Interesting Practical Mathematical Problem

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Discussion Overview

The discussion revolves around a practical mathematical problem related to optimizing the placement of a drill for a PCB drilling machine. Participants explore how to determine the optimal position (value of x) to allow for drilling the largest possible rectangular PCBs, considering the constraints of the drill's reach and the dimensions of the boards.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests placing the drill at x = A/3 to maximize the coverage for boards up to 2A/3 in size.
  • Another participant proposes suspending the drill from the roof to allow for any board size, indicating a non-traditional approach.
  • Several participants reflect on their initial guesses for the optimal position, with some suggesting A/4 before realizing the correct answer.
  • One participant emphasizes the trade-off involved in positioning the drill, noting that moving it in one direction sacrifices space on that side, leading to a 'dead zone' if placed incorrectly.
  • Participants share their thought processes and methods for arriving at their conclusions, including using paper to visualize the problem.

Areas of Agreement / Disagreement

There is no clear consensus on the optimal placement of the drill, as participants present various suggestions and reasoning. Some agree with the A/3 placement, while others explore alternative methods and positions.

Contextual Notes

Participants express uncertainty about their initial guesses and the reasoning behind their conclusions, indicating that the problem may have multiple valid approaches or solutions.

Who May Find This Useful

Individuals interested in practical applications of mathematics, particularly in engineering or DIY projects involving optimization and spatial reasoning.

I_am_learning
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I was making a PCB drilling machine at home with my brother, and came across this mathematical? problem.
drill%2520problem.jpg


I needed to fix the drill machine. But I needed to determine where should it be fixed so that I could drill largest possible PCB boards.
In other words, find the value of x so that you could drill rectangular PCBs of largest possible width.
When I say 'could drill PCB', I mean, you need to be able to place every point of the PCB below the drill so as to be able to drill anywhere in the PCB.

Ask if I didn't make any sense.

The question isn't as simple as it may look.
But its not hard enough to deserve to be posted in maths forum.
You may think you already know the answer when you really don't.
We enjoyed solving this problem, so I shared it here.
 
Mathematics news on Phys.org
can you draw a simpler picture that only contains the relevant information?
 
Let A be the distance wall to wall. Place it so that x = A/3. Then you will be able to drill a hole at any point on a board that is 2A/3 or smaller in it's smallest dimension, and have the greatest coverage for larger boards.
 
you could suspend your drill part to the roof so you want work with whatever sized board you want!

pew pew, thinking outside of the box!
 
Jimmy got it right.
Did you get it immediately, or It was only me that needed to spin his head to get the answer.?
We almost fixed it in the middle, before realizing the correct answer.
 
I_am_learning said:
We almost fixed it in the middle, before realizing the correct answer.

I still don't see it. :blushing::biggrin:

Ah, now I do.
 
Kudos to Jimmy. My solution was: check Craigslist for a used drill press.
 
x->inf
 
I_am_learning said:
Jimmy got it right.
Did you get it immediately, or It was only me that needed to spin his head to get the answer.?
We almost fixed it in the middle, before realizing the correct answer.

Think about it this way: whenever you move the drill in one direction, you are sacrificing room on that side. At 2/3 you are sacrificing the most room while the other side can compensate. If you go further than 2/3 you create a 'dead zone'.
 
  • #10
I_am_learning said:
Did you get it immediately?
We almost fixed it in the middle, before realizing the correct answer.
No, like you, my first guess was also in the middle. It took me a few moments to realize that you can turn the work around and double the reachable area. My second guess was A/4, but I took a piece of paper and slid it around to see what would happen. That's how I found the answer.
 
  • #11
Jimmy Snyder said:
second guess was A/4
Mine too. :)
Jimmy Snyder said:
but I took a piece of paper and slid it around to see what would happen. That's how I found the answer.
Quite differently I took a piece of paper and tried to recall linear Programming lessons.

dirll.jpg
 

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