**Next:** *Construct the Linkage*

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

# Peaucellier's Linkage

by Evelyn Sander
## Part 0. Introduction

A linkage is a series of straight rods connected at the ends, which
are free to pivot in a plane. You can construct a physical version of
such an object. For example, you can make one out of parts from an
erector set or even popsicle sticks. We are going to study a
particular linkage originally constructed by Peaucellier.

Peaucellier's linkage consists of two fixed points at a specified
distance from each other, marked T and U in the figure, and seven
rigid rods of specified size, attached together as indicated in the
picture. Aside from the following constraints, the rods are free to
move.

Constraints: As you see, rods are: PU, PS, QS, QR, PR,
TR, and TS. The specified sizes are: Distance from T to U=PU,
PS=QS=QR=PR, and TS=TR.

Notice that of the seven segments, four are one length, two the next,
and one a third length, the last one being also the distance between
the two fixed points. Do the assumptions about how they are attached
give any additional information about the three possible lengths?

You will construct the linkage of Peaucellier and study it. Before you
begin, consider the following questions. The first question, you
should be able to reason out. The second question is the topic you
will study for the rest of the lab.

- As you move the linkage, how is point P constrained? Remember that U
is a fixed point. On what shape does the trace of point P lie?

- How is point Q constrained as you move the linkage? On what shape does
the trace of point Q lie?

**Next:** *Construct the Linkage*

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

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Created: Jun 09 1996 ---
Last modified: Tue Apr 15 15:14:01 1997