mklotz
Well-Known Member
Fooling around with my sine bar protractor
http://www.homemodelenginemachinist.com/index.php?topic=969.msg6664#msg6664
the other day, I realized that the principle could be used to build what may be the world's simplest indexing head. I have no need for it and thus no intention to build a prototype so I'll throw the idea out here for anyone who may wish to use the concept.
Imagine a circular plate that can pivot on a stationary base. A pin of diameter d1 is mounted to the base near the plate at a distance r1 from the center rotation. A pin of diameter d2 is mounted near the edge of the circular plate at a distance r2 from the center of rotation. Call the "zero" angle of the table the point where the two pins are as close to each other as possible.
Now, if I want to rotate the plate to an angle theta relative to this zero, I calculate the chordal distance from the law of cosines.
c = sqrt [r1^2 + r2^2 - 2*r1*r2*cos(theta)]
then, with the definition
d = (d1+d2)/2
I set my calipers to a distance equal to s = c + d and rotate the plate until the distance between the pins corresponds to s. Piece of cake.
While this probably won't replace a real indexing head for repetitive operations, it has some real advantages for the tool-bereft novice...
No need to buy pricey tooling to set a one-off oddball angle.
Accuracy determined only by one's ability to measure simple linear distances.
If one can tolerate a pin hole in the part (or machine the hole away later), the part itself can replace the "circular plate" I refer to above.
If anyone tries this idea, please report on what you did and how it worked.
---
BTW, if you wish to use the idea and are overcome by the mathematics of calculating "c", let me know and I'll write a program to do it for you.
http://www.homemodelenginemachinist.com/index.php?topic=969.msg6664#msg6664
the other day, I realized that the principle could be used to build what may be the world's simplest indexing head. I have no need for it and thus no intention to build a prototype so I'll throw the idea out here for anyone who may wish to use the concept.
Imagine a circular plate that can pivot on a stationary base. A pin of diameter d1 is mounted to the base near the plate at a distance r1 from the center rotation. A pin of diameter d2 is mounted near the edge of the circular plate at a distance r2 from the center of rotation. Call the "zero" angle of the table the point where the two pins are as close to each other as possible.
Now, if I want to rotate the plate to an angle theta relative to this zero, I calculate the chordal distance from the law of cosines.
c = sqrt [r1^2 + r2^2 - 2*r1*r2*cos(theta)]
then, with the definition
d = (d1+d2)/2
I set my calipers to a distance equal to s = c + d and rotate the plate until the distance between the pins corresponds to s. Piece of cake.
While this probably won't replace a real indexing head for repetitive operations, it has some real advantages for the tool-bereft novice...
No need to buy pricey tooling to set a one-off oddball angle.
Accuracy determined only by one's ability to measure simple linear distances.
If one can tolerate a pin hole in the part (or machine the hole away later), the part itself can replace the "circular plate" I refer to above.
If anyone tries this idea, please report on what you did and how it worked.
---
BTW, if you wish to use the idea and are overcome by the mathematics of calculating "c", let me know and I'll write a program to do it for you.