Geometry quiz

[capricorn]

See attached sketch. Is x + y greater than 90 degrees? :p

[Brandano]

it's exactly 90 degrees, that is, assuming both circles are the same radius

[ghoti]

The angles are specified on the drawing as 45 plus 45 and that is 90. What are you asking? Bill

[mcross]

With the yellow link less than 6 the two angles marked 19.47º can't be the same. I think.
Mike

[mcross]

I take that back, they can be.

[capricorn]

x + y is greater than 90 degrees. (circles are the same radius) Cap

[T-RexxMonster]

it's exactly 90 degrees, that is, assuming both circles are the same radius


:confused: Radius doesn't effect angles on circles?

[capricorn]

Radius would affect the angles, I think Brandano was qualifying his response since the drawing was lacking that bit of info, only one of the two circles was dimensioned. Cap

[KenSt]

According to AutoCad 2006, 2 circles, 6.0000" apart each with a radius of 1.0000", with a link at 19.4700 degrees yields the following results. x = 47.8460 degrees and y = 42.7951 degrees. Adding the two together = 90.6411 degrees

Yes, they are more than 90 degrees apart. :)

BTW, the link is actually 5.6569, not 5.654. If the link IS as dimensioned, then 6" between centers can't be. :eek:

[capricorn]

KenSt, You are right, I shouldn't put a quiz or the like out here with an error in it, sorry all. In any case I guess the point was x + y is greater than 90 degrees. It's very easy to get 90 degrees, when the circles are the same radius etc. Obviously when the link is parallel to the axis and 6.00 inches long x + y = 90 so it's somewhat deceiving. Cap

[KenSt]

Hey Cap, Here's an interesting twist. If you rotate the "slave" (the x and y one)circle's angle just 6.02 degrees from 19.47 to 13.45 and connect with the appropriate link, x becomes 44.705 degrees and y becomes 44.7029 degrees. Now they are for all reasonable purposes equal, and LESS than 90. 44.7050 + 44.7092 = 89.4079 degrees.

[capricorn]

I imagine so. It's amazing when you think of what was done with levers and links on old steam locomotives, with a couple of links and levers here and there they'd obtain nearly any dynamic motion needed to control the engine, back in the days without computers, cad or calculators to boot. Cap