throttle travel equation

rocketbob · #1 12-19-2011, 01:28 PM

Question for a math whiz. I'm fairly good at math but I can't remember how to determine the following geometry problem.

I built a custom throttle quadrant and want to determine mathematically where the location up the throttle lever arm that would give me 2" of cable travel. Lets say the stops are on a 4" radius from the throttle arm pivot. How do I determine the distance from the pivot hole to get exactly 2" of cable travel? Width of the arm is 1/2". The stops are 1/4" in diameter.

Greg Arehart · #2 12-19-2011, 01:39 PM

Bob,

Circumference of a circle is 2 (pi) (radius), so the travel in a complete circle would be slightly over 25 inches.

25 inches divided by 360 degrees = .007 inches/degree

2 inches times 0.007 inches/degree = 29 degrees of travel.

You can do this backwards if you know how many degrees of travel you have, and that would give you the distance out from the center for your pivot point. The width of the arm is irrelevant.

Since your motion is around a circle (not straight-line, which is what you really want to calculate), I would add another few degrees of travel so that you run against the stops at the far end of the cable, not on the quadrant itself.

[edit] just reread the original and I'm not sure I answered the exact question, but to do so requires me to know the degrees of travel (or at least distance along the arc) between your stops.

cheers,
greg

rocketbob · #3 12-19-2011, 01:57 PM

Actually Greg I don't believe you are correct since you're saying that the travel is the same at .007" per degree at a 4" radius and a 2" radius...it would be smaller at a 2" radius. If I'm understanding correctly.

Cadstat · #4 12-19-2011, 02:09 PM

Rocket Bob,
I'm at a CAD station and tried to lay out your problem but I need to know the distance between stops on the 4" radius.

szicree · #5 12-19-2011, 02:18 PM

Put a mark at an arbitrary location on the center line of the arm. Let R be the distance from this mark to the lever pivot. Swing the lever from stop to stop and measure the straight line distance travelled by the mark. Call this distance D. If we let r be the distance that you're trying to find, it will be given by r=2R/D.

Guy Prevost · #6 12-19-2011, 02:19 PM

It's a linear relationship.

Assuming the same angle between the cable and the lever arms (lets say they are perpendicular at mid travel) 30 degrees of throttle lever travel at a 4" radius will provide 1/2 as much travel at a 2" radius.

Without knowing how big of an arc you have, I can't answer specifically.

rocketbob · #7 12-19-2011, 02:45 PM

Quote:

Originally Posted by Guy Prevost

It's a linear relationship.

Assuming the same angle between the cable and the lever arms (lets say they are perpendicular at mid travel) 30 degrees of throttle lever travel at a 4" radius will provide 1/2 as much travel at a 2" radius.

Without knowing how big of an arc you have, I can't answer specifically.

I'll post a pic of the quadrant tonight since I modeled it in Solidworks, and can get the angle of travel between the stops. The real thing is made exactly how I modeled it. So if travel is constrained to be x degrees, what is the formula to get the diameter of a circle with 2" of distance between two secant points x degrees apart.

Guy Prevost · #8 12-19-2011, 03:01 PM

The distance between the two secant points should be 2*r*sin(angle/2). Or more specifically, the radius, r from the pivot should be:

(Cable throw distance) / (2*sin(angle/2))

stevemcgirr · #9 12-19-2011, 03:01 PM

Since you have not set the degrees of travel for this problem, set the degrees as variable "a", and you could visualize this as two right triangles mirrored, and set the desired radius as "r". The "side opposite" the angle (sine) is 1" for each right triangle, giving a ratio of:

1/r=sin a

So if you know the angle, you derive the radius, or vice versa

At least I think so...

BTW in this ratio the angle "a" gives 1/2 the total. Angle a is for each of the two halves, so total angle would be 2a

Flying Scotsman · #10 12-19-2011, 03:03 PM

Quote:

Originally Posted by rocketbob

I'll post a pic of the quadrant tonight since I modeled it in Solidworks, and can get the angle of travel between the stops. The real thing is made exactly how I modeled it. So if travel is constrained to be x degrees, what is the formula to get the diameter of a circle with 2" of distance between two secant points x degrees apart.

Do you want the 2" between points to be arc length, or just point-to-point as measured in the "usual" sense (Euclidean distance)?