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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.
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