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Move it 200 mm in 4 seconds

by Fred Thomas

86
skips
14
questions

Act One

  • Fred Thomas

    Fred Thomas

    October 23, 2014

    What other functions can give the same (or better) results?

  • Teacher note
    LACI uses a "stepper motor" to move. Stepper motors are widely used by engineers and technicians in applications that require precise positioning including the autofocus in cameras, CNC manufacturing, image scanners, 3-D printers and much more.

Act Two

  • Teacher note
    The start and the stop are the major points at which the battery is likely to fall. Other functions that can be used (piecewise or not) to start and stop gradually but still reach a relatively high speed include sine and cosine, exponentials, cubics and much more.

Act Three

  • Teacher note
    Student groups can work out their proposed solutions using any graphing software (Excel, calculators, etc.). They should not be allowed to use trial and error LACI, but the fun comes when they do try a well-justified solution using a battery on LACI

Sequel

  • 1.

    Can you move the battery MORE than 200 mm in 4 seconds?

  • 2.

    Can you move the battery 200 mm in less than 4 seconds?

  • 3.

    Can you find one function, x = f(t) which completes 5 round trips in as little time as possible?

  • 4.

    Can you achieve the same (or better) results using functions for velocity, v = f(t)?

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