Trig help

[3axisrookie]

Having trouble finding a single coordinate on this blueprint. I know I can just draw it up in autocad really fast and get it that way, but since this is for class, would love to figure this out. I have attached the blueprint, and erased all the triangles I made so it would be easier for everyone else to see. I also put a check mark next to the coordinates I have, and the question mark next to the coordinate I can't find. Which is the openings of the slot(s).

I was still able to make the part though. What I did was cut the outside of the part with all the 32mm arcs, and skip the slots with cutter comp on. Then switch to a 6.5mm tool, and cut the slots (6.5mm since the part is supposed to be scaled by 1/2, so would be a 13mm tool if not scaled) with cutter comp off.

But would love to be able to just do it all in one shot. But can't figure out how to get that coordinate for the life of me with just a pen, paper, and calculator. Almost positive it's not possible. But not 100% sure, that is why I am asking. Thanks.

[gar]

080403-1316 EST USA

3axisrookie:

At least two ways.

Write the equation for the 73 radius circle -- X^2 + Y^2 = 73^2.
Then write the equation for the side of the slot. Now you have two equations in two variables and you can solve these.

Second method. Using the bottom vertical slot use right triangles to find the right lower corner of the slot. Rotate that point 60 deg counterclockwise and you have the desired point.

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[3axisrookie]

I'm sorry, but not following you. Any way you can draw the triangle?

The center of the slot point, and the point on the end of the slot are not 6.5mm apart. That line is actually a chord of the circle. That's the whole problem. All I have on the point is the it's 73mm from the center. No angles, and no distance to another point.

[gar]

080403-1648 EST USA

3axisrookie:

Your bottom slot can have a right triangle drawn within such that the hypotenuse is the arc radius (73 MM) and the short side is is the offset from the Y axis of the slot side ( 0.5 * 13 = 6.5 ). Thus, the coordinate of that corner is X 6.5 Y ( ( 73^2 - 6.5^2 )^0.5 ) or X 6.5 Y -72.71.

You can calculate the angle from vertical as ARCSIN (6.5/73) = 5.10844 deg.

You ?ed point is -30+5.10844 deg from the X axis.

(edit)
Since the slot is 13 wide the chord is 13 no matter what the radius of the arc is.
(end edit)

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[3axisrookie]

Boy do I feel silly. Can't believe I didn't see that. What threw me off was I used the point that bisects the slot. So took 2 lines of radius 73mm, and another line that connects them as 6.5mm. Found all the angles in that triangle and made another triangle off it. Then told myself, wait a minute, that line isn't 6.5mm. And never thought to just make a right angle with the line that actually is 6.5mm.

Thanks.