Decoding the Mechanisms of Antikythera Astronomical Device (eBook)

Preface 5
Contents 7
1 A Sketch of Ancient Western Astronomy 11
1.1 Historical Development of Western Astronomy 11
1.1.1 Egyptian Civilization 12
1.1.2 Mesopotamian Civilization 14
1.1.3 Aegean Civilization 15
1.1.3.1 Minoan and Mycenaean Civilization 16
1.1.3.2 Dark Age 16
1.1.3.3 Classical Age 17
1.1.3.4 Ionia School 17
1.1.3.5 Pythagoras School 17
1.1.3.6 Plato School 19
1.1.3.7 Hellenistic Age 20
1.2 Astronomical Cycles and Calendars 23
1.2.1 Egyptian Calendar 23
1.2.2 Metonic Cycle 24
1.2.3 Callippic Cycle 24
1.2.4 Saros Cycle 25
1.2.5 Exeligmos Cycle 25
1.3 Ancient Astronomical Theories 26
1.3.1 Solar Theory 26
1.3.2 Lunar Theory 27
1.3.3 Planetary Theory 27
1.4 Remarks 28
References 28
2 Ancient Astronomical Instruments 31
2.1 Classifications Based on Functions 31
2.1.1 Observation Application 32
2.1.2 Measuring Position and Distance Application 32
2.1.3 Measuring Time Application 33
2.1.4 Computing Application 34
2.1.5 Demonstration Application 34
2.2 Jacob’s Staff 35
2.3 Astrolabe 36
2.4 Sundial 38
2.5 Calendrical Device 41
2.5.1 Astrolabe with Calendrical Gearing 41
2.5.2 Sundial with Calendrical Gearing 42
2.6 Planetarium, Astrarium, and Astronomical Clock 45
2.7 Orrery 47
2.8 Comparisons of Astronomical Instruments 48
2.9 Remarks 51
References 51
3 Amazing Discovery of Archaeology 54
3.1 Origination and Process of the Discovery 54
3.1.1 Historical Background of Salvage 55
3.1.2 Story of the Antikythera Finding 56
3.2 Introduction of the Excavations 57
3.3 Known Antikythera Astronomical Device 59
3.3.1 Front Plate 59
3.3.2 Back Plate 60
3.3.3 Display Pointers 62
3.3.3.1 Axial Rotation 62
3.3.3.2 Radial Rotation 63
3.3.3.3 Axial Rotation and Radial Sliding 64
3.3.4 Interior Structure of Mechanisms 64
3.4 Relative Historical Background and Records 66
3.5 Remarks 68
References 68
4 Modern Reconstruction Research 71
4.1 Early Mentions 71
4.2 Reconstruction Work by Price 72
4.3 Reconstruction Work by Edmund and Morgan 75
4.4 Reconstruction Work by Wright 77
4.5 Reconstruction Work by Freeth et al. 83
4.6 Others’ Research After AD 2000 86
References 91
5 Reconstruction Design Methodology 93
5.1 Reconstruction Research 93
5.2 Reconstruction Design Methodology 95
5.2.1 Design Specifications 97
5.2.2 Generalized Chains 97
5.2.3 Specialized Chains 99
5.2.4 Reconstruction Designs 99
5.3 Historical Archives of Antikythera Device 100
5.3.1 Detected Evidence 101
5.3.2 Decoded Information 101
5.3.3 Ancient Astronomy 102
5.3.4 Ancient Astronomical Instruments 102
5.3.5 Modern Kinematic and Mechanism Analyses 102
5.4 Reconstruction Research by Yan and Lin 103
5.4.1 Concepts of Mechanical Designs 104
5.4.1.1 Mechanical Members 104
Link or Kinematic Link (KL) 105
Gear (KG) 105
5.4.1.2 Joints 105
Revolute Joint (JR) 106
Pin-in-Slot Joint (JA) 106
Gear Joint () 106
5.4.1.3 Degrees of Freedom 106
5.4.1.4 Topological Structure 107
5.4.2 Date Subsystem 108
5.4.3 Eclipse Prediction Subsystem 109
5.4.4 Calendrical Subsystem 110
5.4.5 Lunar Subsystem 111
5.4.6 Solar Subsystem 114
5.4.7 Planetary Subsystem 114
5.4.8 Summary 117
5.5 Comparisons Among Different Reconstruction Researches 117
5.5.1 Comparison with Price’s Design 118
5.5.2 Comparison with Edmund and Morgan’s Design 118
5.5.3 Comparison with Wright’s Design 119
5.5.4 Comparison with the Design of Freeth et al. 120
5.6 Remarks 121
References 121
6 Reconstruction Designs of the Calendrical Subsystem 122
6.1 Historical Archives of the Calendrical Subsystem 122
6.2 Design Process of the Calendrical Subsystem 125
6.2.1 Design Specifications 125
6.2.2 Generalized Chains 126
6.2.3 Specialized Chains 127
6.2.3.1 Ground Link (Member 1) 129
6.2.3.2 Callippic Cycle Link (Member 5) 130
6.2.3.3 Olympiad Cycle Link (Member 4) 130
6.2.3.4 Input Link (Member 2) 132
6.2.3.5 Metonic Cycle Link (Member 3) 133
6.2.3.6 Transmission Link (Link 6) 134
6.2.4 Reconstruction Designs 135
6.2.4.1 Tooth Calculation of the Feasible Designs 135
Feasible Reconstruction Design of Fig. a 136
Feasible Reconstruction Design of Fig. b 137
6.3 Remarks 138
References 138
7 Reconstruction Designs of the Lunar Subsystem 139
7.1 Historical Archives of the Lunar Subsystem 139
7.1.1 Kinematic Analysis of the Lunar Theory 140
7.1.2 Kinematic Analysis of Epicyclic Gear Trains 142
7.2 Design Process of the Lunar Subsystem 146
7.2.1 Design Specifications 146
7.2.2 Generalized Chains 146
7.2.3 Specialized Chains 148
7.2.3.1 Pin-in-Slot Device (Members 3, 5, and 6, and Joint JA) 150
7.2.3.2 Anomalistic Link (Member 4) 151
7.2.3.3 Ground Link (Member 1) 153
7.2.3.4 Sidereal Link and Output Link (Members 2 and 7) 154
7.2.3.5 Revolute Joints (Joints JR) 155
7.2.3.6 Gear Joints (JG) 155
7.2.4 Reconstruction Designs 155
7.3 Remarks 157
References 157
8 Reconstruction Designs of the Solar Subsystem 159
8.1 Historical Archives of the Solar Subsystem 159
8.1.1 Possible Arrangements of the Driving Power 160
8.1.2 Kinematic Analysis of the Solar Theory 161
8.1.3 Eccentric System of the Solar Motion 162
8.1.4 Epicyclic System of the Solar Motion 163
8.1.4.1 Four-Bar Mechanism with 5 Joints 164
8.1.4.2 Five-Bar Mechanism with 7 Joints 166
8.2 Design Process of the Solar Subsystem 167
8.2.1 Type 1 Design of the Solar Subsystem 168
8.2.2 Type 2 Design of the Solar Subsystem 173
8.2.3 Type 3 Design of the Solar Subsystem 177
8.2.3.1 Ground Link (Member 1) 179
8.2.3.2 Input Link (Member 2) 181
8.2.3.3 Output Link (Member 3) 181
8.2.3.4 Transmission Links (Members 4 and 5) 181
8.2.3.5 Pin-in-Slot Joint (Joint JA) 182
8.2.3.6 Revolute Joints (Joint JR) 182
8.2.3.7 Gear Joints (Joint JG) 182
8.3 Remarks 184
References 184
9 Reconstruction Designs of the Planetary Subsystem 186
9.1 Historical Archives of the Planetary Subsystem 186
9.1.1 Type 1 Design: Mechanism with One Gear Joint 187
9.1.2 Type 2 Design: Mechanism with Two Gear Joints 188
9.1.2.1 All Planet Gears Are Adjacent to Each Other by a Gear Joint 188
9.1.2.2 Two Planet Gears Are Adjacent to Each Other by a Pin-in-Slot Joint 188
9.2 Design Process of the Planetary Subsystem 189
9.2.1 Type 1 Design of the Planetary Subsystem 189
9.2.2 Type 2 Design of the Planetary Subsystem 195
9.2.2.1 Ground Link (Member 1) 197
9.2.2.2 Output Link (Member 3) 199
9.2.2.3 Input Link (Member 2) 199
9.2.2.4 Transmission Links (Members 4 and 5) 199
9.2.2.5 Pin-in-Slot Joint (Joint JA) 199
9.2.2.6 Gear Joints (Joint JG) 200
9.2.2.7 Revolute Joints (Joint JR) 200
9.3 Remarks 203
References 205
10 Reconstruction Designs of the Moon Phase Display Device 206
10.1 Historical Archives of the Moon Phase Display Device 206
10.1.1 Related Evidence and Available Designs 207
10.1.2 Possible Driving Power Arrangements 209
10.1.3 Possible Design Types 209
10.2 Design Process of the Moon Phase Display Device 210
10.2.1 Example 1: Ordinary Gear Trains 211
10.2.2 Example 2: Epicyclic Gear Trains with 1-DOF 212
10.2.3 Example 3: Epicyclic Gear Trains with 2-DOF 214
References 216
11 Assembly Work and Models 218
11.1 Complete Interior Mechanisms 218
11.1.1 Assembly Constraints of the Lost Mechanisms 219
11.1.1.1 Driving Power of Lost Mechanisms 219
11.1.1.2 Gear Sizes 219
11.1.1.3 Types of Planets 220
11.1.1.4 Epicyclic System of Superior Planets 221
11.1.2 Assembly Work 222
11.2 3D Reconstruction Model 223
11.2.1 Tooth Calculation 224
11.2.1.1 Calendrical Subsystem 225
11.2.1.2 Solar Subsystem 226
11.2.1.3 Planetary Subsystem 227
11.2.2 Detail Designs of Gears 228
11.2.3 Space Arrangement 230
11.2.4 Simulation Model 232
References 232
Appendix A All 48 Feasible Designs of CompleteInterior Mechanisms 234
Appendix B Detailed Design of Model 9 282
Index 284