This is an idea I saw somewhere else, though modified a little.
There is a wheel with weights on it, putted symmetrical on its circle, where one quarter (the upper left one) is empty. I put power to turn (anti-clockwise) this empty part down to the place of down left. Now I let the wheel roll over 180 degrees by the axis that is going diagonal through the center. This happens only using the gravitational force. By doing this, the empty quarter now is again on the upper left side. I repeat and put power to turn (alsways anti-clockwise) the empty part from its upper left to the down left position. Again my wheel rolls over and this empty part goes to the upper left position, and so on.
I have calculated that I need only half the energy to turn the wheel, that it gives me back by rolling over the other axis.
will it work?
Moderator: scott
Let me analyze this!
First let’s see if I understand the idea? We have a wheel that turns on two axis, kind of like a toy gyroscope.
The first axis in like a conventional wheel. The wheel starts with weights in three quadrants and with no weight in quadrant #2 which is the upper left using standard quadrant numbering. Now it is obvious that the weights in quadrant #1 and #3 will always balance; so they are just dead weight and could be eliminated. That leaves a weight in quadrant #4 only. The wheel is now turned CCW 1/4 turn using a motor. This moves the weight from quadrant #4 to up to quadrant #1.
The second axis is horizontal so the top of the wheel tilts down either toward or away from us; the direction is irrelevant, so we will choose toward us. If we now step over to the right side and look at the wheel we will see it rotate CCW a 1/2 turn with the weight dropping from straight up to straight down.
Looking at the front again we will see the weight has dropped from quadrant #1 to quadrant #4, which is the same place where it started and the cycle now repeats.
So we lift the weight up a certain distance by rotating the weight by 90 degrees then we recover some of the energy as the weight falls 180 degrees. During the lifting the radius out to the weight is longer while during the falling the radius out is shorter by a factor of 0.707106, which is the Sin(45º).
I have a formula in my old HP-48sx scientific calculator that will tell me the average torque during any segment of wheel rotation. The formula is ∫(Cos(n), A1, A2), which gives the average torque for a radius of 1 and a weight of 1 from an angle of A1 to an angle of A2.
Since this is the average from Angle1 to Angle2 assuming a radius of 1 and since the wheel turns 90 degrees then the total torque for the motor would be ∫(Cos(n), -45º, 45º)•1•R•90º = 81.028468.
Now as the weight drops the radius will be Sin (45º) •R and the wheel turns sideways 180 degrees so the total torque output would be ∫(Cos(n), 90º, 270º)•Sin(45º)•R•180º = -81.028468.
Golly, they are the same but opposite, conservation of energy trumps again!
One problem with a wheel like this would be the constant starting and stopping of the weight. Unless a method is used to conserve the kinetic energy during stopping and starting that energy is wasted. For this reason a smooth flowing movement is preferred.
First let’s see if I understand the idea? We have a wheel that turns on two axis, kind of like a toy gyroscope.
The first axis in like a conventional wheel. The wheel starts with weights in three quadrants and with no weight in quadrant #2 which is the upper left using standard quadrant numbering. Now it is obvious that the weights in quadrant #1 and #3 will always balance; so they are just dead weight and could be eliminated. That leaves a weight in quadrant #4 only. The wheel is now turned CCW 1/4 turn using a motor. This moves the weight from quadrant #4 to up to quadrant #1.
The second axis is horizontal so the top of the wheel tilts down either toward or away from us; the direction is irrelevant, so we will choose toward us. If we now step over to the right side and look at the wheel we will see it rotate CCW a 1/2 turn with the weight dropping from straight up to straight down.
Looking at the front again we will see the weight has dropped from quadrant #1 to quadrant #4, which is the same place where it started and the cycle now repeats.
So we lift the weight up a certain distance by rotating the weight by 90 degrees then we recover some of the energy as the weight falls 180 degrees. During the lifting the radius out to the weight is longer while during the falling the radius out is shorter by a factor of 0.707106, which is the Sin(45º).
I have a formula in my old HP-48sx scientific calculator that will tell me the average torque during any segment of wheel rotation. The formula is ∫(Cos(n), A1, A2), which gives the average torque for a radius of 1 and a weight of 1 from an angle of A1 to an angle of A2.
Since this is the average from Angle1 to Angle2 assuming a radius of 1 and since the wheel turns 90 degrees then the total torque for the motor would be ∫(Cos(n), -45º, 45º)•1•R•90º = 81.028468.
Now as the weight drops the radius will be Sin (45º) •R and the wheel turns sideways 180 degrees so the total torque output would be ∫(Cos(n), 90º, 270º)•Sin(45º)•R•180º = -81.028468.
Golly, they are the same but opposite, conservation of energy trumps again!
One problem with a wheel like this would be the constant starting and stopping of the weight. Unless a method is used to conserve the kinetic energy during stopping and starting that energy is wasted. For this reason a smooth flowing movement is preferred.
re: will it work?
Your analysis is really marvelous. It's now clear why it won't work. I thank you very much. The original Idea was to have doubled weights on the corners, and by this it was supposed to be self-starting, without any help. In a simple model in wm2d I saw that it will never flip over, and my next idea was to help it a little bit. The next idea might be to use a flywheel and periodically connect and de-connect the gyroscopic wheel to it, so that the kinetic energy is stored, but I guess it won't be that much of any help.