Displacement measurement system and sheet feed system incorporating the same

A sheet feed system, comprising:

• a support arm having a first end and a second end and configured to turn about a pivot axis on a pivot located closer to the first end than the second end so that displacement of the first end causes a greater corresponding displacement of the second end;
• a roller mounted at the first end of the support arm and configured to rotate about a roller axis substantially parallel to the pivot axis;
• a sheet feed surface disposed adjacent to the roller and configured to receive a sheet between the sheet feed surface and the roller;
• a biasing member coupled to the support arm at a location between the pivot axis and the second end of the support arm and configured to urge the roller against the sheet feed surface;
• an optical encoder having at least one component mounted at the second end of the support arm and configured to generate signals responsive to movement of the second end of the support arm;
• and
• a controller configured to sample signals generated by the optical encoder and to compute one or more displacement values based upon one or more sampled signals.