scissor jack mechanisms

Dear will_usher:

"Lifting oneself by one's bootstraps..."

It can work, but the system will be largely indeterminate. Meaning you don't know what the forces will be, and will definitely be different even for the same individual through a few minute routine.

The weight of the individual will be applied constantly to the central pin, plus/minus accelerations of the body. Note that downward force components on the "handles" will also serve to lift weight off the "foot rest".

Statics will be sufficient to design this. Also search for "four bar mechanism", which your apparatus has defined (1: central pin to outboard pin, 2: outboard pin to foot pin, 3: foot pin to midpoint of foot platform, 4: "slider" from midpoint back to central pin.)

I don't find much in the way of on-line resources on this. If you think it will be a product, you may need to hire a professional for safety concerns.

David A. Smith

As i've modelled this on CAD I was thinking of measuring the total vertical distance moved downwards by the handle and comparing it to the total upwards movement by the seat and by comparing the ratio I could calculate the force required for the handle (by using the weight of the user).

this method you are assuming that someone else (not the user sat on the seat) is pulling the handles to lift the weight.

I'm assuming I'd have to take into account the force that is lifting the user created by pulling on the handles in the first place (as you mentioned).

What if have done is;

1. (I am assuming the user wants to apply a total force of 600N to the handles) so I calculated the upwards force lifted the user off the seat that this would create.
2. I then subtracted this force from the force needed to lift the body weight and the result is the force applied to the handles to simulate

600N.

Is this a suitable way of calculating this?

Dear will_usher:

Escher can be modelled in CAD...

The force on each handle is a vector. Since the loading on the handle is simple, it vector representation is not. A significant portion of loading can be directed from the handle towards the central pin. So you will need to concentrate on force components normal to the member's long axis, and simply realize that the co-linear force components are there simply to provide the proper balance. Since you have pinned joints, those pinned joints will have net torques to consider (net to zero, but this is only contraining the problem, and helps). The central pin will have torques applied, as it will see the manual loads and the redirected "butt loads" as counter acting torques.

No, I was assuming that the person was standing on the platform, however. But indeterminate it still is.

Look at the mechanism again. The exercisee will have to push outwards to lift his/her weight. And will have to restrain an internally directed force to keep the handles from crushing his/her ribs/gut. And if one of your hands gets sweaty and slips... lawsuit.

No.

This will take quite a while to set up, and just a little bit to solve. I'm off to work now. If someone else doesn't set it up for you, or provide a link to "teach the man to fish", I may take a stab at it tonight.

David A. Smith

No... the handles are above head height and the user pulls them downwards, so no crushing of ribs. The flat piece at the bottom is the seat. Thats why I'm assuming that as you pull down you are slightly lifting your own weight (i.e. this is different from someone else, stood on the ground, pulling the handles to lift the user).

I would be very grateful if you could give this a go!

no... those handles are above head height. The user it pulling them down to lift their own weight. The flat piece at the bottom is the part that they sit on. Thats why I'm thinking that when they pull on the handles they are lifting their own body weight slightly... its different from someone standing on the ground and pulling on the handles to lift the weight of that person sat on the seat, right?... the force that they'd have to apply to the handles would be slightly less.

If you could have a go at this I would be very grateful!

wrote

Let me jump in here.

Consider a _very_ simple system: a man weighing 600N ties a noose around his neck, throws the rope over a pulley in the ceiling, and pulls down on the other end with his arms until his feet are clear of the ground. How much force are his arms pulling the rope with?

Clearly, 300N. His neck is pulling on the noose with the other 300N :-)

Clearly, too, if it is _another_ man, standing on the ground, who pulls on the rope, _that_ man would have to exert 600N with his arms to keep the first man suspended off the ground.

Your machine is much less gruesome, but the same physics applies. The user's 600N body weight is supported by his arms and his butt. When he just sits in the seat, it's 600N for his butt, zero for his arms. If, at some point in the stroke, his arms are pulling on the handles with 300N, then at that point:

1) His butt is pushing on the seat with 300N, and 2) Moving the handles 1cm closer to the ground will move the seat 1cm farther from the ground.

A linkage is nothing but a combination of levers. That's nice because a lever keeps the same force ratio (in a given direction like "up/down") all through its stroke, because it keeps the same "gear ratio" all through its stroke.

Does this help?

-- TP

Dear will_usher:

...

your mechanism is a version of the "crank-slider mechanism" The slider is one half of the "butt plate", and it sees one half the load. The crank is the lower "half" of the member containing your hand grip. The minimum force applied will be when your hand delivers force normal to the long axis of this "crank plus extension" member.

A few more hits on google with: "four bar mechanism" "crank-slider" site:.edu

I won't be solving it.

David A. Smith

My first question is why not use a couple of pulleys and some weights?

With a very simple device you can accomplish the same thing, unless there is a reason why you want to make is so that you flap like a bird. In that case, you could easily make it so that you can do that too. If this is for exercise, you will be better off using pulleys because with them you can stay on the floor and have constant resistance, versus the variable resistance that you would have on your system.

If you described what you intend to use your device for, it may help.