Find Some Equidistant Set of Points on a Circle Farthest From Another Set of Points
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I am trying to drill holes in a bicycle hub to fit it on a different style rim. I currently have a 36 hole rim with 18 holes on each side, and I'm transitioning to a 32 hole rim with 16 holes on each side. I need to drill new holes in the rim, and I need the 16 new points to be far away from the old 18 holes for stability.
Picture of bicycle hub similar to mine; for reference.
Here is a summary of what I think I am trying to do: Given x points on the circumference of a circle equidistant to each other, find y other points on the circumference of the circle which are equidistant to each other, farthest away from the x points.
Here I drew a graph and plotted points to illustrate what I am trying to do: https://www.desmos.com/calculator/mdzqhqhhwb
On my graph the red X's are existing holes, and the blue points are the holes that I plan to drill. I have used variable h to shift the points about the circle. I have used variable k to change the distance between two pairs of holes (I realize this breaks the condition of equidistant points that I mentioned earlier, but it would work in my bicycle application). Currently I'm going by eye and just punching in random shift (variable h) values. It is possible to re use existing holes (ie overlap).
geometry
asked Nov 24 at 8:15
James Meas
162
add a comment |
up vote
3
down vote
favorite
I am trying to drill holes in a bicycle hub to fit it on a different style rim. I currently have a 36 hole rim with 18 holes on each side, and I'm transitioning to a 32 hole rim with 16 holes on each side. I need to drill new holes in the rim, and I need the 16 new points to be far away from the old 18 holes for stability.
Picture of bicycle hub similar to mine; for reference.
Here is a summary of what I think I am trying to do: Given x points on the circumference of a circle equidistant to each other, find y other points on the circumference of the circle which are equidistant to each other, farthest away from the x points.
Here I drew a graph and plotted points to illustrate what I am trying to do: https://www.desmos.com/calculator/mdzqhqhhwb
On my graph the red X's are existing holes, and the blue points are the holes that I plan to drill. I have used variable h to shift the points about the circle. I have used variable k to change the distance between two pairs of holes (I realize this breaks the condition of equidistant points that I mentioned earlier, but it would work in my bicycle application). Currently I'm going by eye and just punching in random shift (variable h) values. It is possible to re use existing holes (ie overlap).
geometry
asked Nov 24 at 8:15
James Meas
162
1
If you have a blue point exactly on top of a red point, does that also compromise stability, or can you just reuse the existing hole? I ask because it changes the mathematical formulation a bit, since then you would exclude those coincident points from the objective.
– Rahul
Nov 24 at 9:30
I was thinking about that after I posted the question; yes, I suppose it is possible to reuse existing holes.
– James Meas
Nov 24 at 19:01
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I am trying to drill holes in a bicycle hub to fit it on a different style rim. I currently have a 36 hole rim with 18 holes on each side, and I'm transitioning to a 32 hole rim with 16 holes on each side. I need to drill new holes in the rim, and I need the 16 new points to be far away from the old 18 holes for stability.
Picture of bicycle hub similar to mine; for reference.
Here is a summary of what I think I am trying to do: Given x points on the circumference of a circle equidistant to each other, find y other points on the circumference of the circle which are equidistant to each other, farthest away from the x points.
Here I drew a graph and plotted points to illustrate what I am trying to do: https://www.desmos.com/calculator/mdzqhqhhwb
On my graph the red X's are existing holes, and the blue points are the holes that I plan to drill. I have used variable h to shift the points about the circle. I have used variable k to change the distance between two pairs of holes (I realize this breaks the condition of equidistant points that I mentioned earlier, but it would work in my bicycle application). Currently I'm going by eye and just punching in random shift (variable h) values. It is possible to re use existing holes (ie overlap).
geometry
asked Nov 24 at 8:15
James Meas
162
I am trying to drill holes in a bicycle hub to fit it on a different style rim. I currently have a 36 hole rim with 18 holes on each side, and I'm transitioning to a 32 hole rim with 16 holes on each side. I need to drill new holes in the rim, and I need the 16 new points to be far away from the old 18 holes for stability.
Picture of bicycle hub similar to mine; for reference.
Here is a summary of what I think I am trying to do: Given x points on the circumference of a circle equidistant to each other, find y other points on the circumference of the circle which are equidistant to each other, farthest away from the x points.
Here I drew a graph and plotted points to illustrate what I am trying to do: https://www.desmos.com/calculator/mdzqhqhhwb
On my graph the red X's are existing holes, and the blue points are the holes that I plan to drill. I have used variable h to shift the points about the circle. I have used variable k to change the distance between two pairs of holes (I realize this breaks the condition of equidistant points that I mentioned earlier, but it would work in my bicycle application). Currently I'm going by eye and just punching in random shift (variable h) values. It is possible to re use existing holes (ie overlap).
geometry
geometry
asked Nov 24 at 8:15
James Meas
162
asked Nov 24 at 8:15
James Meas
162
edited 6 hours ago
asked Nov 24 at 8:15
James Meas
162
asked Nov 24 at 8:15
James Meas
162
asked Nov 24 at 8:15
James Meas
162
162
1
If you have a blue point exactly on top of a red point, does that also compromise stability, or can you just reuse the existing hole? I ask because it changes the mathematical formulation a bit, since then you would exclude those coincident points from the objective.
– Rahul
Nov 24 at 9:30
I was thinking about that after I posted the question; yes, I suppose it is possible to reuse existing holes.
– James Meas
Nov 24 at 19:01
add a comment |
1
If you have a blue point exactly on top of a red point, does that also compromise stability, or can you just reuse the existing hole? I ask because it changes the mathematical formulation a bit, since then you would exclude those coincident points from the objective.
– Rahul
Nov 24 at 9:30
I was thinking about that after I posted the question; yes, I suppose it is possible to reuse existing holes.
– James Meas
Nov 24 at 19:01
1
1
If you have a blue point exactly on top of a red point, does that also compromise stability, or can you just reuse the existing hole? I ask because it changes the mathematical formulation a bit, since then you would exclude those coincident points from the objective.
– Rahul
Nov 24 at 9:30
If you have a blue point exactly on top of a red point, does that also compromise stability, or can you just reuse the existing hole? I ask because it changes the mathematical formulation a bit, since then you would exclude those coincident points from the objective.
– Rahul
Nov 24 at 9:30
I was thinking about that after I posted the question; yes, I suppose it is possible to reuse existing holes.
– James Meas
Nov 24 at 19:01
I was thinking about that after I posted the question; yes, I suppose it is possible to reuse existing holes.
– James Meas
Nov 24 at 19:01
add a comment |
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If you have a blue point exactly on top of a red point, does that also compromise stability, or can you just reuse the existing hole? I ask because it changes the mathematical formulation a bit, since then you would exclude those coincident points from the objective.
– Rahul
Nov 24 at 9:30
I was thinking about that after I posted the question; yes, I suppose it is possible to reuse existing holes.
– James Meas
Nov 24 at 19:01