Modeling a Three-Pendulum Harmonograph – tutorial: part #2

Hi guys, here is the second part of a tutorial describing the matematical equations used in modeling a three-pendulum harmonograph (automatic drawing machine). It pertains to the second version of the model. This section describes the kinematic equations involved in the articulated linkage mechanism on the top of the table, the custom spreadsheet functions used in the model and some overall considerations about the partition of the spreadsheet.  This is an advanced tutorial so you need a minimum of high-school physics and geometry background. So what do you think? Cheers, George


This article has 3 Comments

  1. Thanks Peter for the thumb up. This particular model is way more complicated than it needs to be since I had the vain ambition to model the exact linkage used in the wooden model. You can just assume simple linear sinusoidal movenemts along the axes and perhaps vary the angles of travel and you can get a much simple model. Unfortunately I don’t do Python. I should be even easier in Python but I am not sure about the real time graphics. The math is very easy so it should be very fast too. In excel the charting hogs most of the speed.

  2. I had no idea something this sick could be done in Excel. Great job! I just saw the physical harmonograph in action at the San Francisco Exploratorium and wondered if anybody had done a computer version in Python. You’re a genius.

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