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Anonymous
617 Vistas, 6 Respuestas

A double eccentric problem

 In the attached dwg file, there is the large red circle.

 

Inside there are two blocks, also a red circle entity.

 

The green block consists of a larger circle and a smaller eccentric circle.

 

The blue block consists of a larger circle that is equal to the green block's small circle, and its own smaller eccentric circle.

 

As you can see, I've assembled those 3 entities together where the blue's small circle is concentric with the green's larger circle and also the large red circle. I've also drawn a point (well, actually a very small circle) in an arbitrary target location that should be within the scope of the eccentrics.

 

The double eccentric problem? I'd like to know some steps that are required that rotates both green block central to its large circle and blue block central to its large circle -- so that the center of the blue block's smallest circle is exactly central to the target -- and central to the large red circle. (I hope that is all not too confusing.

 

Any help? Cuz I'm stymied.
Len Miller

Kent1Cooper
en respuesta a: Anonymous


@Anonymous wrote:

.... so that the center of the blue block's smallest circle is exactly central to the target -- and central to the large red circle. ....


Since the target circle and the large red circle are not concentric, I don't see how anything can be "central to" [if that means concentric with] both of them.  Can you explain differently, or show some kind of before-and-after image?

Kent Cooper, AIA
Anonymous
en respuesta a: Kent1Cooper

Hi Kent,

 

An old timer from my machine shop told me years ago that he could make a pair of eccentric bushings that when rotated just so could place the smallest diameter (a hole) precisely to some target location within the eccentric (he called it throw) scope of both eccentrics. This way, craftsmen in the field could manipulate the bushing pair to a precise target by rotation of both bushings, each in a certain way.

 

The way he explained it, you rotate the large and the small bushing together a certain number of degrees, then rotate only the small bushing a certain number of degrees.

 

....  or the small bushing first, then the large and small bushings together -- next.

 

I can't remember the sequence it's been so many years.

 

I'm fixing to try it like the old days -- plot the drawing to several pieces of paper, cut out each bushing and find me a board and a thumb tack -- and do some rotating this and rotating that.

 

Len

parkr4st
en respuesta a: Anonymous

Len

 

if I understand your puzzle, the challenge is to rotate the various discs until the hole axis in the centermost disc is congruent with the shaft axis on layer 4. 

correct?

 

the shaft is centered on the largest disc.

 

dave

 

 

leeminardi
en respuesta a: parkr4st

I think this may be a solution if I correctly understand the problem.

 

I modified the blocks in your drawing so that each is on a different layer and I added a crosshair for the two eccentric circles and a smaller circle at the center of the green and blue larger circles.

 

Since the center of the larger blue circle should be centered with the smaller of the green circles I added a parametric concentric constraint. This will ensure that the two block maintain a common pivot.

 

The process (use my "start" file):

 

1. Since the target is further from the center of the blue block than the blue crosshair, I want to rotate the green block clockwise to shorten this distance. An angle of about 15° is a good first guess.

 

2. Now rotate the green block counterclockwise about its center to bring the blue crosshair inline with the target.

 

Another iteration or two should place the blue crosshair pretty close to the center of the target.  

 

Refer to the "soln" file.

 

There may be a way to to automate this using numerical methods.

 

Lee 

 

lee.minardi
SEANT61
en respuesta a: leeminardi

To continue with Lee's excellent advise above:

 

Here is a spreadsheet (limited testing) that provides rotation values to apply to each block.  The resultant alignment is demoed in the accompanying AutoCAD file.


************************************************************
May your cursor always snap to the location intended.
leeminardi
en respuesta a: SEANT61

Here's a way to get an exact solution graphically using AutoCAD.  Start with my "start drawing" that has the concentric constraint (see my previous post).

 

1. Create a circle with a radius equal to the eccentricity of the blue block (rBlue = 1.0) centered at the target (yellow circle).

2. Create a circle with a radius equal to the eccentricity of the green block (rGreen = 1.0) centered at the center of the red circle (cyan).

 

These two circles intersect at two locations. You can use either solution.  

 

Using the top left intersection we measure the angle to rotate the green block:

  - from the top left intersection point of the two circles

  - to the insertion point of the green block (the center of the large green circle

  - to the center of the small blue circle

( rotate the green block  -29.774 in the step1 drawing)

 

After rotating the green block measure the angle for the blue block rotation:

- from the center of the target

- to the insertion point of the blue block 

- to the center of the eccentric circle of the blue  block

( rotate the blue block -27.061 in the step 2 drawing yield the Done drawing)

 

DoubleEccentric.JPG

 

~Lee

 

 

 

 

 

 

 

 

lee.minardi