show you how to use the ability of Geometry Expressions to animate with
respect to different variables to create a model of a cam. In the
picture on the left, the cam rotates about A, while the follower F
moves vertically with a sinusoidal motion. A model of the working cam is
on the web here
are used by mechanical engineers to create specified motion. The
cam synthesis problem is this: given a desired motion of the
follower, what shape should the cam be?
To create the cam shape,
we invert the problem, hold the cam fixed and rotate the follower, while
making its distance from the center of the cam vary appropriately
The cam profile is the envelope
of the circle (obtained by selecting the circle and using Construct/Locus
So how do we get the cam to move and the follower to stay put?
The trick is to add a parameter t to the argument of the sin function, then hold the angle fixed, while varying t.
The end effect of this is a model where the cam rotates, and the follower reciprocates.
Look again at the web model
. This was created with Geometry Expressions 3.0 beta.
Can you work out how the output curve was created? (Hint: it involved adding another parameter.)