Posted by Scott Ellis (216.87.95.64) on February 14, 2003 at 00:27:43:
In Reply to: An observation on Wheels and circles posted by Jeff on February 13, 2003 at 20:22:08:
Hi Jeff,
Thanks for your post. Although it is a little tricky to follow you exactly through so much verbage (a picture is worth a thousand words!), I think I understand the arrangement you are describing and the question you are asking.
My first thought is that perhaps the device you descibe might behave like a sort of parallel beam apparatus, where the net torque or balance is actually independent from the horizontal distance of the weights on either side of the axle.
For a description of what I'm referring to, please see the following diagram and text from Gardner D. Hiscox's Curious Mechanical Motions (Lindsay Publications 1986), which descibes a famous parallel beam demonstration by Desaguliers in 1719:
I am not saying that this is the definitive answer to your question, just that your hypothetical device might be a variation of the same theme.
Thanks also, MrTim, for your response. Please note that ASCII diagrams (text and spaces) will only appear correctly in a web browser if you surround them with the HTML <pre> </pre> tags (preformatted text). This ensures that the diagram will be displayed with a fixed width font and maintain your intended spacing.
Best,
Scott
: This is something I have noticed when drawing wheel designs and many of you have probably already done this. Lets say you have a wheel with an axle and 8 spokes, and say the radius of the wheel is 28 inches or what ever you want. Now draw on each spoke a hanging weight. Make the weight about 8 inches long and an inch wide and have it hang from one end. All the weights should be the same and each is attached to a spoke at the same distance from the axle or radius point. Lets say the attach point is 18 inches from the radius point. Now connect the bottom of one weight to the next with a wooden strip. Connect the bottoms of all the weights. You will see the connecting strip is the same length for all the connections. These connecting strips will form an octagon. Now when the wheel is rotated you will see that this octagon will rotate but will remain in the same position, namely directly below the axle. If the wheel is rotated 15 degrees, the octagon will remain directly below the axle. If the wheel is rotated 90 degrees, the octagon will remain directly below the axle. By drawing two bisecting lines, the center point of the octagon is found and a circle can be constructed in place of the octagon. You will find the radius of this circle to be the same as the distance from the radius point of the axle to the connection point of the hanging weight on the spoke, namely 18 inches. This circle I call the inner circle. Now the interesting thing is that this circle can be placed almost anywhere you wish within the main wheel, and when the wheel rotates this inner circle will not change location. For example, lets say the hanging weight is designed so that it now has an arm extending from the spoke connection point horizontally to the right for a distance of 8 inches, so each hanging weight now looks like a carpenter's square standing on one end. The weight is such that the horizontal arm stays horizontal. Now instead of connecting the bottom of the hanging weights, connect the ends of the horizontal arms of the weights. The inner circle is now located so that the radius of the inner circle is at the same elevation as the radius of the wheel axle and the radius of the inner circle is 8 inches to the right of the radius of the wheel axle. This inner circle will remain at this position regardless of the rotation of the wheel. This inner circle does rotate, but it remains at the same position. If the wheel rotates 90 degrees, the inner circle remains at the same elevation and 8 inches to the right of the wheel axle. Now lets say this inner circle has a width of say 4 inches, and inside of this inner circle or inner wheel is placed a ball weight. What happens?