MTs, WM2D, and WM Basic Language Script Code

[Fletcher]

I imagine you can get the RB to work on WM2D if you are super accurate but are you going to be that accurate building a device that you are not sure how it will react and where you need to be super accurate?

There's no substitute for having a reasonable grasp of your basic physics and mechanics before you start simming. It's a great tool to accelerate the learning of these things. But as a cross check against what I anticipate will happen before the sim is run I include a System Kinetic Energy Equation Output. Then I calculate what GPE all the elements have at the start (another Output) and which without any frictional losses can convert to System KE. If System KE rises above the GPE lost then I need to dig further into why that might be, bugs'n'all.

[Wubbly]

It didn't like my left and right polygon "T" braces. When I replaced each of them with two rectangles pinned together with a rigid joint, the sim didn't explode, or suddenly stop or start, or suddenly rotate backwards. Here's a very low frame rate fuzzy video in MP4 format. Guess it's the next best thing to an animated gif.

Isn't KE gain what we are all looking for?

[Fletcher]

Yah .. those polygon's are more trouble than they are worth.

Isn't KE gain what we are all looking for?

Yup .. it depends how you look at the problem I think.

We sim users have an extra layer to deal with, than the simless (pertaining to Mechanics).

1. Does our sim program we are using fairly represent the known Laws of Physics so that it can on the whole be trusted, except for bug problems which we hopefully can identify as abberant behaviour and work around ? Sharing our experiences, as we tend to do with wm2d, decreases the chances of being caught out and raises the trust factor imo.

2. Do we trust that the known Laws of Physics are full and complete for every mechanical instance ? Or do we suspect that some Laws are incomplete or even unknown - we just have to find an example ?

3. Do we trust that the Laws of Physics always have symmetry for every mechanical instance ? Or do we suspect that there may be certain mechanical contrivances where the Conservation Laws do not hold and the axiom of symmetries are violated - we just have to find an example ?

The short answer is yes I expect to see a legitimate KE gain in my sims and in a real world build counterpart. If I have the right example !

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How did you make the MP4 (played on my VLC viewer) vid Wubbly ? I know I can save a sim as an .avi file ?

[Wubbly]

I used a video editor.

I knows there's a lot of free video editing software out there, but I decided to buy one instead. I chose Movavi Video Suite 2020. Movavi has various software packages (Video Editor, Video Converter, Screen Recorder, photo editor ...). I chose the Movavi Video Suite 2020 because it has the Video Editor and the screen recorder.

Build your model in WM2D and get it running.

From the World -> Skip Frames menu choose a number so the model runs fast enough to show the basic movement quickly.

Zoom out so your model is small but still viewable.

Launch the Movavi video suite 2020 and then from the splash screen, launch the screen recorder.

Select the lowest frame rate on the screen recorder from the options.

The screen recorder lets you select a window or portion of your screen that you want to record. Make a small box around the part of the screen that you want to record.

Start the screen recording, then run your WM2D model.

Let the model run for two or three revolutions, then stop the screen recorder, and then stop the WM2D sim run.

In the screen recorder, save the screen recording (it has its own extension) then open that in the video editor.

From the video editor you can snip off the front and the end of the video that you don't need so you only have one revolution of movement. Then you export that out to a video format. There are several formats to choose from, MP4 being one of them.

There's an Advanced button where you can select the output resolution to be the lowest (320x240), and the frame rate to be the lowest (8) to keep the filesize small.

That's it.

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The trick is to keep the filesize small. Select low resolutions and low frame rates and get the model to run quickly enough to show the movement.

You might be able to skip the screen recorder since WM2D lets you export to an avi file and lets you select the start and ending frames of the output. If the filesize is small enough, you're good to go with the avi. Otherwise open the avi file in a video editor and export at a low resolution and low frame rate.

I'm new to video editing and you might be able to do all this with a free video editor. You can google "free video editing software"
or search youtube for "free video editing software review".

You can also search youtube for "free screen recorder for windows 10".

[Wubbly]

MT143 Version 1.2

Version 1.2 is a stable version of V1.

This version uses rectangles pinned together instead of the polygon "T" braces for the vertical members.

Input dialog box is shown along with a model. It builds two opposing weights that can have different mass values.

This is the model shown in the video from 3 posts ago.

[Wubbly]

How to make an animated GIF

Build the model in WM2D and verify it is working correctly.

Run the model, then select World -> Skip Frames. Change the number from 1 to 2 or 4 or 8 or N to get the model to run fast.

Zoom out on the model so it is small enough to show the desired movement but uses as little screen space as possible.

Open a screen recorder. You can find free screen recorders by searching youtube for "free screen recorder", and choosing one that meets your needs. You only need to record a few seconds of a small area of your screen.

Start the screen recorder and select a small window around your zoomed out WM2D model.

Run the model while recording using the screen recorder. Try to record for the shortest amount of time that shows your desired movement.

Save the screen recorder into a video format (e.g. avi or mp4)

Edit the video using a video editor. Snip off the front and back of the video to only show enough of the movement. If your wheel has 8 mechanisms, you only need 45 degrees of wheel rotation. If played on a loop, the 8 mechanisms will look like a complete rotation. 4 mechanisms would need 90 degrees of wheel rotation. 2 mechs, 180 degrees. Your screen recorder might have editing capabilities built in, of you can find free video editors by searching youtube for 'free video editor review'. My screen recorder let's me snip the file and save directly to MP4.

Convert the video into a gif. If you google "MP4 to gif conversion" there are various sites that will do the conversion.
Here's a youtube video showing one site and how to use it: https://www.youtube.com/watch?v=Ov90r3Zg7s0

Here's the site in the previous youtube video and the one that I used: https://www.onlineconverter.com/mp4-to-gif

Check the file size to verify it is small enough to be uploaded to BW.

It was fairly easy once you figure out all the steps.

[Wubbly]

MT143 Version 2

Changes in Version 2:

Replaced rect1 & 2 with circles.

Replaced vertical rectangles with rod constraints as per Fletcher's comments.

Added an input for the mass of one of the large background circles.

Changed all sliding weights to have the same mass value.

Changed all rectangles to point in the same direction.

Added a spring to each of the sliding circles and an input for the K value of the spring.

Added an input for the number of mechanisms to build (1-8).

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Observations:

Spring constant = zero:

When a small circle is moving laterally from one end of the rectangle to the other, the angular velocity of the wheel slows down.

When the small circles hit the other end of the rectangle, the system's angular velocity bumped up, but not enough to compensate for the angular velocity loss during the lateral slide.

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Spring constant non-zero:

If the spring constant is non zero and adjusted correctly, the wheel does not slow down much when a small circle moves laterally along the length of the rectangle.

The spring captures energy of the lateral movement, and the correct K value paired with the geometry will make the system run for a very long time as is seen with the other MTs.

[Wubbly]

MT143 V3

This version is based on Fletcher's Roberval Balance Gearing System (RBGS) from his 2014 thread here: Fletcher's Wheel - Ingenuity verses Entropy.

Changes to Version3:

Incorporated RBGS into the model.

Added an Angle variable so the platforms can be at a fixed angle other than zero (horizontal).

Added a rod locking mechanism and ActiveWhen logic to hold the spring locked at its farthest extension point.
i.e. it activates between a start and end angle,
and when the spring Constraint[N].dv.x <= 0 (meaning it stopped extending and started retracting).

Added logic to catch the condition when the user presses OK with bad data entered.

Observations:

This one runs very similar to Version2. The rod lock didn't do anything magic.

Still building sims. Guess I'm still wearing my whiskey glasses.

[Wubbly]

Spirograph V1

These gear thingies are kinda neat. They inspired me to write a spirograph program.

The program draws a main circle pinned to the background at (0,0) with radius R1.
A rectangle with a half-width of R2 has its center pinned to the edge of the main circle.
The Pen is another circle that does the drawing and has a diameter D1 and is pinned to the far end of the rectangle.

A gear constraint is connected between the background and the rectangle. A motor spins the main circle and makes everything dance.

The main circle is not shown. The gear system is initially shown. If you want to hide the gear system, that option is available in the initial dialog box.

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How to use the program:

Run the script, choose values for your input variables, and build the model.

WM Basic won't let you set tracking to a body, so you have to do that manually.

After the model is built, open the Appearance dialog box and use the Dropdown to find the body named "Pen". It was drawn first so it will be at the top of the list.

Play with the settings "track outline", "track center of mass", and "track connect".
You can modify the color of the pen if you are tracking the outline.

Run the model and watch it draw.

Change the gear ratio and run again. Observe changes.

Path_Finder had some posts regarding hypocycloid curves that are interesting to read and perhaps have some relevance to this: https://www.besslerwheel.com/forum/view ... 07&start=0

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"wm.ActiveDocument.AutoEraseTrack" is set to "False" so you can run again without erasing the track, but if you pan or zoom, it will erase the track anyway. Change the gear ratio and the color and run again to create the overlay.

Don't set the gear ratio to -1. It won't run correctly. If you do this during the build phase, I programmed it to adjust it to -1.00001, but if you do this during run-time, it throws geometry off into never-never land.

Overkill: using a $3000 simulation program to draw spirograph pictures.

There should be enough fun in there to kill an afternoon or two.

[Wubbly]

Comparing Linear vs Rotational motion - variables and equations.

Vectors are colored in red.

Scalars are colored in blue.

Note that momentum and angular momentum are vectors, whereas kinetic energy, rotational kinetic energy, and work are not vectors.

Also note that torque and work have the same units, but one is a vector and the other is not.

[Wubbly]

Comparing Vectors describing Linear vs Rotational Motion.

The third picture describes the Kinetic Energy vector. Or maybe it's a polar bear on an iceberg in a snowstorm. Take your pick.

[Wubbly]

Torque - Direction

Torque is the vector cross product of the distance (or radius) vector and the Force vector.

The Direction of the torque vector is perpendicular to the plane containing the force vector and the distance vector.

The direction of the torque vector follows the right-hand rule.

The picture below shows the direction of the torque vector in 3-D space.

[Wubbly]

Torque - Magnitude

The Magnitude of the torque vector is the area of the parallelogram described by the force vector and the distance vector.

The vector cross product uses the sine of the angle between the two vectors. The sine function makes one of the vectors perpendicular to the other.

It doesn't matter which vector is the perpendicular one.

Depending on how the coordinate system is set up, it may be easier to use the Cosine function to find the perpendicular vector.

This is the case in WM2D where angles are defined with the positive x-axis being zero degrees. CCW rotations are positive, and CW rotations are negative. If the force vector due to gravity is always straight down, then the cosine of the angle of the radius vector would always produce the perpendicular component of the radius vector.

[Wubbly]

Torque and Work

In linear motion, work is Force x Distance.

In rotational motion, work is torque x angle (in radians) through which the force acts.

Torque is force x distance (with units of [N-m]), and radians is a dimensionless quantity. If you multiply the two together to get the work, you still end up with units of [N-m] or Joules, but now it represents the work performed by the torque through the angle.

Since the torque is changing as the wheel rotates (the perpendicular lever arm is changing), you need to take an integral of the force x angle to determine the total work.

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Condition:
A mass is attached to the end of a light rod in quadrant I.
Calculate the work done by gravity as the mass drops down through quadrants I and IV.
To do this, you integrate the torque over the angle swept.
Break the angle down into smaller increments.
Calculate the torque at the start and end of the angle increment, calculate the average of those two torques, then multiply the average torque by the angle increment (in radians), to find the work for that angle increment.
Keep a running sum of the total work done.
Increment the angle and repeat the process.
When the angle you are incrementing reaches the ending angle, you have a calculation of the total work done by gravity.
This should match the PE=mgh calculation of the initial potential energy.

If you do the calculation on the right side of the wheel and the mass is rotating CW, the torque vector sign would be negative, the angle increment would be negative, and multiplying the two together would give positive work performed.

[Wubbly]

Torque and Work - Examples

A 1 kg mass is attached to the end of a light rod (which can be ignored).
The rod pivots about the other end and the mass falls 2 meters.
Calculate the work performed by gravity as the mass falls downward using the integral of torque and angle.
Keep the height drop constant, but use the following rod lengths: 1 meter, square root of 2 meters, 2 meters, 3 meters.
Set g = -10 kg m/s^2
PE = mgh = 1 x 10 x 2 = 20 Joules
Compare the work calculations for the various rod lengths to the PE calculation.
Use various numbers of increments to see how many increments it takes to get an accurate number.
Attached is a spreadsheet to do the calculations.

Observations:
If you only use a few increments, you get an inaccurate number for the work performed.
The more increments you use, the more accurate the integral becomes.
If you change the radius from 1, to the square root of 2, to 2 to 3, and you use enough increments for the angle, they all produce the same answer: 20 Joules.

Conclusion:
The work integral of torque x angle always produces the same answer as the PE lost.
i.e. for this example, at the end of the sweep angle, you lost 20 Joules of PE, but you did 20 Joules of work.