Compact, high torque ratio, high efficiency transmissions are required in many applications, such as robotics. However, compact size and high torque ratios often come at the expense of surprisingly low efficiency. Here we apply Del Castillo's sensitivity framework (Del Castillo, J. M., 2002, “The Analytical Expression of the Efficiency of Planetary Gear Trains,” Mech. Mach. Theory, 37(2), pp. 197–214) to explain the low efficiency of a subset of transmissions that exploit small differences in tooth number between gears to generate high torque ratios. We add adjustment factors for several transmissions within this category, such as cycloids and harmonic drives; demonstrate that the models match empirical results for the case of cycloids across a range of torque ratios, topologies, and roller conditions; and compare and optimize the topologies of the various mechanisms. We demonstrate that for this subset of transmissions, the efficiency approaches a function of the torque ratio.

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