Bessler's Kinematics

[agor95]

Here are 2 images with the ramp at 35 and 15 degrees.

You can see the difference in the path taken by the internal cylinders.

Regards

[agor95]

The web page in the zip file attached shows a mass dropping like in experiment 1.

Then a pivot point accelerating up while the mass at the end of the rod is floating. In effect the mass gets pulled along due to this connection.

In simulation time the mass drops for 1 second.
The pendulum reaches vertical from horizontal in 1.34 seconds from when it starts too move.
Then reaches horizontal in another 1.28 seconds.

If you zoom in you will see ticker-tape dots below the green mass.
Also if you pan [left+shift] you can follow it to the starting point.

Note. No cos or sin functions were harmed during this run.

All the Best

[agor95]

This is a conventional implementation.

Instead of acceleration of the pivot up. I have accelerated the mass down.
The duration of the simulation is 10.45 seconds and the pendulum length is 4.9 m.

The algorithm is

1. Displace the mass down by a faction of 9.807 using small time slices.
2. Move the mass by it's velocity from the last time slice.
3. Displace the mass radially to make the mass 4.9 m from the pivot.
4. Add the extra displacement to the mass velocity

Repeat

Note. We now have code that allows us to explore a pendulum moving and allow us to study the effect of the pivot moving on the pendulum's swing.

There are two electronic affects of atom to atom connection binding/repulsion. Also the protuberance of the space by the electromagnetic fields.

All the Best

[agor95]

The jack fires. The bow twangs

Those who have viewed and considered the pendulum may have spotted a few points.

For example the pulling sling shot effect. The deceleration in the x-axis matched by the acceleration of the y-axis. The gravity acceleration effect increases as the pendulum moves towards the vertical.

However to integrate the other part of the verse;
We need the pendulum as a rope; for that is the way to get a 'twang'.

If there was a well shaped peg fixed to the stand holding the pivot.
Then the pendulum rope can interact with it to change it's path to a near vertical trajectory.

This would be in effect a smaller pendulum were the rope winds around the peg. However the peg is shaped to force the rope off the end of the peg.

I imagine a tapered spiral design.

The angle of the 'twang' can be adjusted by rotating the peg.

The pendulum swing as we see goes from horizontal to horizontal.

The smaller pendulum converts the x-axis motion to a near y-axis vertical path.

The time it take for the mass to reach the horizontal is less due to the more direct path. Time is important as the more time the more gravity based y-axis acceleration.

Note. Any increase of height is lost so do it quick and supply physical support to prevent what is gained being lost.

All the Best

[Georg Künstler]

by agor95 » Sat Dec 18, 2021 1:45 pm

The jack fires. The bow twangs
Those who have viewed and considered the pendulum may have spotted a few points.

For example the pulling sling shot effect. The deceleration in the x-axis matched by the acceleration of the y-axis. The gravity acceleration effect increases as the pendulum moves towards the vertical.

However to integrate the other part of the verse;
We need the pendulum as a rope; for that is the way to get a 'twang'.

If there was a well shaped peg fixed to the stand holding the pivot.
Then the pendulum rope can interact with it to change it's path to a near vertical trajectory.

This would be in effect a smaller pendulum were the rope winds around the peg. However the peg is shaped to force the rope off the end of the peg.

I imagine a tapered spiral design.

The angle of the 'twang' can be adjusted by rotating the peg.

The pendulum swing as we see goes from horizontal to horizontal.

The smaller pendulum converts the x-axis motion to a near y-axis vertical path.

The time it take for the mass to reach the horizontal is less due to the more direct path. Time is important as the more time the more gravity based y-axis acceleration.

Note. Any increase of height is lost so do it quick and supply physical support to prevent what is gained being lost.

If you have a pendulum on a stick and move the stick horizontal you have a wandering pivot point of the pendulum.
The pendulum is moving along in x direction.
When you then stop suddenly the movment in x direction, the pendulum is swinging up in a flash in y direction and also x direction.
Depending on the prior speed in x direction and the pendulum length, the pendulum is rotating upwards.
For the Bessler construction we only need a part of this rotation, 90 degrees up is enough.
The forces are splitted in an up and in an down force, when the sidewards moved stick is stopped suddenly.

If you use a rope and the rope is fixed on the suspension point you will get a spiral form of the movement because the rope is winding around the pivot point.
But you can also wind rope on the suspension point which is loose, like a slope, then the mass is turning up and will turn in an exact circle.
Besslers way.

[agor95]

:-) quoting the entire post directly above is amusing.

A comment referring to the post works without double reading.

stop suddenly

I find it's best to use 'decelerate rapidly'. It is best to keep away from sudden or instantaneous changes of movement. Objective errors lurk within the subjective realm.

Investigating pendulums on moving/accelerating/jerking motion help too see fresh options. Of cause a pendulum on a stick is in effect a double pendulum with one restricted/controlled.

A pendulum is the best way to convert x-axis via deceleration into y-axis acceleration. When momentum is transferred between two objects by collision the result is only partial. One accelerates and the other decelerates until both are moving at the same speed.

x-mass

[Georg Künstler]

Hi agor95,
we learn, so the quoted comment cannot be deleted.

[agor95]

Update

I am working on a demo of 'The jack fires. The bow twangs' description.

And a crystal dropping not by gravity but by an increase in distance travelled.
Which looks like time slowing down from the top of the crystal down towards the ground.

Also moving the pivot of the pendulum down a slop at a constant velocity.

Ultimately the integrating the rule that total acceleration of the system needs to be a minimised.

Thus a object rolling down a slop is accelerating to reduce the total acceleration of the object. There is a optimal acceleration rate that is found.

P.S. you can edit a post for three hours. Thus editing the quote section away is possible. No need to delete the post.

x-mass

[Georg Künstler]

hi agor95,

A pendulum is the best way to convert x-axis via deceleration into y-axis acceleration. When momentum is transferred between two objects by collision the result is only partial. One accelerates and the other decelerates until both are moving at the same speed.

And exactly here is the common error.
The pendulum is accelerated upwards, and the pivot point is pulled down.
We have a split of the forces in an up and an down force during the indirect impact.
That the pivot point is pulled down is the reaction that the pendulum can swing upwards.
The pull on the pivot point is depending on the speed in x direction and the pendulum length, the deceleration time of the pivot point is zero.
because you stop the movement in x direction of the suspension point.
You get therefore the function excess weight.
A weight is heavier than the normal weight, because it is underlying a higher acceleration during the upswing of the mass.
So what is missing is the force which occurs on the pivot point, suspension point.

Normally the force at the pivot point is transferred to the support structure.
The support structure is transferring the force to the ground.
And here Bessler did it different.
He transferred the forces to an intermediate structure which is able to move inside of the wheel.