[math-fun] Paper-cutters
Why do paper-cutters have curved blades? Is the usual design intended to optimize something? Jim Propp
I'd expect it's to maintain a constant rate of cut as you operate the handle at a constant speed. On Fri, Apr 13, 2018, 20:19 James Propp <jamespropp@gmail.com> wrote:
Why do paper-cutters have curved blades? Is the usual design intended to optimize something?
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I am going to guess that it is to make the cutting speed more constant, given that the operator will likely move the cutting arm at a constant angular speed. On Fri, Apr 13, 2018 at 11:19 PM, James Propp <jamespropp@gmail.com> wrote:
Why do paper-cutters have curved blades? Is the usual design intended to optimize something?
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I think it's intended to keep the length of paper cut per unit angle relatively constant; so that the operators force remains constant. Brent On 4/13/2018 8:19 PM, James Propp wrote:
Why do paper-cutters have curved blades? Is the usual design intended to optimize something?
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Another way to look at it: the angle at which the blade cuts remains roughly constant. On 4/13/18 22:02 , Brent Meeker wrote:
I think it's intended to keep the length of paper cut per unit angle relatively constant; so that the operators force remains constant.
Brent
On 4/13/2018 8:19 PM, James Propp wrote:
Why do paper-cutters have curved blades? Is the usual design intended to optimize something?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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This all begs the question (ire anticipated)... what's the optimal angle for a paper cutter to cut paper, and why? On Sat, Apr 14, 2018 at 12:09 AM, Andres Valloud <avalloud@smalltalk.comcastbiz.net> wrote:
Another way to look at it: the angle at which the blade cuts remains roughly constant.
On 4/13/18 22:02 , Brent Meeker wrote:
I think it's intended to keep the length of paper cut per unit angle relatively constant; so that the operators force remains constant.
Brent
On 4/13/2018 8:19 PM, James Propp wrote:
Why do paper-cutters have curved blades? Is the usual design intended to optimize something?
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Google says those in the business say the angle is an increasing function of paper strength, between 19 degrees for soft paper and 30 degrees for hard paper. Further, there is also a note that the harder the paper, the tighter the blade clamp should be adjusted. Given these observations, one might guess that, if the blade is moving at constant speed, the shearing force applied increases with the blade angle. The tighter the blade clamp, one would expect the shearing forces (including friction with the blade) to be magnified in the now smaller paper region experiencing the cutting action. So the force and the blade clamp setting would determine whether the blade bends, cuts, or tears the paper. What's your take? On 4/13/18 23:53 , James Davis wrote:
This all begs the question (ire anticipated)... what's the optimal angle for a paper cutter to cut paper, and why?
On Sat, Apr 14, 2018 at 12:09 AM, Andres Valloud <avalloud@smalltalk.comcastbiz.net> wrote:
Another way to look at it: the angle at which the blade cuts remains roughly constant.
On 4/13/18 22:02 , Brent Meeker wrote:
I think it's intended to keep the length of paper cut per unit angle relatively constant; so that the operators force remains constant.
Brent
On 4/13/2018 8:19 PM, James Propp wrote:
Why do paper-cutters have curved blades? Is the usual design intended to optimize something?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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There's no well defined optimum. It's a matter of trading off force required from the 110lb secretary trying to trim a 20pg document versus having the blade push the paper out of the way at a high blade angle which the secretary has to resist by holding the document in place. Brent On 4/13/2018 11:53 PM, James Davis wrote:
This all begs the question (ire anticipated)... what's the optimal angle for a paper cutter to cut paper, and why?
On Sat, Apr 14, 2018 at 12:09 AM, Andres Valloud <avalloud@smalltalk.comcastbiz.net> wrote:
Another way to look at it: the angle at which the blade cuts remains roughly constant.
On 4/13/18 22:02 , Brent Meeker wrote:
I think it's intended to keep the length of paper cut per unit angle relatively constant; so that the operators force remains constant.
Brent
On 4/13/2018 8:19 PM, James Propp wrote:
Why do paper-cutters have curved blades? Is the usual design intended to optimize something?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (6)
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Allan Wechsler -
Andres Valloud -
Brent Meeker -
James Davis -
James Propp -
William R Somsky