Sunday 4 August 2019

How To Convert Centrifugal Force Into Unidirectional Linear Force


First of all, if you are able to create a force or combination of forces into a single force which always
points to a fixed direction in any 3-dimensional space, you have found the solution to create a
unidirectional linear force.
The approach here is to convert 2 or more centrifugal forces into a unidirectional linear force.
Basically, there are 2 ways to create a centrifugal force:
(1) A mass or pendulum rotates on a pivot,
(2) A mass or pendulum swings back and forth on a pivot.
A pendulum is defined as a mass or a heavy object which has its own centre of gravity a distance (r)
away from its own pivot, figure (1).
A heavy mass at a far end of a very light arm moves the centre of gravity further away from the pivot.
The total mass of the heavy mass and arm themselves determine the actual centre of gavity of the
pendulum.



A pendulum in full rotation on a pivot




When a pendulum rotates on a pivot at an angular speed (w), centrifugal force (F) will be generated.
A drive shaft supplies the torque, thus the input force (Fn), to rotate the pendulum. An equal amount
of reaction force will be exerted on the pivot.
The centrifugal force along the pendulum pulls the pivot outward into all directions as it completes a
circle, figure (1a).
The kinectic energy from the drive shaft is being converted into potential energy to throw the pendulum
outward.
Without a grip, the pendulum will be thrown outward.
A centrifugal pump is an example in which the fluid is being thrown outward by the rotating blades,
as the centrifugal force is being exerted on it but there is nothing to hold the fluid in place.



Centrifugal force, F = mw²r (Newton)
wherein  m= mass (kg)
                 w = angular velocity (rad/s)
                 r = distance between centre gravity of mass and pivot (m)



As the pendulum rotates at a constant speed, a constant amount of centrifugal force will be generated,
figure (1b).
The amount of centrifugal force is dependent on the value of m, w and r, based on the formula above.
A pendulum with a small value of m, w or r generally creates a small amount of centrifugal force, and
vice versa.



A pendulum in a back and forth swing




A drive shaft with cam is mounted on the arm of the pendulum, and is used to swing it back & forth
within a small angle, figure (2a).
As the cam rotates, it forces the sliding block to travel inside the slot of the swing arm. At the same
time, it exerts a input force (Fd) in the -x-direction to push the pendulum to swing a small angle on the
 pivot. The same amount of reaction forces (red arrow) are reflected to the pivoting shaft, which must
be born by the whole casing of the device.
The cam transfers the rotary motion of the drive shaft into linear force in x-direction and pushes the
arm of the pendulum, of course at a slightly varying point of contact along the slot.
The position of a cam on the arm of the pendulum also acts to stop the heavy pendulum at the 2
designed end points of the back and forth swing.





The rotating cam exerts an input force (Fd) in x-direction to swing the pendulum. An equal amount of
reaction force will be exerted on the pivoting shaft, thus the whole body of the device.
Centrifugal force being generated is confined to the space within the angle Ɵ1 and Ɵ2 only, figure (2c).
The kinetic energy from the rotating drive shaft is now being transferred to the potential energy on the
swinging pendulum, tending to throw it outward.
This one-sided centrifugal force is the first but important property in our quest to convert centrifugal
force into unidirectional force.
As the pendulum swings back and forth from point A to point B then back to point A, angular velocity
(w) increases from zero to the maximum ( at y-direction) then decreases again to zero as it decreases
again to a stop at the opposite side of the swing.
In other word, there is an acceleration and deceleration of speed from point A to point B, and vice
versa. The centrifugal force being generated will thus increases from zero to the maximum value, then
decreases again back to zero.



There is no force acting on the Z-direction, as shown in the top view and right side view in figure (2b).
What we can see from the top view is the driving force (Fd) pushes the drive shaft C-D to the right, as
the pendulum is being pushed to swing from point A to point B.
The creation of centrifugal force is in close correlation to the input force. A larger input force (Fd)
create a bigger centrifugal force, an vice versa. The energy to swing the pendulum is now being
transferred to the potential energy to throw it outward.




Subsequently, as the pendulum swings from B back to A, the similar form of centrifugal force will be
 generated, figure (2e).
Now, the shaft C-D will be pushed to the left.



Figure (2f)  Centrifugal force on a playground swing

Playground swing is a typical example of centrifugal force being generated on the back and forth
swing of a mass, figure (2f).
Apply a push ( input force ), the swing will swing forward to the maximum potential height, stops and
then reverses course.  The generated centrifugal force will pull the overhead hanging bar to sag in
the direction of the swing.
Next, when the gravity pulls it to swing back to the right, it will pull the pivot to the right.
The repetitive back and forth swing forces the structure to wobble from the left to the right, then
back to the left.
Gradually the centrifugal force fades out as the input energy is being depleted, and the swing will
come to a stop.
The whole structure of the playground swing must be able to withstand the force and thus the
moment of the swing.
Try to imagine what forces will be exerted to the hanging bar of the  if both loaded swings are
a). making a harmonic swing against each other, or
b). making a synchronic swing.

Two pendulums  swing against each other

This section shows a way to convert 2 centrifugal forces into a unidirectional linear force (Fn), with only a small deviation from the y-direction.
The solution is to put 2 identical pendulums closely on the same pivot, and to make a synchronic swing against each other.

(i) 2 pendulums swing toward each other

Figure (3a) shows the 3 planes of the 2-pendulum device. Our goal is to create a force which will always
point to one fixed direction in within any 3-dimensional space in the the device.



In figure (3a), 2 identical pendulums m1 & m2 are aligned closely side by side on the same pivot.
The 2 offset cams on the same rotating drive shaft swing both pendulum m1 and pendulum m2 from their respective starting point A and point B toward the y-axis.
As both pendulums accelerate from their respective stops (point A and point B), they will create their own centrifugal forces (F) with increasing values.
Both horizontal input forces (Fd) are very close to each other, and their respective reaction forces always pointing away from each other on the pivoting shaft. They are cancelling each other in the x-y plane, as shown on figure (3a1). This means there is no apparent net force in the x-direction.
Instead, the 2 input forces create a moment along the pivoting shaft , as shown in the top view. The pivoting shaft C-D will be twisted in anti clock-wise direction.
The moments will be much smaller if both pendulums are closely mounted side by side.
There is no force in either the z-direction along the pivoting shaft.
In the front view of figure (3a1), we have 2 centrifugal forces at the positive side of the y-axis; never at the negative side of it.




The 2 centrifugal forces  are now being merged to form a net resultant force (Fn) on the pivot.
Figure (3a2) shows the vector of the net resultant force (Fn), which ideally only points to the y-axis.
The value (Fn) increases from zero to the maximum as both pendulums swing toward each other.
The net resultant force (Fn) on the pivot increases toward the mid-point of the swing, i.e. y-axis.
On the x-axis, both 2 opposing input forces cancelling each other. Instead, they create the moment
to twist the pivoting shaft counter clock-wise, as shown in the top view of figure (3a).



(ii) 2 pendulums swing away from each other




After stage (i), the 2 pendulums swing pass each other, figure (3b1).
Both horizontal input forces (Fd) are always pointing away from each other on the pivoting shaft, thus they are cancelling each other on the x-direction.
As both pendulums decelerate from y-axis toward point B and point A respectively, the 2 pendulums will have their own centrifugal forces decrease.
Thus the net resultant force (Fn) on the pivot decreases toward the end of the swing, i.e. points A and point B.
Figure (3b2) shows the vector of the net resultant force (Fn), which also ideally only points into the +y-direction.




Figure (3c) shows the reversing swings of the pendulums. The only change is the reversal of the
moment on the pivoting shaft C-D.
The continuous and repetitive back and forth swing of the 2 pendulums from (i) to (ii) create wavy net
resultant force (Fn), as shown in figure 3(d) below.
With this simple 2 counteracting pendulums working in tandem, we are able to convert 2 centrifugal
forces created by the pendulums into one unidirectional linear force ( Fn) which always pull the pivot
into the +y-direction; this is what we are searching for!



3-pendulum configuration reduces vibration




Figure (3e) A 3-pendulum configuration eliminates the moment along
                     the pivoting shaft

There is way to reduce the moment exerted on the pivoting shaft. The solution is to have 3 closely

mounted pendulums instead of  2 pendulums, figure (3e).
The 2 conditions are:
(a). Both pendulum 1 and pendulum 3 are identical, while pendulum 2 is 2 X the size of pendulum 1.
(b). Both pendulum 1 and pendulum 3 swing synchronously in the same direction while pendulum 2
swings in opposite direction.
The 2 opposing moments exerted on the pivoting shaft is confined to the span between pendulum 1
and pendulum 3, and they cancels out each other.
The 2 moments will reverse directions when the pendulums reverse their respective swings.
Nevertheless, the net moment in the pivoting shaft C-D is almost zero at all time.
By minimizing the oscillating forces on the bearings of the pivoting shaft, this configuration reduces
vibration on the pivoting shaft.
What being left is the net resultant force which pulls the pivoting shaft into +y-direction.


Summary



One pendulum swinging back and forth on a pivot will generate centrifugal force but pulls and wobbles the pivot along the direction of the swing.
2 pendulums swinging against each other on the same pivot will combine 2 centrifugal forces into a singular linear force on the pivoting shaft. The resultant force is always at the fixed +y-direction.
A 3-pendulum configuration is better than a 2-pendulum configuration in order to minimize moment
being generated in the z-direction of the pivot.

The counteracting pendulum system is able to convert centrifugal forces into a singular linear force.



Application Of Linear Force



Irrespective of how complex the machine is, the main purpose of a jet engine or propeller is to
produce a linear force.
Linear force is used to move a vehicle or an object, eg. car, truck, train, ship, submarine, aircraft,
helicopter, drone, rocket, missile, space-ship, lift, personal flyer, ... etc.
The advantage of the pendulum system is it does not rely on the ejection of material, such as hot jet
and accelerated ions, in order to create the linear force,  as what happens in a conventional jet engine, propeller and ion propulsion.
The pendulum system converts kinetic energy of a drive shaft into potential energy which always pushes to one direction only.
The source of kinetic can be a rotating electric motor or an engine.



Next, I will show you an idea of a device called Force Engine, which utilizes this theory.
I have posted the idea on the Google+ ( ceased in April 2019) & Facebook back in year  2012.

The main error on my previous posts was in the force analysis of the system, in which I did not
mention the driving force and reaction force in the x-direction. Anyway, there is no net force in the
x-direction, but instead a moment being generated in the z-direction.
Nevertheless, the fundamental idea to convert 2 centrifugal forces into one unidirectional force
remains intact.



Here is my video clip on YouTube about this subject :