Ask HN: How can mechanical movements be designed systematically?

Is there any systematic method for designing/"programming" passive mechanical movements where, given mechanical input behavior, an output behavior is produced by the design? If one can come up with a solution which produces the desired behavior, it can be modeled in a CAD tool. But how do you come up with what to model?

Here are several resources I am aware of but do not know how to piece together.

- http://507movements.com/

- https://www.youtube.com/user/thang010146

- https://www.youtube.com/user/YesYenGraphiTech

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My specific input is a row of rods which over time independently actuate (go up) and return to their initial position (return back down). No more than, say, 6 rods are ever up at a given time.

The output is a separate register of rods (o_1,o_2,o_3,o_4,o_5,o_6) with the following behavior: At any time, say the input rods (b_1,...,b_k) are actuated, and became actuated in their labeled order. When some of them, say (b_i), i in S, de-actuate, then (o_i), i in S, should rapidly "fire," i.e. actuate then de-actuate.

This process has to be able to repeat over and over, so after an output o_i fires the (o_{i+1},...,o_6) need to somehow get reset to anticipate future input rod actuations.

I know an easy answer is to just use a microcontroller but I am really only interested in a purely mechanical solution.