Do curved levers change the mechanical advantage?

If you think about the two alternate drawings, it is obvious that those would be inefficient because the most efficient motion for the travel of the piston is straight up and down. The two alternate drawings would be creating force oblique to the travel of the piston, and would obviously create too much friction on the lever connected to the piston and on the piston itself, causing it to wear out much faster. The curved lever as the top (the top of the S shape) accommodates the necessary up and down efficiency of the piston for most effect and least friction. And the curvature in the other direction of the bottom, continues the efficiency from the upper half of the lever, accommodating the piston motion while simultaneously giving a leverage advantage to the user from the pivot point (fulcrum). I've been fascinated by the advantage of curved levers in dispersing force ever since I got my riding mower stuck in a tight spot on a downward slope. Since it was a downward slope on wet grass, with a very heavy mower, the option of reversing it was ruled out due to the slick grass, and the downward force of the mower's mass (kinetic force?). Plus, my mower engine couldn't get the power to go in reverse and just avoid the situation. I didn't have the power on my own to lift the mower over the obstacle in front, and because of the tight space, there was no way I could use ropes or chains attacked to my truck to pull it out. Moreover, I didn't have any kind of winch to pull it out and had no stable object I could have attached the winch to in order to offset all the forces involved. It was quite a conundrum, and I was by myself, so I would have to solve it myself. I started thinking about the machine advantage I would have by use of some kind of lever to lift the front over the primary obstacle, which would have solved the entire problem. But getting some kind of fulcrum into that tight space made that seemingly unworkable. So I starting thinking about curved levers and various uses in many machines in places where I had worked. I think the basic idea is that the force is not simply linear force applied to linear movement, but rather, the force is dispersed by the curve along a broader plane of the fulcrum, in this case the ground. I wasn't sure if I had thought it out completely, but thought that it was worth a try. As luck would have it, I already possessed a pair of metal ramps for loading wheeled objects into the bed of my truck, which had a somewhat curved shape. In this case, there was more of an angular shape along the plane of the ramp, so it wasn't perfectly curved, but I thought it might test this principle of dispersal of force. Sure enough, it worked like a charm. I was able to surprisingly easily leverage my heavy lawnmower and its low deck over this Gordian knot of an obstacle. I've been thinking about curved levers ever since and trying to understand all the dispersal of mass and force principles involved, but I'm pretty sure I have seen such things in machinery, engineering, and, indeed, the lever design of the pump handle that started this discussion.