A Simple, Or Not So Simple, Gesture

When people are introduced one of my automata pieces they always ask, "How does it work? How do you figure it out?" This blog entry will take a stab at answering a bit of both questions. 

Lets take our character below, Otto Mata, and have him raise his hand to wave at his adoring public! To make Otto's hand, (Point A) rise in a waving gesture 1-1/4", (distance "a" in the diagram) how much do we need to cut into cam G. This amount will be distance "g" in the diagram, the difference between the minimum and maximum cam diameter.

The answer lies in understanding the length of the levers and fulcrums that are part of the linkages between these to points.  I'll perform the calculation with the arm in the neutral, position, that is half way up. There are minor corrections that can be applied for fact that many points are following arcs not straight lines, but they will be ignored in this example.

Since Point B is fixed on Otto's shoulder and only allowed to rotate, Point C will move down as Point A moves up. It will move in portion to the leverage around the fulcrum at Point B. For Point A to rise 1.25", Point C must move 1.25" x 1/3 = 0.4167" downward.

Point D on the cam follower will travel the same distance since C and D are pinned connections (i.e. distance "c" = "d"). Since the end of the follower, Point F, can only rotate, the amount Point E will move is also a function of the lever length. Because the two points are on the same side of the fulcrum at F, the calculation to determine the distance "e" is a little different that the previous one. Point E  will move (0.4167" x 2/(1.5 +2)) = .238"  Translating  this to the cam means that the difference between the minimum and maximum diameter on the cam must be 0.238", slightly less than 1/4"

If the nominal diameter of the cam was to be 2" then the cam should have a (2+0.238/2) = 2.129" outside diameter, and a  diameter of (2-0.238/2) = 1.88" where the arm is to be raised.

How fast Otto's arm rises and falls, and how long it stays up is a whole other story! Who knows, it could be a future blog posting.