[Arm-netbook] physics analysis needed of belt-driven pulley system

[Luke Kenneth Casson Leighton]

---
crowd-funded eco-conscious hardware: https://www.crowdsupply.com/eoma68


On Sat, Aug 19, 2017 at 3:00 PM, Hrvoje Lasic <lasich at gmail.com> wrote:
> below are answers
>
> On 19 August 2017 at 12:52, Luke Kenneth Casson Leighton <lkcl at lkcl.net>
> wrote:
>
>> ---
>> crowd-funded eco-conscious hardware: https://www.crowdsupply.com/eoma68
>>
>>
>> On Sat, Aug 19, 2017 at 11:38 AM, Hrvoje Lasic <lasich at gmail.com> wrote:
>> > Ok, so correct me if I am wrong but you are asking some mechanical
>> > questions.
>>
>>  mechanical / physics, yes.
>>
>> > so, I speak in general now and if you have question ask deeper.
>> >
>> > Force needed to drive whatever you want to drive will be exactly the same
>> > at the end part of system.
>>
>>  on the print-head yes.  but because of the doubled speed, the DRIVE
>> end *NO*, the force is NOT the same.
>>
>
> so, if on the print head-side force is the same then it is on the drive
> side same as well (work can not be missing somewhere). However, if you are
> doubling the speeds, then overall work required will be some higher value

 doubling the speed of the *belt* but not the print-head.  we're
comparing like-for-like scenario (pulleys / no-pulleys).

 btw benson kindly answered on the forum (thank you!) and i think i
have a handle on the situation now.

> so, correct would be to say that because of double speed you are having
> more force on print head needed and as result drive will also have to work
> more, losses will be bigger etc.

 no, the speed of the print-head should be the same in both scenarios
(pulleys / no-pulleys) therefore the force should be the same.

 now, what benson kindly pointed out is that in a pulley system the
force is *SHARED* between the two belt segments, therefore the amount
of "stretch" (which is what i was concerned about) should also be
HALVED compared to a non-pulley system.

 where i got confused was, i thought that the belt's actual travel
speed was somehow involved in the equation: it would be.... *if* the
belt's mass was significant.

> I think backlash here will be your biggest problem here. Backlash is in
> fact inertia of the system. So, for example when you run you want to stop
> you cant do it right away, you need some time/distance. Or comparing to
> electrical engineering you can compare it to inductance. Inductance is
> resistance plus reactance.

 indeed.  so, because the force is halved (for the same speed compared
to a non-pulley system) we *should* also get less backlash as well.
yay.

> You said that you expect lesser backlash on pulley system. If that is the
> case (I am not sure why or why not this statement would be truth) you will
> be able to increase speed up to certain point but you will have to test
> where is that point. Basically you will have to do a lot of testing.

 indeed :)  the aim is to use the extra wiggle-room (less backlash,
less load) to increase speed by some factor... probably not double but
a good fraction of that, and see what happens.

 certainly someone pointed out that the speed of the NEMA17s, when you
go faster, you actually get less torque.  whoops.  and the rated
maximum seems to be around 1800 mm / sec.  at that point you get
*significantly* less torque.

 so it's not going to be a straightforward "go twice as fast" thing.

l.