**Next:** *Inversion*

**Up:** *Peaucellier's Linkage Table of Contents*

**Prev:** *Introduction*

# Peaucellier's Linkage

## Part 1. Construct the Linkage

Construct the linkage as follows. Once you have a sketch, make this
procedure into a script.
- Start with three segments off to the side which determine your
three lengths.

- Use Translation by Fixed Cartesian on the endpoints of one of the
segments you just constructed to get U and T.

- You can now construct P. The only requirement is that P is a
specified distance from U. How can you construct it?

- How do you determine the placement of R and S? Remember that they
are both a specified distance from T and a specified distance from
P. Construct them.

- To determine the placement of Q, what do you know about a polygon
with four sides of equal length? Mathematically, you could
construct Q using either intersections of parallel lines or
intersections of circles. However, for technical reasons,
intersections of parallel lines works better. Construct Q.

- After completing your sketch, move P while you trace P and Q to
form conjectures as to the shapes their traces lie on.

- Change the lengths of the three segment and move P while you trace
P and Q again. Does your conjecture remain true?

By now you have formulated a conjecture for the shape traced by Q as P
moves. The next question is: Why do P and Q behave as they do? In the
next section, you will learn about inversion. In part 3, you apply
this knowledge to your linkage to understand why P and Q move as they
do.

**Next:** *Inversion*

**Up:** *Peaucellier's Linkage Table of Contents*

**Prev:** *Introduction*

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Created: Jun 09 1996 ---
Last modified: Jun 11 1996