Calculus Geometry Trigonometry

Peaucellier Apparatus

Introduction

The apparatus in the right figure is invented by M.Peaucellier in 1864. It has six pieces or links. There are two long links of equal length and four short links that form a rhombus. Tracing the original figure by dragging the red point, we can obtain a transformed figure at the blue point.

Problems and Activities

1.    Let OA=OB=15, PA=PB=QA=QB=8, and OP=10. Find the length of OQ.

2.    Find the relation between the lengths of OP and OQ.

3.    What is the locus of Q when P moves along a line? Use "Line" radio button of the applet.

        Prove what you have found.

4.    What is the locus of Q when P moves along a circle that goes through point O?

        Use "Circle" radio button of the applet. Prove what you have found.

Applet

How to use the applet.

1. Drag the red point.

2. The red point moves on a line when "Line" option is selected.

3. The red point moves on a circle when "Circle" option is selected.

Picture

Reference

A.B.Kempe, "How to draw a straight line" NCTM classics 1977, originally published in London by Macmillan and Company in 1877.

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