Introduction to Linkages

Professor McCarthy, Dec 3, 2014

This book presents the construction of a number of interesting linkages to illustrate their variety and utility.

Table of Contents

  1. Parallelogram linkage
    1. Parallelogram linkage
  2. Straight-line linkages
    1. Watt's linkage
    2. Robert's linkage
    3. Tchebychef's linkage
  3. Peaucellier linkage
    1. Peaucellier linkage
    2. Robert's linkage driven
    3. Tchebychef's linkage driven
  4. Linkages by Kempe
    1. Kempe's Reversor
    2. Kempe's Reversor 2
  5. Kempe's rectilinear linkage
    1. Kempe Rectilinear Linkage

1.

Parallelogram linkage

The parallelogram and contra-parallelogram linkages are among the simplest and most useful four-bar linkages

  • 1. Parallelogram linkage

1.1.

Parallelogram linkage

Example of the parallelogram and contra-parallelogram linkages.
Parallelogram linkage
– Professor McCarthy

2.

Straight-line linkages

The Watt, Roberts and Tchebychef linkages are approximate straight-line linkages.

  • 1. Watt's linkage
  • 2. Robert's linkage
  • 3. Tchebychef's linkage

2.1.

Watt's linkage

This is an example of Watt's straight-line linkage. The point between the moving pivots traces an approximate straight-line.
Watt's linkage
– Professor McCarthy

2.2.

–

2.3.

–

3.

Peaucellier linkage

The Peaucellier linkage generates and exact straight-line by transforming a circle into a straight line. Additional linkages show the benefit of a driving crank.

  • 1. Peaucellier linkage
  • 2. Robert's linkage driven
  • 3. Tchebychef's linkage driven

3.1.

Peaucellier linkage

This illustrates the movement of the Peaucellier linkage which transforms the circle traced by B into straight-line traced by F.
Peaucellier linkage
– Professor McCarthy

3.2.

–

3.3.

–

4.

Linkages by Kempe

Kempe's book How to draw a straight line includes a number of interesting linkages. Here we show the reversors.

  • 1. Kempe's Reversor
  • 2. Kempe's Reversor 2

4.1.

Kempe's Reversor

This linkage is Kempe's reversor, which generates equal and angular movement of two links.
Kempe's Reversor
– Professor McCarthy

4.2.

–

5.

Kempe's rectilinear linkage

Kempe shows how to use the geometry of a rhombus and parallelogram to create a number of rectilinear linkages. This is just one of them

  • 1. Kempe Rectilinear Linkage

5.1.

Kempe Rectilinear Linkage

This linkage was introduced by Kempe in his book How to draw a straight-line. It guides a link on a purely rectilinear movement.
Kempe Rectilinear Linkage
– Professor McCarthy

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