Mechanical system clarification needed.

[Eastjack]

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

 

[marcusl]

Welcome Eastjack! A diagram would help me since I'm having trouble visualizing the toggles in this:

"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."

 

[Eastjack]

Ok I'll make a diagram and post it this evening. What sort of attachments are allowed?

 

[Farsight]

Ditto as per marcus, Eastjack. Until then it maybe sounds as if the vertical component of the toggle force is pressing fruitlessly down on the platform at the bottom of the swing. What's the machine? I wonder if there's anything in some unrelated mechanism that might be of interest here, eg a pendulum clock but where a "clock" drives the "pendulum" rather than vice versa.

 

[russ_watters]

Ok I'll make a diagram and post it this evening. What sort of attachments are allowed?

.jpg is probably best because of the size limit, but pretty much anything zipped will do.

 

[Eastjack]

Diagram of system

Hi all,

OK I have attached a PDF stick drawing of the simplified system.
P1 thru P4 are fixed position pivots.
The swing platform has a track that the toggle rollers run in keeping the toggles attached at all times but allowing the platform to swing thru BDC.
The guide link ensures that the toggles collapse thru a controlled path.
The series of diagrams A thru E show the sequence should the platform be raised up to the right and released.
This is a simplified diagram of a press assembly that has two tools that swing into and out of the work position.
The mass of the swing platform and support arm is probably a factor of 10 more than the combined mass of the toggles and connecting links.

During the downswing the toggles are collapsing and possibly exerting a downward force to the swing platform. However the swing platform is also accelerating downward so depends on the difference between the accelerations.
At BDC the toggles come to rest momentarily.
As the platform rises on the left side it must drag the toggles up with it.
The question.
Is any of the potential energy released during the collapse of the toggles recovered? Do the toggles add any velocity to the swing platform or is the energy from the toggles lost? How would one go about calcualting this?

Thanks

 

[Cyrus]

Is any of the potential energy released during the collapse of the toggles recovered?

No, I don't see any spring elements on the toggles to store the lost potential energy. It is driven by the guide link.

Do the toggles add any velocity to the swing platform or is the energy from the toggles lost?

No, becasue they can only fall as fast as the guide link will let them. (If I am to understand your picture correctly)

How would one go about calcualting this?

A ton of messy dynamics.

Edit: I can see how this thing moves, but how is it driven?

 

[Eastjack]

Thanks for the reply cyrusabdollahi.
In real life there are a series of toggles coupled at the center pivot and at the tops. They move in unision the path controlled by the guide link.
One of the bottom pivot shafts is used to drive the system during operation via a lever and cylinder. A separate start system raises the assembly to start it. The toggle drive only provides a kick to accelerate the downward motion and another kick to ensure that the swing is completed.
If the toggle energy is lost each cycle then it becomes important to reduce the mass of the toggles as much as possible. If it were recovered then the mass is far less important. I could not see how the toggle energy could be transferred to the platform but can not explain where the energy goes.

 

[Q_Goest]

Hi Eastjack. I design reciprocating pumps for a living, and this is not totally unlike that. Take for instance a piston on a reciprocating pump which is accelerated by the crank from bottom dead center to half way through the stroke. During this motion, the piston accelerates from 0 (at the rear most point of the cycle) to some maximum velocity at the half way point. As it passes the half way point, the piston begins slowing down again from some maximum velocity back to zero. It will reach zero velocity again when it hits top dead center.

Regardless of whether the piston is moving horizontally or vertically, there is energy being transferred into the piston, raising it's kinetic energy during the first half of the stroke, and an equal amount of energy is being transferred back out of the piston during the second half of the stroke (when the piston decelerates from the maximum velocity back to zero). The only thing taking energy out of this system is friction in the form of heat.

The point is that energy is conserved for this system, with frictional losses being the only losses. Energy is transferred into and back out of the moving components, just like a pendulum.

Your system is very similar. The links are (presumably) being accelerated at some period in the cycle, and decelerated during another period of the cycle. Energy is conserved, with only the frictional forces removing energy from the system. The only way for energy to escape the system is in the form of heat from friction, heat from aerodynamic drag, or work. But your system isn't doing any work.

How do you calculate it? In your case, the energy of the accelerating and decelerating toggles is going into rotational and translational motion. They are rotating and translating as they accelerate and decelerate. That energy is conserved. The only energy losses are frictional losses at the joints and of course aerodynamic losses due to air resistance. You would need to calculate the rotational and translational inertia of each component to accurately model the mechanism.

 

[LURCH]

Welcome Eastjack! Just to add to what Q Goest has already said:

As the entire device moves downward, it gains momentum in that direction. As the swing platform reaches the bottom of its arc, its motion becomes less and less vertical and more horizontal. As the swing platform tries to translate to purely horizontal motion, the toggle assembly will still be trying to move downward. This means that the platform must bring the downward motion of the toggle assembly to a halt, since the two components are attached to one another (through the rollers). As a result, the swing platform will be absorbing the momentum of the toggle assembly. This transfer of momentum will be "felt" by the swing platform as a downward pull just before the platform reaches the bottom of its swing.

This downward pull will be translated into horizontal motion at the bottom of the swing (where the downward momentum of the toggle assembly reaches zero). Of course, this increase in horizontal momentum will result in a greater upward force immediately thereafter. The energy gained just before the bottom of the swing should be nearly equal to the energy added to the upward motion of the swing platform just after the bottom of the swing (minus frictional losses, of course). This added momentum will help get the toggle assembly moving upward.

So, as has been stated, frictional losses should be your only losses. However, it might be worth noting that fiction will be increased slightly in the areas immediately before and after the bottom stroke, where the momentum of the two assemblies is at its most divergent. More importantly, structural stresses will be greatest in this area, and a heavier the toggle assembly will put a greater load on the rollers and the track in which they move.