Polar Plots Drawn by a Mechanical Linkage

bar lengths

r

1

1.5

r

2

0.5

r

3

1.5

bar angular speeds

ω

1

1

ω

2

-5

ω

3

-2

draw the polar plot

ϕ

0.

This Demonstration simulates the drawing of polar plots by means of an open mechanical linkage. The three polar plots considered are of the form

r(ϕ)=

n

∑

i=1

r

i

(sin(

ω

i

ϕ)+cos(

ω

i

ϕ))

with

n∈(1,2,3)

. These can be interpreted as the sum of up to three vectors with

r

i

as magnitudes and

ω

i

ϕ

as directions, and can be simulated by an

n

-bar open linkage

n=1,2,3

, with

ω

1

ϕ

as the direction of the driver bar.