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Magnetic resonance imaging (MRI) compatible force sensors are important components in medical robotics, as they enable force feedback in a challenging environment for surgical and assistive robots. This paper analyzes a novel MRI compatible force sensor comprised of a displacement amplifying compliant mechanism (DACM) made up of polymers. Hysteresis is an inevitable problem for sensors made up of polymers, which reduces the precision in measurements. Displacement amplification affects both the sensitivity and hysteresis error of a sensor, yet does not ensure an improvement in either of them. Optimization methods based solely on amplification ratio or sensitivity may be ineffective on reducing the hysteresis issue and result in a design with insufficient signal-to-noise ratio. Unlike previous works that are focused on optimizing topologies with regard to a specific objective function; this paper presents an analysis that accounts for both sensitivity and hysteresis. An iterative method capable of performing nonlinear analysis is established in order to monitor sensitivity and hysteresis error of the proposed sensor topology and find out how those are affected by the amplification. Optimal configurations for sensitivity and precision are deduced and the predictions made by the analysis are confirmed by experiments. This paper indicated that sensitivity of a compliant mechanism could be traded for a lower hysteresis error i.e., higher precision. DACMs could be targeted to achieve a low hysteresis error rather than improving the sensitivity in a sensor. Compared to a nonamplifying, basis structure of our proposed design achieved a 3-4 times higher SNR, mostly due to its higher precision.