Elastic biasing element and encoder arrangement for precise control of force or torque

A feed system for a feeding and applying a feed force to an abrasive element of a bore finishing tool in a lateral direction relative to an axis of rotation thereof, comprising:

• a drive apparatus controllably operable to move a drive element in a first direction and an opposite second direction within a predetermined range;
• an elastic biasing element having a first end and a second end, the first end disposed in predetermined relation to the drive element so as to be displaced by the movement thereof to cause the biasing element to elastically store a quantity of energy proportional to the displacement and representative of the feed force, and the second end being disposed in predetermined relation to an output element disposed to move generally axially in cooperation with a feed element of the bore finishing tool to transfer and apply the feed force laterally to the abrasive element and to displace jointly with the output element responsive to changes in the applied force;
• and
• a first sensor positioned and operable to determine a value representative of the displacement of the second end of the biasing element and output a signal representative thereof, a second sensor positioned and operable to determine a value representative of the displacement of the first end of the biasing element and output a signal representative thereof, and a processor connected to the first sensor and to the second sensor to receive the signals outputted thereby and to determine a responsive value for moving drive element of the drive apparatus to apply a selected feed force.