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For the rest, today was a slow day. We bought more #41 chain in order for the chain to go the whole length of the erg. Joining the sections of the chain proved to be difficult. We then attached the retracting bungee in parallel according to the plan as mapped out in Figure 3. 
Figure 1: The original design, from Drew Tennant's 2004 paper. The floating pulley kept running into the flywheel during stroke. In addition, we wanted to separate the motion of the handlebar and the flywheel. This made us switch out the floating pulley with the differential, as show in Figure 2\.
Figure 2: Version with differential replacing floating pulley and resistances (bungees) connected. This did not seem to work as well as the floating pulley design, and we were scratching our heads wondering why. After skyping with Prof Ruina on Saturday 2013.06.01, we concluded to try to recreate the gear ratios from the floating pulley design. This is reflected in our modified schematic in Figure 3\.
Figure 3: This is an updated schematic of Figure 2.
We ordered S2a and S2b and S3a sprockets yesterday, in the number of teeth as shown Figure 3\.
Tomorrow, we plan on finishing assembling the bungee and chains according to the updated figure.