--- In gingery_machines@yahoogroups.com, "Brite" <coldtoo2000@...> wrote:
> The Gingery Shaper, for example, in "first gear" has a CS of 5 1/2 ft/min at 1 inch stroke, but CS is 33 ft/min for 6" stroke - still in first gear.
OK, I like to understand, so I did the math...
I draw the kinematics of the bull gear, yoke and ram (based on the various pictures found on the net).
And I brushed up my trigonometry :-)
I don't really know for sure how shapers are operated, so I made the assumption that the stroke length is adjusted by moving the crank pin position on the bull gear (I tried to simulate other geometries like a "sliding" lower pivot point, but it's action on the stroke length is much weaker)
Here are my results, experienced shaper users, please, correct me:
I calculated the ram speed along the stroke, and I found that it's almost constant for over 80% of the stroke !
Amazing: those guys who invented it were geniuses (or lucky).
I would really have guessed a more or less sinusoidal speed curve from such a cycling system.
There is an undulation of the speed near the center of the stroke for some geometries (the longer strokes). For those who know radio receivers, the speed curve vs ram position I found has the "quasi rectangular shape" of two coupled tank FI filters...
The point to notice is that, as the stroke gets smaller, the speed is less and less constant along the course, and for the smaller strokes, it is very sinusoidal in shape (max speed at the center of the stroke, indeed). In the same time, forward and return strokes tends to become symmetrical.
BTW, for the larger part of the stroke, the instantaneous speed I simulated is reasonably close to the "mean speeds" given the table.
>
> Aren't shapers fun!!
Yes, they are!!
Pierre.
http://groups.yahoo.com/group/gingery_machines/app/peoplemap/view/map
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