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Author Topic: Sum of torque  (Read 119849 times)

Offline EOW

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Re: Sum of torque
« Reply #300 on: June 14, 2016, 12:25:25 PM »
I found an error in my device, if I reduce the size of the semi disk the force decreases in the same time. I tried to find a good simulator on Linux but they are difficult to use.

I'm trying to find where is my error in this case with 2 wheels.

1/ The two wheels move to the right
2/ One wheel rotates clockwise, the other counterclockwise
3/ The pressure is at 0.01 P everywhere except in the square shape delimited by the green/red walls
4/ The pressure is at P inside the shape delimited by the green/red walls
5/ Altitude of the wheels don't change
6/ There is no gravity
7/ The green V shape is free to rotate around the orange axis
8/ The orange arm is free to rotate around the black axis
9/ The red V shape is free to rotate around the blue axis
10/ The black arm is free to rotate around the pink axis
11/ Like there is a difference of pressure, the green V shape has a torque on the orange axis, this torque is 1
12/ Like there is a difference of pressure, the red V shape has a torque on the blue axis, this torque is 1
13/ I add a spring between the green V shape and the red V shape (not at the axes), to cancel the torque on each V shape, I need a force of 1/sqrt(2) because the distance is sqrt(2) and the torque is at 1
14/ So, now with the spring, each V shape don't want to rotate, they keep their relative position
15/ The force from the difference of pressure on the V shape on the orange axis is f11, this force =1
16/ The force from the difference of pressure on the V shape on the orange axis is f10, this force =1
17/ Each wheel receives a torque of 1-sqrt(2)*R,  like each wheel turn they can give an energy
18/ All volumes are constant, the gas don't lost any potential energy (I hope...)

I have only a problem with the wall of the circle between the V shapes but it's possible to take wheels just side by side at start, like the straight velocities are the same, the wheels are always side by side, an example:

The equation of the cycloid with a radius of the circle of 1:

x=a-sin(a)
y=1-cos(a)

But be careful that the reference is not the same for the left wheel and the right wheel.

For the spring at start:
Left wheel, the point at start is (0,0)
Right wheel, the point at start is (2,0)
For the spring at final, after 0.01 rd for each wheel:
Left wheel, the point at final is (0.02,50e-6)
Right wheel, the point at final is (2+1.666e-7,50e-6)

The difference of length is 0.02

The force needed to compensate the torque is 1/sqrt(2)

The energy for the spring is 1.414 e-2

The force from the V shape is 2 so the force on each axis is 2-1/sqrt(2). Note I take a big V shape, the radius of the wheel is 1 and a side of the V shape is sqrt(2).

The energy from the wheels is 2*1*(2-1/2)*0.01 = 2.58 e-2

There is a difference

The forces:

F1 and F4 come from the spring
F1 gives F2 to the orange axis and F2 gives F3 to the center of the left wheel
F4 gives F5 to the blue axis and F5 gives F6 to the center of the right wheel
F10 come from the pressure on the red V shape
F11 come from the pressure on the green V shape
« Last Edit: June 14, 2016, 10:56:23 PM by EOW »

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Re: Sum of torque
« Reply #300 on: June 14, 2016, 12:25:25 PM »

Offline dieter

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Re: Sum of torque
« Reply #301 on: June 14, 2016, 07:38:33 PM »
Wikipedia has a long list of open source simulations:

 https://en.m.wikipedia.org/wiki/Physics_engine

Sorry, I don't see where the error is.

Offline EOW

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Re: Sum of torque
« Reply #302 on: June 14, 2016, 09:41:24 PM »
Thanks for the link, if I don't find my error I will simulate the device.

With the following example and an angle of 0.001 rd:

spring lost 0.0010005
wheels win 0.001

In this example I can find near the sum of energy at 0. But not others examples.

It seems before pi/4 the wheels win more energy than the springs lost and after it is the contrary. I calculated for pi/8 (near like the first case I drawn in a last message). I found 2.7e-4 for the springs and 7.8e-7 for the wheels (the force on the axis is near 0)
« Last Edit: June 15, 2016, 07:03:58 AM by EOW »

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Re: Sum of torque
« Reply #302 on: June 14, 2016, 09:41:24 PM »
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Offline EOW

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Re: Sum of torque
« Reply #303 on: June 15, 2016, 01:18:33 PM »
I took another example:

Radius of the wheels = R = 1
β = pi/6 rd
δ = 0.01 rd (the small angle I calculate the energy)

The length of one V shape's wall is R/2*√2, so the force is  R/2*√2 = 1/√2 for each wall (I consider the pressure outside at 0 to simplify), like forces are at 90° the force from the difference of pressure is 1 N

The torque is 2*R/4*√2 = 1/√2 Nm

The force Fs for the spring is 1/√2 /(2*sin(β)) = 1/√2 N

The force on the orange or the blue axis is 1-1/√2 = 0.2929 N
The energy for the spring is 2*(cos(β)-cos(β+δ))*Fs = 7.13 e-3 J
The energy for the wheels is δ*2*Fa*Rf = 2.93 e-3 J

Maybe I can take Fb in another position and the red object could be not half square (an angle different of 90°)

I can replace the spring by 2 stems (telescopic stems like hydraulic cylinders) like that I don't lost any energy.

If I cancel the torque from the center I lost sqrt(2)*angle but I win angle/2
« Last Edit: June 16, 2016, 12:30:40 AM by EOW »

Offline EOW

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Re: Sum of torque
« Reply #304 on: June 16, 2016, 09:23:39 AM »
I was wrong about the torque with a constant pressure.

If I use small balls attracted from the center or use a fluid (liquid is better, centrifugal forces are higher), the force and the torques are not the same.

« Last Edit: June 16, 2016, 09:24:00 PM by EOW »

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Re: Sum of torque
« Reply #304 on: June 16, 2016, 09:23:39 AM »
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Offline EOW

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Re: Sum of torque
« Reply #305 on: June 17, 2016, 08:31:21 AM »
Maybe if I transmit the torque from one arm to another.

The yellow arm can turn around the pink axis. The black arm can turn around the white axis (center of the circle). Each arm has a different torque, higher to the yellow.
« Last Edit: June 17, 2016, 08:07:33 PM by EOW »

Offline EOW

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Re: Sum of torque
« Reply #306 on: June 18, 2016, 06:04:53 AM »
I drawn all forces and details. I supposed the torque can be at 2/3 for the yellow arm and 1/3 for the black arm, it's an example. Like I can adjust the law of attraction I can have this example. But maybe my forces are wrong.

With gears it's logical.

I can rotates the device around the pink axis to have a continuous movement. Look at the epicycloïde. But I need to have N device with a phase angle at 360/N.

If the wheel moves to the right the energy is destroyed, if it moves to the left the energy is created.

« Last Edit: June 18, 2016, 03:55:43 PM by EOW »

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Re: Sum of torque
« Reply #306 on: June 18, 2016, 06:04:53 AM »
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Offline EOW

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Re: Sum of torque
« Reply #307 on: June 19, 2016, 09:02:05 AM »
I had a problem with the force from the gears, like the radius of the gear is 2 times lower, the force is 2 times higher so the sum of energy is at 0.

Now, I used a torus (like a wheel of a bike that moves in translation and rotates). There are small balls in a part of the torus.

« Last Edit: June 19, 2016, 08:48:07 PM by EOW »

Offline dieter

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Re: Sum of torque
« Reply #308 on: June 19, 2016, 09:30:29 PM »
I am currently using the open dynamics engine ODE with an Api wrapper for Blitz3D.

So now I can do this in a BASIC programming language / compiler. This is good not only due to simplicity, but also due to extremly fast compilation/run times, compared to bulky, complicatified Cpp paths.

But the accuracy / precision of ODE is low, so maybe it's too low for you. Anyway, I could send you the wrapper. ODE is open source, Blitz3D too, on github I think.

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Re: Sum of torque
« Reply #308 on: June 19, 2016, 09:30:29 PM »
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Offline EOW

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Re: Sum of torque
« Reply #309 on: June 20, 2016, 07:15:03 AM »
Thanks for the name of the software  :) do you use it to simulate some devices ?

I can give the torque from the ground and give the force at the bottom from the ground in the same time.



« Last Edit: June 20, 2016, 07:17:04 PM by EOW »

Offline EOW

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Re: Sum of torque
« Reply #310 on: June 21, 2016, 12:13:59 AM »
This case is better, I found the torque at 0.74 at top, 0.37 at the center and 0.26 from the torque of the blue wall. 0.74-0.34-0.26=0.11
« Last Edit: June 21, 2016, 07:24:26 AM by EOW »

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Re: Sum of torque
« Reply #310 on: June 21, 2016, 12:13:59 AM »
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Offline EOW

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Re: Sum of torque
« Reply #311 on: June 22, 2016, 07:21:46 AM »
I added all informations for verify my calculations, if someone has a little time to verify and tell me if it is correct ?

« Last Edit: June 22, 2016, 06:03:06 PM by EOW »

Offline dieter

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Re: Sum of torque
« Reply #312 on: June 24, 2016, 05:36:12 AM »
Sorry, I was offline for a while.

I had in mind to simulate magnets together with normal newtonian physics, but it turned out to be rather complicated, so I started programming a magnet simulation entirely in Blitz (without ODE).

It works, a bit too well tho: my permanent magnet motor works in almost every configuration :-) very much unlike in real live.

ODE has all kinds of links, also friction and things. I did some basic tests, like a curtain or chains, a rotor with hinge, stuff like that.

If one takes some time to get into ODE, I think such devices as you designed can be simulated quite effectively.

At least this is a package that works out of the box and you don't have to compile the ODE Api by your own.  (that is for "DC"'s api distro)

Offline EOW

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Re: Sum of torque
« Reply #313 on: June 25, 2016, 08:59:06 AM »
It could be useful to simulate.

I drawn the device in many positions. Note if I don't use the ground for the force F1, the sum of energy is always at 0. If I use the ground for F1, I can win an energy in a few positions like the first I drawn, the angle is pi/2 I think. In other cases when I can't win an energy, I don't use the ground for the force F1. I wait the next good position and I use the ground.
« Last Edit: June 25, 2016, 08:48:45 PM by EOW »

Offline dieter

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Re: Sum of torque
« Reply #314 on: June 27, 2016, 02:58:29 AM »
To me equations are the secret code of the academic class ... invented to disguise simple terms in a dense fog of mysterious haze and archaic greek letters . <:^)

Anyway, I made a package for ODE , see also PM.

 

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