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One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
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Degrees of Freedom01:02

Degrees of Freedom

The degree of freedom for a particular statistical calculation is the number of values that are free to vary. As a result, the minimum number of independent numbers can specify a particular statistic. The degrees of freedom differ greatly depending on known and uncalculated statistical components.
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Related Experiment Video

Updated: Jun 23, 2026

Video-rate Scanning Confocal Microscopy and Microendoscopy
14:10

Video-rate Scanning Confocal Microscopy and Microendoscopy

Published on: October 20, 2011

Five-degrees-of-freedom diffractive laser encoder.

Chien-Hung Liu1, Hsueh-Liang Huang, Hau-Wei Lee

  • 1Institute of Electro-Optical and Materials Science, National Formosa University, Huwei, Yunlin, Taiwan. carus@nfu.edu.tw

Applied Optics
|May 9, 2009
PubMed
Summary

A novel five-degrees-of-freedom (5-DOF) laser encoder precisely measures position and motion errors. This advanced system uses circular polarized interferometry and ray-tracing for high-accuracy linear stage control.

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Area of Science:

  • Metrology and Measurement Science
  • Optical Engineering
  • Precision Engineering

Background:

  • Linear laser encoders are crucial for precision positioning control in linear stages.
  • Existing encoders often have limitations in simultaneously measuring multiple error components.

Purpose of the Study:

  • To develop a novel five-degrees-of-freedom (5-DOF) laser encoder.
  • To simultaneously measure position, straightness, pitch, roll, and yaw errors along a single axis.

Main Methods:

  • Integration of circular polarized interferometric technique with 3D diffracted ray-tracing.
  • Decoding phases from +1 and -1 diffraction orders for linear displacement.
  • Analyzing diffracted ray tracing to calculate motion errors using quadrant photodiode detectors.

Main Results:

  • Achieved measurement accuracy better than +/-0.3 microm/+/-41 microm for straightness.
  • +/-1 arc sec/+/-215 arc sec for angular error components.
  • +/-160 nm/2 mm for linear displacement with a 0.83 microm grating period.

Conclusions:

  • The developed 5-DOF laser encoder offers simultaneous multi-error measurement capabilities.
  • The novel integration of techniques provides high accuracy for precision positioning systems.
  • This advancement is significant for applications requiring precise control of linear stages.