3 Point hitch upper link

[TerryR]

Last pic: just like second pic, but top link lifts the other end:
View attachment 1335225
Other funky cylinder thing at the angle is the top link... part of it. The rest of it extends to the far end weight, whether via piston or chain or what.
There’s no more weight on the lift links - still 100.
Top link has all 100 of the other end.

That is not correct. The top link is forcing the "implement" to lift, applying weight to the bottom link. When the top link is at an angle like this it is lifting part of the load, but far from all of it. How much depends on the angle. As your last diagram correctly points out, when the top link is horizontal it lifts none of the load. At the angle you sketch it carries maybe one-third of the 200 lb. load.

 

[LouNY]

I drew these up earlier, then deleted, but after yet more "the math doesn't matter" kind of posts I figure I'll post it anyways.

In these illustrations, pretend the implement is a barbell, 100# each end. Really a rotary mower isn't much different from this example but making things as simple as possible is good.

First pic: Ends are on the ground, no tractor involved.
(Not pictured: ground pushing up 100# on the weights, this is called "the normal force"):
View attachment 1330227

Next pic:
Tractor lifts one end with no top link:
View attachment 1330228
Funky cylinder thing is the lift arm.
The 100# of the close end is on lift links. The other end's 100# is still on the ground.

Last pic: just like second pic, but top link lifts the other end:
View attachment 1335225
Other funky cylinder thing at the angle is the top link... part of it. The rest of it extends to the far end weight, whether via piston or chain or what.
There’s no more weight on the lift links - still 100.
Top link has all 100 of the other end.

Final pic: top link pulled strongly enough to raise the end to be level with the top link itself (I got tired of drawing 100's and arrows sorry)
View attachment 1335226
In this case, the bottom link is now carrying a chunk of the weight of the far end as well as its end.
The tension in the link is shown by the diagonal line going from top right to bottom left; the components are the horizontal compression and the vertical weight pulling down
Top link is carrying some; the higher the angle that the implement has with the bottom link, the more goes onto the bottom link (as soon as the end of the implement goes above the bottom arms, the bottom arms start getting some of the end load).

Consider if the top link lifts the barbell completely vertical (assuming it would fit, ok) - then the top link would end up with zero tension and the bottom arms would be carrying the weight of both ends of the barbell (200#).
That's the situation with a perfectly balanced ballast box.

Nice math but no, as the rear weight gets pulled up the load on the lift arms will increase. Not going by math or geometry just by what I have seen and experienced.

 

[TerryR]

The ballast box example is perfect....assuming such a ballast box exists where the load is balanced.
But the center of gravity explanation........that loses me.
...
That will affect the balance / center of gravity. I think the formula is solid....but implements are varied in their lower arm attachment point....which changes the balance point.
...
Now part of the reason I started this thread was my wonderment of how the top link can be relatively slight in construction compared to the robust arms and lower end of the 3 PT mechanism.

Such a ballast box would be easy to construct. Take a barrel, upright, and cut holes in opposite sides a bit above the center vertically. Slide one of those 3-point drawbars through the holes, and fill it with concrete. Now you can pick it up with the lower arms, and it stays balanced.

The center of gravity is the imaginary point where all the weight of the item seems to be located. You can envision how to find its horizontal location if you think of an angle blade. Put a post in the ground upright, tall enough to hold the blade off the ground when it's resting on the blade frame. Lower the blade's center beam onto the post at the point where it balances, probably around 6 inches in front of the blade. If you position it perfectly, you can unhook the blade and it will just balance on top of the post. The point here the post bears on the frame is the center of gravity.

It's the same for any implement, but it's harder to image with something like a mower because the post likely would have to come up through the working parts.

To analyze the forces at play on the 3-point hitch members, if the implement itself is rigid, as most are, you can treat the entire weight of the implement as being located at the center of gravity.

CalG has explained the reason the top link is so slender compared to the bottom link.

 

[SPYDERLK]

That is not correct. The top link is forcing the "implement" to lift, applying weight to the bottom link. When the top link is at an angle like this it is lifting part of the load, but far from all of it. How much depends on the angle. As your last diagram correctly points out, when the top link is horizontal it lifts none of the load. At the angle you sketch it carries maybe one-third of the 200 lb. load.

Plus, in all cases of 3ph implement use, the ball ends are connected and articulate on a vertical plane established by the implement. The plane sees tensive or compressive loads when the // form moves above or below its neutral/horizontal position.

 

[ning]

Pretty sure if the implement's attachment point to the top link is level with the lower links, there's no weight transfered to the lower links. While that point is below the lower links, with tension on the top link, there's weight removed from the lower links, and then once that point is above the lower links it's transferring weight to the lower links, going from 0% at level to 100% at vertical.

 

[SPYDERLK]

Pretty sure if the implement's attachment point to the top link is level with the lower links, there's no weight transfered to the lower links. [[[While that point is below the lower links, with tension on the top link, there's weight removed from the lower links,]]] and then once that point is above the lower links it's transferring weight to the lower links, going from 0% at level to 100% at vertical.

No. The // system is instantly reactive to angle changes ensuring that the sum of all forces in the articulated linkage remains the implements weight acting downward on the lift arm balls. The effect is driven by the angles of the elements and the forces of the cantilevered weight.
-- Using the part of your description that I bracketed, Lift arms and Top link are aimed down at like angle ensured by the fixed spacing of the implement connection. The Cantilever forces are always horizontal and balanced holding the implement up - rearward at the top and forward at the bottom. The opposite direction of these forces act on the link angles such that the up/down resultants cancel. The lift arms thus always have a downward load equal to the implements weight.

 

[MoArk Willy]

Apply the math to these specs. The weight is 350#

 

[Mud2Money]

One implement I find could be hard on a top link is long ones like brush cutters. I actually sheared a few bolts on my NH top link mount. That’s a lot of weight bouncing around.

 

[CalG]

Guys and Gals (if any)

The many comments on this thread appear to have failed in one aspect. We have neglected to give significance to the vital aspect for resolving the forces on the top link, in that ALL THE LIFTING IS DONE BY THE UPPER LIFT ARMS!. You know, the pair of arms fixed to the rock shaft powered by a hydraulic piston under your seat.

All the other system element forces are due to the eccentricity of the load attached to the lower lift arms that are acted on by the side links.

The top link is only an anti- torque link, to resist the turning moment of the eccentric load around the far ends of the lower lifting arms. It can do no LIFTING , with ball swivels at each end. (A hydraulic top link could provide a vertical component to lift a load, but then it would be an actuator, not a link ;-)

The forces acting on the top link are measured in pound feet. (torque)
The loads seen by the top link are measured in pounds. (the feet "drop out" based on geometry)

Clear as mud , right? ;-)

I can explain it for you, but I can't understand it for you. ;-)

 

[ning]

Guys and Gals (if any)

The many comments on this thread appear to have failed in one aspect. We have neglected to give significance to the vital aspect for resolving the forces on the top link, in that ALL THE LIFTING IS DONE BY THE UPPER LIFT ARMS!. You know, the pair of arms fixed to the rock shaft powered by a hydraulic piston under your seat.

All the other system element forces are due to the eccentricity of the load attached to the lower lift arms that are acted on by the side links.

The top link is only an anti- torque link, to resist the turning moment of the eccentric load around the far ends of the lower lifting arms. It can do no LIFTING , with ball swivels at each end. (A hydraulic top link could provide a vertical component to lift a load, but then it would be an actuator, not a link ;-)

The forces acting on the top link are measured in pound feet. (torque)
The loads seen by the top link are measured in pounds. (the feet "drop out" based on geometry)

Clear as mud , right? ;-)

I can explain it for you, but I can't understand it for you. ;-)

I guess not.
Somehow I just can't get past the fact that without a top link, my rotary cutter sits on the back wheel no matter how hard the lift arms are pulling upwards. I guess it's just magic that with a top link, the rear end levitates and *checks notes* apparently puts all of the rear end weight back on the lower arms? Perhaps my understanding of vector forces, that the tension pulling diagonally upwards equaling an upward pull plus a horizontal pull... and that an upward pull is typically known as "lifting"... is wrong?
I guess I learn something new every day!