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Eastjack
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First post from a new member looking for clarification of a mechanics issue.
Several of the designers in our office, myself included, were in an active discussion over the energy losses of a pendulum system in a machine we build.
Consider a platform suspended near each end by arms of equal length with their top ends is supported by fixed pivot points. This platform can swing like a pendulum from the rest position (arms vertical), 90 degrees to the left or right (arms horizontal). If raised to the horizontal position and released it will swing through the rest position and climb up the other side to a position dependent on frictional losses. Adding mass to the platform should not change the position reached assuming friction remains constant. However the kinetic energy of the system as it passes through the rest position will increase with the mass of the system.
Now consider a pair of links joined by a rotational joint at one end (toggle pair center). A pivot point is located at a point central to the platform and the bottom end of one toggle is pivoted to it. The upper end of the other toggle has a bearing running in a linear track along the swing platform. When the platform is at rest the toggles fold up to form a horizontal V and when the platform is up they straighten out to be in line and vertical. (This is an over simplification as more than one toggle set is used but will suffice for my question).
Assume the platform starts on the right side with the swing arms horizontal and swings down and through the rest position. Gravity will accelerate the platform and translate the motion from vertical to horizontal at the lowest point. The inertia will carry it through and up the other side. The mass of the toggles will also assist their collapse until the center position at which point they will have no momentum. Once past the rest position the toggles will be pulled up by virtue of the bearing in the captive track. The energy for this must come from the platform inertia and so the platform will not rise as high as it would without the toggles attached.
Now the subject of the discussions.
Will the energy generated by the collapsing toggles add to the velocity of the platform thus increasing its inertia or is the energy of collapse lost.
One school of thought was that the vertical velocity of the platform decreases as it approaches the rest position slowing the fall of the toggle assembly. This braking effect would be translated into a higher platform velocity thus recovering some of the energy of fall. The other school is of the opinion that the energy is lost and all the subsequent toggle lifting force must be taken from the platform inertia.
To further complicate matters the toggles are the driving force for the platform and apply force during collapse and extension. How does this effect things.
I hope this clear, I would post a diagram but am not sure if this forum allows attachments. All help is appreciated.
Thanks
Several of the designers in our office, myself included, were in an active discussion over the energy losses of a pendulum system in a machine we build.
Consider a platform suspended near each end by arms of equal length with their top ends is supported by fixed pivot points. This platform can swing like a pendulum from the rest position (arms vertical), 90 degrees to the left or right (arms horizontal). If raised to the horizontal position and released it will swing through the rest position and climb up the other side to a position dependent on frictional losses. Adding mass to the platform should not change the position reached assuming friction remains constant. However the kinetic energy of the system as it passes through the rest position will increase with the mass of the system.
Now consider a pair of links joined by a rotational joint at one end (toggle pair center). A pivot point is located at a point central to the platform and the bottom end of one toggle is pivoted to it. The upper end of the other toggle has a bearing running in a linear track along the swing platform. When the platform is at rest the toggles fold up to form a horizontal V and when the platform is up they straighten out to be in line and vertical. (This is an over simplification as more than one toggle set is used but will suffice for my question).
Assume the platform starts on the right side with the swing arms horizontal and swings down and through the rest position. Gravity will accelerate the platform and translate the motion from vertical to horizontal at the lowest point. The inertia will carry it through and up the other side. The mass of the toggles will also assist their collapse until the center position at which point they will have no momentum. Once past the rest position the toggles will be pulled up by virtue of the bearing in the captive track. The energy for this must come from the platform inertia and so the platform will not rise as high as it would without the toggles attached.
Now the subject of the discussions.
Will the energy generated by the collapsing toggles add to the velocity of the platform thus increasing its inertia or is the energy of collapse lost.
One school of thought was that the vertical velocity of the platform decreases as it approaches the rest position slowing the fall of the toggle assembly. This braking effect would be translated into a higher platform velocity thus recovering some of the energy of fall. The other school is of the opinion that the energy is lost and all the subsequent toggle lifting force must be taken from the platform inertia.
To further complicate matters the toggles are the driving force for the platform and apply force during collapse and extension. How does this effect things.
I hope this clear, I would post a diagram but am not sure if this forum allows attachments. All help is appreciated.
Thanks