Deriving the Relation between Input and Output Forces

Known to whom?

I see no dimensions.....

More information, please. For example, how's that "sliding link" work?

Some dimensions, too. Your information so far is too vague.

Hmm...or is it school work. A decent schematic would help (i.e. a dot for a pivot and little parallel lines to indicate a sliding guide etc.) This would help ease the explanation no end. As other have mentioned, some dimensions and velocities would. help.

HOWEVER you have begged one enormous question ! In the absence of friction, the input work/power requirement that you want will be equal to the output work/power requirement.

The critical unknowns not mentioned by others so far are output power required, and the level/s of friction as detereminedby force-slide angles and friction materials/lubrication etc.

You probably need to redraw this for others to make sense of it. Is link 3 pivoted at the end opposite the force F1, or is it fixed (e.g. welded) to link 2? What permits link 1 to pivot as it translates?

If link 1 is purely sliding, (presumably along the axis of the line representing it) then no rotation of link 2 is possible, because the end of link 2 moves in an arc.

You might also work on your description. Assuming the linkage moves without appreciable friction, then energy in = energy out, and the cooling requirement of the prime mover depends only on the energy consumed by whatever is at the output of the linkage.

A linkage like this, if not designed to waste energy, will be 98-99 percent efficient, so at this early stage in design, has no appreciable effect on prime mover cooling.

If you are concerned about the relationship between forces F1 and F2, then you should draw the linkage centered and at its extremes of its motion. The relationship between the forces will change continuously.

The directions of forces F1 and F2 seem strange. Applying a force F1 at one end of the linkage will the cause force F2 to be in the direction opposite to that shown.

But in any case, a good first step is to show the linkage in its center and extreme positions. Then people can make some sense of how it is intended to move. Using the fulcrum as a center, draw arcs at the connection points of link 2 to links 1 and three. At all positions of the linkage, the connection points will have to fall on those arcs.

You could also take a couple minutes to make a model, in paper. Then photograph it in its extremes of position, and post the photographs. Because link 2 is under a bending load, you might want to replace it with a triangle shape in your model.

hi,

can you indicate the dimensions and force on your drawing?