# Immersive Virtual Reality Experience of Historical Events Using Haptics and Locomotion Simulation
## 2 Materials and Methods
### Educational Content  
Even though our proposed system is proof of concept the facts about the Antikythera Mechanism and its way of working are based on research and are accurate. The information about the real shipwck is given to the user during their underwater exploration as they come across certain items which provide information in text and image format. Additionally, the model of the part of the mechanism found in the shipwck is a 3D model based on the highest resolution CT scan of the main fragment of the Antikythera Mechanism based on the improvements discussed in [36]. Because of the fact that the Antikythera mechanism was made of bronze and was recovered from the sea 2000 years after the sinking, the metal corroded to the form of a shapeless lump. For this reason, it is difficult to extract all the details with a CT scan and some parts may seem'missing'. The front face of the mechanism has the twelve zodiacal signs distributed in equal 30-degree sectors, the months and days of the Sothic Egyptian calendar, and the pointers indicating the positions of the celestial objects (Figure 5a). On the back panel, there are five dials: two large displays, the Metonic and the Saros, and three smaller indicators, the Games Dial, the Callippic, and the Exeligmos (Figure 5b). The user can operate the mechanism by turning a small hand crank linked with a crown gear to the largest gear, the gear with the name b1 (Figure 6). This moves the date pointer on the front dial about 78 days per full rotation. Every gear in the inside of the mechanism is interlocked so by rotating the hand crank every gear rotates so it simultaneously calculates the position of the Sun and Moon, the moon phase, eclipse, and calendar cycles, and the locations of planets. The movement of each gear is calculated from the formulas shown in Table 1.  
All the variables shown in Table 1 correspond to the gears named in Figure 6. These are the gears inside the mechanism including the Freeth and Jones reconstruction [37]. In addition to each gear's name, in Figure 6 for each gear the number of its cogs is given. Every gear is also represented in the 3D model in the internal of the mechanism as shown in Figure 7.  
Figure 4: Our whole system utilizing the HTC Vive HMD, Cyberith’s Virtualizer treadmill, haptic gloves and Vive Trackers. \begin{table}
\begin{tabular}{c l l c} \hline \hline
**Gear Name** & **Function of the Gear/Pointer** & **Mechanism Formula** & **Gear Direction** \\ \hline x & Year gear & 1 (by definition) & cw \\ b & the Moon’s orbit & Time(b) = Time(x) \(\times\) (c1/b2) \(\times\) (d1/c2) \(\times\) (e2/d2) \(\times\) (k1/e5) \(\times\) (e6/k2) \(\times\) (b3/e1) & cw \\ r & lunar phase display & Time(r) = 1/((1/Time(b2 [mean sun] or sun3 [true sun])) - (1/Time(b))) & cw \\ n* & Metonic pointer & Time(n) = Time(x) \(\times\) (l1/b2) \(\times\) (m1 /l2) \(\times\) (n1/m2) & ccw \\ o* & Games dial pointer & Time(o) = Time(n) \(\times\) (o1/n2) & cw \\ q* & Callipipic pointer & Time(a) = Time(n) \(\times\) (p1/n3) \(\times\) (q1 /p2) & ccw \\ e* & lunar orbit precession & Time(e) = Time(x) \(\times\) (l1/b2) \(\times\) (n1/2) \(\times\) (e3/m3) & ccw \\ g* & Sarose cycle & Time(g) = Time(e) \(\times\) (l1/e4) \(\times\) (g1/f2) & ccw \\ i* & Exeligmos pointer & Time(i) = Time(g) \(\times\) (h1/g2) \(\times\) (i1/h2) & ccw \\ \hline \multicolumn{4}{c}{**The following are proposed gearing from the 2012 Freeth and Jones reconstruction:**} \\ \hline sum3* & True sun pointer & Time(sun3) = Time(x) \(\times\) (sun3/sun1) \(\times\) (sun2/sun3) & cw \\ mer2* & Mercury pointer & Time(mer2) = Time(x) \(\times\) (mer2/mer1) & cw \\ ven2* & Venus pointer & Time(ven2) = Time(x) \(\times\) (ven1/sun1) & cw \\ mars4* & Mars pointer & Time(mars4) = Time(x) \(\times\) (mars2/mars1) \(\times\) (mars4/mars3) & cw \\ jup4* & Jupiter pointer & Time(jup4) = Time(x) \(\times\) (jup2/jup1) \(\times\) (jup4/jup3) & cw \\ sat4* & Saturn pointer & Time(sat4) = Time(x) \(\times\) (sat2/sat1) \(\times\) (sat4/sat3) & cw \\ \hline \hline \end{tabular}
\end{table}