Bell cranks

Is there a formula for bell cranks where I am using a linear movement from a
cam follower and linkage on the input to a bell crank that is translated to
rotational movement. The output of the bell crank moves a pin in the ark of
the output radius. I then use just the "X" movement of the pin to move a
table. I need more movement on the "X" and want to make a bigger radius on
the output of the bell crank. I can't change the input radius. My mind is
saying that at the extremes of input movement the "X-only" movement gets
funky and falls off of input/output ratio because of "Y" motion of the pin.
It seems that if I keep in the 45 deg. range it works out to input. Is
there someway of predicting the "X-only" movement of a bellcrank at whatever
angle? Or, does the fact that the input is translated from linear movement
to rotational movement them to linear movement cancel the funky stuff going
on at the ends of the strokes?
This has turned to mush for me and I need to be educated.
Reply to
Tom Gardner
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"Tom Gardner" wrote in news:Gokwd.47672$
It's all just ratios and trigenometry.
So the pin is riding in a slot perpendicular to the axis of motion, and you basically lose any movement along the slot, yes? Basic trig. X motion is the sine (or cosine, depending which angle you pick) of the angle of the bellcrank motion. If instead of a slot you had another output link which pivoted on the X axis mechanism, you still have loss at the ends of the stroke, but now it changes relative to BOTH angles. More trig.
My gut feeling is that if you need more X movement, a longer output arm of your bellcrank will give it to you, but the tradeoff is that it is exactly proportional to the loss of actuation force for the same input. Double the range, halve the force. Simple levers at this point.
Websearch "sine" and "cosine".
Depends on how it is done, sometimes yes, sometimes no. My gut feeling in this case is that there is enough difference in your linkages that the answer is no. Searching on: linkage, kinematics may get you some useful answers, too.
HTH, --Glenn Lyford
Reply to
Glenn Lyford
The two common variations of this mechanism are known as the "slider crank" and "Scotch yoke". The typical IC engine is a slider crank. Formulas for displacement, velocity, and acceleration can be found in general ME references (Mark's, Kent's, Eshbach, etc.), the derivations will be in any basic mechanism text. The formulas for the Scotch yoke are easy to derive (pure harmonic motion). The slider crank is uglier, but there are simplified formulas that are adequate in most cases.
This page apparently shows the equations, but I don't have the proper plug-in.
formatting link
Ned Simmons
Reply to
Ned Simmons
Yep, gets ugly! -cool page!
Reply to
Tom Gardner

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