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Compliant mechanisms and voice coil motors can be used in haptic device designs to eliminate bearings and achieve smooth friction-free motion. The accompanying return-to-center behavior can be compensated using feedforward control if a suitable multidimensional stiffness model is available. In this paper we introduce a method for automatic self-characterization and compensation, and apply it to a planar haptic interface that features a five-bar compliant mechanism. We show how actuators and position sensors already native to typical impedance-type haptic devices can readily accommodate stiffness compensation. Although a portion of the motor torque is consumed in compensation, the device achieves smooth friction-free articulation with simple, low tolerance, and economic components. Empirical models built on self-characterization data are compared to standard empirical and analytical models. We produce a model by self-characterization that requires no inversion and is directly useable for compensation. Although our prototype compliant mechanism, which we fabricated in plastic using fused deposition modeling, exhibited hysteresis (which we did not compensate), the return-to-center behavior was reliably reduced by over 95% with feedforward compensation based on the self-characterized model.