### Resolution

Whether you’re measuring distance with an encoder or tracking servo motion, resolution describes the distance per increment from the feedback device.  In some systems, resolution describes the increments per arbitrary distance.

Rotary encoders are often used to measure length in roll forming applications.  Typically, the model number of the encoder reflects the optical pulses per revolution of the encoder shaft.  Since most roll formers can move the material forward or back, the encoders used are bi-directional, capable of tracking distance in either direction.

As a function of their bi-directionality, the digital length measurement system that reads the encoder can use quadrature to increase the base optical resolution of the encoder by a factor of four.  If you’re using a quadrature length measurement system, the you must multiply the encoder’s pulses per revolution (PPR) by 4 before calculating resolution.

Resolution = C ÷ PPR, where:

C = Circumference of the measuring wheel

PPR = Post-quadrature Pulses per Revolution of the Encoder

Example 1

A model 2500 encoder is connected to a 12″ circumference measuring wheel.

Post-quadrature pulses from encoder = 2,500 x 4 = 10,000

Resolution = C ÷ PPR

0.0012″ per pulse = 12″ ÷ 10,000

Example 2

A servo system is connected to a belt-driven actuation system.  The drive pulley has a circumference of 12.566″.  There’s a 7:1 gearbox between the servo motor and the drive pulley, and the servo is set to emulate 5,000 PPR post-quadrature.

Resolution = C ÷ PPR

0.0003590286 per pulse = 12.566″ ÷ 7 ÷ 5,000