystem) were decoded dials. These pointers are illustrated in Fig. 2. by this procedure. The research results are respectively presented in the authors’ previous publication works[23–28]. 4.2 Axial rotation plus radial sliding Then, 48 feasible reconstruction designs with the complete The pointer type with axial rotation plus radial sliding, interior structure of the Antikythera mechanism were which contains the Metonic cycle pointer and the Saros systematically generated. Fig. 4(b) shows one of 48 feasible cycle pointer, is the combination of a link and a slider, as designs presented by LIN and YAN, and its corresponding shown in Fig. 2. Two designs of the pointer type are 3D simulation model is shown in Fig. 3. Certainly, all presented in the previous research, as shown in Fi. 6[19].

LIN Jian Liang, et al: Decoding the Moon Phase Display Device over the Front Dial ·680· of the Antikythera Mechanism

The indicator in the design of Fig. 6(a) is the slider, but the contrate gear. Thus, the device must be a gear train. indicator in the design of Fig. 6(b) is the link. Whatever design types could generate the spiral output motion along the spiral tracks. Also, these designs appeared in the research by Freeth et al. one after another.

Fig. 7. Relevant evidence of the moon phase display device[9]

Indeed, WRIGHT and FREETH, et al, restored the moon Fig. 6. Two existing designs of the pointers phase display device in their reconstruction designs. with axial rotation and radial sliding FREETH, et al, respectively presented two different designs, three-bar mechanism and four-bar mechanism. 4.3 Radial rotation Whatever available reconstruction designs of this device, Only the pointer of the moon phase display device (the all of them are epicyclic gear trains with two degrees of ball with black and white) belongs to the pointer type with freedom. The essential concept of these available designs is radial rotation, as shown in Fig. 2. By the engagement of that the change rate of moon phase is based on the rate two gears, the axis directions of which are vertical over the difference between the daily motion(solar motion) and the front, and the motion of the moon pointer can be lunar motion. And the visible bronze disk was rotatable. transmitted to the ball with black and white to display the The device is closely related to the interior structure, and moon phase corresponding to the moon’s position on the the roles of the bronze disk are the key for reconstructing sky. The ball with black and white should rotate around its the various designs of the device that meet the surviving shaft, i.e., to rotate along the radial direction based on the evidence. Studying the authors’ 48 reconstruction designs orientation of mechanism. Therefore, in most of the complete interior structure, it is understood that the reconstruction models, it is shown that the moon phase moon pointer is the most inner shaft and is not always next display device is combined with a bronze disk, a bronze to the sun pointer or the date pointer[23]. Undoubtedly, these cover, and a gear train. results affect the role identification of the bronze disk. For At , the pointer type with axial rotation and the that reason, two conditions that the bronze disk is rotatable pointer type with axial rotation plus radial sliding are or fixed are investigated to present different design absolutely without problems. The corresponding pointers examples further. Mechanical analysis(consisting of are clearly identified and reconstructed in previous research. kinematic and mechanism analyses) is utilized to evaluate There are slight differences between the appearance designs the feasibility of the design examples. What follows are of pointers of the existing reconstruction models. However, three feasible designs examples of the moon phase display some questions about the moon phase display device still device. Meanwhile, their moon phase pointers can be exist. It is not confirmed that if the bronze disk is a pointer rotatable or not rotatable around the axial direction of of the Antikythera mechanism. This condition affects if the mechanism. moon phase display device rotates around the axial direction of mechanism except for its own radial rotation. 5.1 Design example 1: Ordinary gear trains Hence, this paper resolves the problem regarding how to While the bronze disk has to be fixed as the frame in this restore all feasible designs of the moon phase display example, the gear train of the moon phase display device is device. an ordinary gear train, i.e. all gears rotate around the fixed axes. Therefore, the bronze disk itself is not the moon pointer. There should be 8 pointers with axial rotation on 5 Reconstruction Designs of the Moon Phase the front dial (including Sun, moon, date and five planets). Display Device Moreover, by the mechanical analysis of ordinary gear trains, the simplest structure of ordinary gear trains is a Fig. 7 shows the surviving fragment corresponding to the three-bar mechanism with two revolute joints and one gear moon phase display device. The visible bronze disk was a joints. It includes a ground link(link 1, KF), an input link part of the device, and a partial wreck of contrate gear (link 2, KI) and an output link (link 3, KO). hided in this fragment. It is reasonably to suppose that a The number of the generalized chain with three links and gear should engage the contrate gear so as to make the three joints is one, and its feasible specialized chain can be contrate gear meaningful. Therefore, the moon phase obtained by direct inspection, as shown in Figs. 8(a) and (b). display device is defined to have at least three elements: a Fig. 8(c) shows the corresponding mechanical drawing. The visible bronze disk, a contrate gear connected to the ball input link is the sun gear and connected by the shaft of the pointer of moon phase and a hypothetical gear engaging the moon pointer. The input link rotates once per month. The

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·681· output link is the contrate gear, i.e., the ball pointer with sun gear of the epicyclic gear train, has to be fixed as a part black and white. According to the kinematic analysis of this of the frame. The corresponding kinematic analysis reveals ordinary gear train, it is concluded that the teeth number of that the teeth number of the hypothetical gear a1 must equal the hypothetical gear a1 has to equal the teeth number of to the teeth number of the contrate gear so as to meet the the contrate gear. requirement that the moon phase pointer rotates once a month. For this design, the ball pointer of the moon phase display device rotates around not only the radical direction but also the axial direction, like the revolution and the rotation in astronomy. Moreover, the sun pointer is not necessarily next to the moon pointer. For that reason, this design example is suitable for all of the authors’ 48 feasible reconstruction designs with complete interior structure.

5.3 Design example 3: Epicyclic gear trains with 2 DOF

In this design example, the condition that the bronze disk Fig. 8. Design example 1 is rotatable and can be the moon pointer is applied again. In this design example, the pointer of the moon phase But the epicyclic gear train must have two degrees of display device is with a radial rotation but without an axial freedom. The relevant mechanism analysis reveals that the rotation. It is not necessary that the moon pointer is always simplest structure of epicyclic gear trains with two degrees next to the sun pointer or date pointer. Therefore, this of freedom is a four-bar mechanism with three revolute design concept is suitable for all of 48 feasible joints and one gear joint. It contains a ground link(link 1, reconstruction designs with complete interior structure KF), two input links(links 2 and 3, KI1 and KI2), and an presented by the authors. output link(link 4, KO). One feasible specialized chain is obtained by direct observation, as shown in Fig. 10(b). The 5.2 Design example 2: Epicyclic gear trains hypothetical gear in each design is rotatable as one input with 1 DOF link. The other input link is the bronze disk(carrier). In This example indicates that the bronze disk is rotatable accordance with the assignments of input sources, two as the carrier of epicyclic gear trains. According to the corresponding mechanical drawings are shown in Figs. mechanical analysis of epicyclic gear trains with one 10(c) and (d). degree of freedom, the simplest structure of epicyclic gear trains is a three-bar mechanism with two revolute joints and one gear joints. It includes a ground link(link 1, KF), an input link(link 2, KI) and an output link(link 3, KO). Only one feasible specialized chain can be obtained by direct observation, as shown in Fig. 9(a). Fig. 9(b) shows the corresponding mechanical drawing.

Fig. 10. Design example 3 Fig. 9. Design example 2 Fig. 10(c) shows one of feasible mechanical drawings. In this feasible design, the bronze disk is the input link This design example is the same as the previous research[13, that is connected to the output shaft of the moon pointer, 18–21]. The hypothetical gear a1 is connected to the shaft i.e., the disk rotates once per month. Certainly, the disk can transmitting the solar motion or the daily motion as one also be the moon pointer. The existing gear a1, which is the input source. And, the bronze disk, as the carrier of the

LIN Jian Liang, et al: Decoding the Moon Phase Display Device over the Front Dial ·682· of the Antikythera Mechanism epicyclic gear train, is connected to the shaft transmitting the lunar motion as the other input source. Therefore, for References the epicyclic gear train, the sun gear rotates once a year and [1] BEDINI S A, MADDISON F R. Mechanical universe: The the carrier rotates once a month. Based on the kinematic Astrarium of Giovanni de Dondi[J]. Transactions of American analysis, the difference of rates between the motions of the Philosophical Society, 1966, 56(5): 1–69. [2] PRICE D. de S. An [J]. , sun and the moon is the variation rate of moon phase, while 1959, 200(6): 60–67. the teeth number of the hypothetical gear a1(sun gear) is [3] PRICE D de S. Gears from the : The Antikythera mechanism equal to the teeth number of the contrate gear( gear). ––A calendar computer from ca. 80 BC[J]. Trans Am. Phil. Soc. Fig. 10(d) is the other feasible mechanical drawing. Its New Ser., 1974, 64(7): 1–70. An Ancient Greek Computer[M]. New two input sources are exchanged, by comparing with the York: Science Publications , 1975. [4] EDMUNDS M, MORGAN P. The Antikythera mechanism: still a design in Fig. 10(c). The hypothetical gear a1 is connected mystery of Greek astronomy[J]. Astron. Geophys., 2000, 41(6): to the shaft transmitting the lunar motion. The bronze disk, 10–17. as the carrier of the epicyclic gear train, is connected to the [5] WRIGHT MT, BROMLEY A G. Towards a new reconstruction of shaft transmitting the solar motion or the daily motion. The the Antikythera mechanism[C]//Proc. Conf. Extraordinary variation rate of moon phase also could be generated and Structures in Antiquity, Patras, Aug, 2001: 81–94. through the kinematic analysis of this epicyclic gear train. [6] WRIGHT M T. A Planetarium display for the Antikythera mechanism[J]. Horological Journal, 2002, 144(5):169–173. Simultaneously, it is necessary that the teeth numbers of the [7] WRIGHT M. T. In the steps of the master mechanic[C]//Proc. Conf. contrate gear and the hypothetical gear a1 are the same. In Ancient Greece and the Modern World, University of Patras, Patras, fact, the only difference between these two designs Greece, 2002:86–97. respectively shown in Figs. 10(c) and (d) is the radial [8] WRIGHT M T. and the Antikythera mechanism: rotation direction of the ball with black and white. Once the part 1[J]. Antiquarian , 2003, 27: 270–279. [9] WRIGHT M T. The scholar, the mechanic and the Antikythera ball of one synthesized device rolls forward, the other rolls mechanism[J]. Bulletin of the Scientific Instrument Society, 2004, backward. 80: 4–11. After the above design analysis, it is concluded that the [10] WRIGHT M T. The Antikythera mechanism: a new gearing shaft for the lunar motion has to be next to the shaft for the scheme[J]. Bulletin of the Scientific Instrument Society, 2005, 85: solar motion or daily motion, either Fig. 10(c) or Fig. 10(d). 2–7. Based on this critical constraint, 34 of the authors’ 48 [11] WRIGHT M T. Epicyclic gearing and the Antikythera mechanism: part 2[J]. Antiquarian Horology, 2005, 29: 51–63. reconstruction designs of the complete interior structure [12] WRIGHT M. T. Counting months and years: the upper back dial of could apply this design example in the reconstruction of the the Antikythera mechanism[J]. Bulletin of the Scientific Instrument moon phase display device. Among these 34 feasible Society, 2005, 87: 8–13. designs, 18 designs show that the moon pointer is next to [13] WRIGHT M T. The Antikythera mechanism and the early history of the date pointer. And the remaining designs show that the the moon phase display[J]. Antiquarian Horology, 2006, 29(3): 319–329. moon pointer is next to the sun pointer. [14] WRIGHT M T. Understanding the Antikythera mechanism[C]//Proc. the 2nd International Conf. , Athens, Oct, 6 Conclusions 2006: 49–60. [15] WRIGHT M T. The Antikythera mechanism reconsidered[J]. Interdisciphinary Science Review, 2007, 32(1): 27–43. (1) The modern knowledge of mechanical engineering [16] FREETH T. The Antikythera mechanism: 1. Challenging the classic research[J]. Mediterranean Archaeology & Archaeometry, 2002, 2: could be successfully used to reconstruct the lost ancient 21–35. machinery. [17] FREETH T. The Antikythera mechanism: 2. Is It (2) A systematic design methodology for the orrery[J]. Mediterranean Archaeology & Archaeometry, 2002, 2: reconstruction designs of the Antikythera mechanism is 45–58. presented. [18] FREETH T. Decoding an ancient computer[J]. Scientific American, (3) According to the orientation of the device, three 2009, 301(6): 79–83. [19] FREETH T, BITSAKIS Y, MOUSSAS X, et al. Decoding the pointer types with different display motions of the ancient greek astronomical calculator known as the Antikythera Antikythera mechanism are concluded. mechanism[J]. , 2006, 444: 581–591. (4) Three feasible design examples of the moon phase [20] FREETH T, JONES A, STEELE J M, et al. with display device are generated by mechanism analysis of gear Olympiad display and eclipse prediction on the Antikythera trains and the design methodology. One example is the mechanism[J]. Nature, 2008, 454: 614–617. [21] KOETSIER T. Phase in the unraveling of the secrets of the gear design of ordinary gear train and the remaining two system of the Antikythera mechanism[C]//Proceedings of HMM, examples are the designs of epicyclic gear trains. These Tainan, Tainan, 2008: 269–294. design examples respectively correspond to the authors’ [22] EVANS J, CARMAN C C, THORNDIKE A S. Solar anomaly and forty-eight reconstruction designs of the whole interior planetary displays in the Antikythera mechanism[J]. Journal for the structure, and satisfy the surviving evidence. And, one of History of Astronomy, 2010, 42: 1–39. them could be the original design of the lost ancient [23] EVANS J, CARMAN CC. Mechanical astronomy: a route to the ancient discovery of epicycles and eccentrics[M]//From Alexandria, machinery. Through Baghdad: Surveys and Studies in the Ancient Greek and

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·683·

Medieval Islamic Mathematical in Honor of J.L. Berggren, [32] YAN H S. Creative design of mechanical devices[M]. Singapore: Berlin Heidelberg: Springer-Verlag, 2014:145–171. Springer-Verlag, 1998. [24] EFSTATHIOU K, BASIAKOULIS A, EFSTATHIOU M, et al. [33] YAN H S. Reconstruction designs of lost ancient Chinese Determination of the gears geometrical parameters necessary for the machinery[M]. Netherlands: Springer, 2007. construction of an operational model of the Antikythera Mechanism[J]. Mechanism and Theory, 2012, 52: Biographical notes 219–231. LIN Jian Liang received his PhD degree in mechanical [25] LIN J L. Systematic Reconstruction Designs of Antikythera engineering from National Cheng Kung University, Taiwan, China Mechanism[D]. National Cheng Kung University, Taiwan, 2011. [26] YAN H S, LIN J L. Reconstruction synthesis of the calendrical in 2011. He is a staff at Department of Suspension, KYMCO. His subsystem of Antikythera mechanism[J]. ASME Transactions, major research areas are conceptual design of mechanisms and Journal of Mechanical Design, 2011, 133(2): 021004. reconstruction design of ancient machinery. He published seven [27] YAN H S, LIN J L. Reconstruction synthesis of the lunar subsystem journal papers and four conference papers, as well as has one with an unexplained feature of Antikythera mechanism[J]. patent(Taiwan, China). Proceedings of the Institute of Mechanical Engineers, Part C, Tel: +886-6-2082703; E-mail: [email protected] Journal of Mechanical Engineering Science, 2012, 226(4): 1053–1067. [28] YAN H S, LIN J L. Reconstruction synthesis of the lost interior YAN Hong Sen received his PhD degree in mechanical structure for the solar anomaly motion of the Antikythera engineering from Purdue Univ., USA in 1980. He is an university mechanism[J]. Mechanism and Machine Theory, 2013, 70: chair professor at Department of Mechanical Engineering, 354–371. National Cheng Kung Univ., Tainan, Taiwan, China. His major [29] YAN H S, LIN J L. Reconstruction synthesis of the lost subsystem for the planetary motions of Antikythera mechanism[J]. ASME areas of interests are conceptual design of modern mechanisms Transactions, Journal of Mechanical Design, 2012, 134(1): 011003. and reconstruction designs of ancient machinery. He is the [30] LIN J L, YAN H S. Historical development of reconstruction (co-)author more than 300 academic papers and 12 books. He designs of Antikythera mechanism[J]. Applied Mechanics and received many honors and awards inside and outside Taiwan, Materials, 2012, 163: 1–6. China, including the honorary membership of IFToMM in 2011. [31] YAN H S. A methodology for creative mechanism design[J]. Tel: +886-6-2082703; E-mail: [email protected] Mechanism and Machine Theory, 1992, 27(3): 235–242.