Help needed please - Toggle mechanism force calculations

[FreddyB]

Hi,

I've searched everywhere trying to work out how to calculate the spreading force of a simple toggle mechanism. I have a two equal length arms that are hinged together. One end is fixed on a pivot pin and the other can slide along a flat plane but is resisted by a fixed stop. The hinged arms are not quite in line and aligning them would increase their overall length. If I apply a force to the hinge, perpendicular to the base plane, what force along the plane will I get?Is there an equation I can use? I don't need to consider friction in the pins or sliding surfaces just now.

Help!

[turtlefish]

As I understand it (please someone correct me if I'm wrong), the clamping force will never be more than the force you are applying. It's just going over a shorter distance so the work input required is reducing. So if you apply 100N of force to the toggle, as you approach the toggle point, you are simply approaching 100N at the toggle output.

you can work it out really simply by just drawing shapes (I like shapes, not equations :P). You will need to pick a point in the travel of the linkages. The example I give you below is if there was 100N loaded onto the hinge, and the linkages were 20º away from being parallel to the sliding plane. Then you just draw a diagonal line 100mm long and 30º from horizontal, and draw a rectangle around it. The horizontal distance is your horizontal force on the sliding plane, in this case 94N.
toggle diagram.jpeg

I'm not sure how to work this out purely mathematically, but this gives you a rough idea.

[jboggs]

Do you know how to calculate force vectors on a free body diagram?

[FreddyB]

Not really. :-(

[JAlberts]

I am confused by the statement that the toggle arms are not aligned. If you can explain this better then maybe I can give you some guidance.

[FreddyB]

I am confused by the statement that the toggle arms are not aligned. If you can explain this better then maybe I can give you some guidance.

I mean not in a straight line. Imagine a leg bent slightly at the knee. Straightening the leg would increase overall length but if it can't straighten because of an obstruction then obviously there is a force generated. The force will vary due to the input force at the knee but also effected by leg lengths and relative angle between legs.

[jboggs]

turtlefish,
Actually there is an error in your logic. The 100N downward force is just that - downward. Because the two links are equally offset from the vertical, each links absorbs equal shares of it, 50N each. That is a vertical force. In your second diagram it is analogous to the 34mm dimension. Which means that the horizontal force is analogous to the 94mm dimension, which means the horizontal force is 94/34 x 50N = 138N. So the horizontal force does exceed the vertical applied force.

[turtlefish]

Oh! I need to revise my mechanics!

[JAlberts]

I previously overlooked turtlefish's above attached link diagram until I saw the reference in jboggs' above post.

The bottom right triangle in this diagram with the toggle pins at each triangle point accurately illustrates the basis for your toggle force calculations; and, the post by jboggs is correct way to calculate the forces except his horizontal force value being divided so that it applies 1/2 of the vertical loading to each end assumes that the center pin travel is restricted from moving horizontally so that as it lifts or falls both ends of the toggle will move horizontally in and out.

For your application with one end of the toggle pinned and fixed you will want to allow the center pin to be capable of moving horizonally with the block as it slides and in this arrangement the horizontal force applied to both the back pin and your sliding block from the 100N vertical load will be 94/34 x 100N = 276N.

With regard to the elbow bend(s) in one or both of your legs, as long as the legs are in the same vertical plane with the lower end connections then legs shapes are unimportant in calculating the applied vertical and horizontal forces of your linkage assembly and those forces will always be determined by the vertical and horizontal dimensions shown in the right triangle in your diagram.

To best understand how toggle forces work, think of the extreme cases of your triangle. Regardless of the length of vertical leg of the triangle, as the length of the horizontal leg approaches 0, then the horizontal force approaches zero; inversely, regardless of the length of the horizontal leg, as the vertical leg approaches 0, the horizontal force increases theoretically to infinity, or in an actual case, to the maximum load that the legs and pins will withstand without failure.

On the other hand, the shape of the legs will effect the stresses applied to the toggle legs. If a leg is straight then it experiences a purely compressive loading; however, with a bent knee shaped toggle leg there will also be bending stress applied due to the offset of the leg bend to the direct line of force between the ends of the toggle end.

[gopisetty vivek]

Dear jboggs,
Would u please elaborate "the horizontal force is analogous to the 94mm dimension, which means the horizontal force is 94/34 x 50N = 138N" the highlighted sentence. let me know on what basis was the calculation done

turtlefish,
Actually there is an error in your logic. The 100N downward force is just that - downward. Because the two links are equally offset from the vertical, each links absorbs equal shares of it, 50N each. That is a vertical force. In your second diagram it is analogous to the 34mm dimension. Which means that the horizontal force is analogous to the 94mm dimension, which means the horizontal force is 94/34 x 50N = 138N. So the horizontal force does exceed the vertical applied force.

[jboggs]

gopisetty, Are you familiar with vector force analysis? That is the basis for my statement.

[JAlberts]

gopisetty

Regardless of the method of analysis, if the the linkage contains two equal length arms the ratio of the horizontal force of the toggle to its vertical force is equal to 1/2 of the the horizontal distance between the two bottom pins divided by the vertical distance from the centerline of the pin connection at the top of the arms to a line drawn between the centers of the pins at the bottom of the arms.

For example: If 1/2 of the distance between the two bottom pins is equal to the vertical distance (which will give a 45 degree angle to both arms) and the vertical force is 50N then the horizontal force will be 1/1 X 50N = 50N; but as the linkage moves downward the horizontal force will increase until, for example, the horizontal distance is 10 time that of the vertical distance, then the horizontal force will be 10/1 X 50N =500N. Conversely, if the horizontal distance is 1/10 of the vertical distance then the horizontal force will be 1/10 X 50N = 5N.

If the two linkage arms are of unequal length, then the horizontal measurement is the horizontal distance from a vertical line from the linkage top pin centerline to the shortest arm bottom pin centerline.

[Cragyon]

See:

Toggle Clamp Equal Length Arms Equations and Calculator