Mechanical Advantage of a Leveraged Squat Machine?

[emc36f]

Can someone explain how squat machines like these seem to allow people to lift an extraordinary amount of weight (more than they would be able to with free-weights)? Would really appreciate a breakdown of how the force applied by the lifter translates to torque across the levers and gears. Thanks!

 

[Orodruin]

You have mechanical advantages both in where you apply the force at the shoulder pads vs where the chain attaches to the same part and the chain attaches to a cogwheel ov larger circumference than the one connecting the chain to the lever that the weight is on. You have mechanical disadvantage for the chain connecting to the weight level vs where the weight is placed.

You can easily measure the total mechanical advantage by considering how far the shoulder pads have to move relative to high the machine lifts the weights.

There is also another factor in terms of how easy it is to lift the weights that would be present even without mechanical advantage: When you are using a machine your only focus is pressing with as much force as possible. No energy is needed to provide stability, which engages many other supporting muscle groups when you do a free squat (or any other free exercise). As such, a machine will be isolating the main movers to a much larger extent, whereas free weights gives you a better full body exercise with support muscles coming into play.

 

[emc36f]

For assessing the torques and forces in a simplified way... am I headed in the right direction? (Just making up relative lengths, radii, etc.) Or am I completely confused about this calculation process?

 

[A.T.]

For assessing the torques and forces in a simplified way... am I headed in the right direction? (Just making up relative lengths, radii, etc.) Or am I completely confused about this calculation process?
View attachment 353327

You have the angle θ in the diagram, that is not used anywhere in the formulas. Also note that Fperson is also not exactly perpendicular to the bar. And unfortunately for you, both angles are changing during the lift.

As @Orodruin suggested, if just want the total effective mechanical advantage, you can just look at the kinematics and find the difference in movement between shoulder pads and weights. You don't need to write down the individual forces and torques for this, just apply geometry.

 

[sophiecentaur]

And unfortunately for you, both angles are changing during the lift.

Not actually "unfortunately", I would say; Using the same machine for all your sessions, you would notice this changing effort needed over the cycle but the profile would be consistent for all loads so you can validly assess your personal improvements. Performance with actual weights would be a better way to judge between different individuals. I imagine that competitive lifting would not use machines - for the reasons discussed here. But controlling free weights is a large part of the skill of free weight lifting so a champ needs both strength and skill.

I have noticed how many gym users 'cheat' themselves by rushing, jerking etc.. For genuine muscle improvement you need proper effort over whole cycles; slow and steady - except when there's the word 'jerk' in the description of the lift.

 

[A.T.]

Not actually "unfortunately", I would say

"Unfortunately" for calculating the mechanical advantage, as it potentially changes.

 

[sophiecentaur]

"Unfortunately" for calculating the mechanical advantage, as it potentially changes.

Well, yes. But, of course as we all know that MA cannot be calculated because MA is the actual ratio of load and effort forces. The 'ideal' geometrical estimate is referred to as the VT (velocity ratio). VR stays the same MA improves when you use oil etc.

The VR of a machine screw will imply that it could come undone. MA knows better. So we really should be a bit careful in use of terms. PF is normally healthily fussy about these things but not when 'machines' are concerned.

 

[emc36f]

Ok, so easiest/best to just compare the work done by the difference in distance the person moves (squat to standing) vs. the distance the weight moves, which is much smaller?

As an aside then, (although I didn't carry the calculations all the way through) shouldn't the sequence of calculations involving the cogs and torques work out mathematically, though, if done correctly (though not for the purposes of finding mechanical advantage per se)? Say, if we simplified it to choose the stationary position at the top of the squat so that we don't worry about a changing angle? Force exerted by the person to hold the weights up against gravity?

This is not a homework problem or anything, just a curiosity. I'm less concerned about calculating a value for mechanical advantage, and really just want to understand the details behind how this works.

 

[Orodruin]

I have noticed how many gym users 'cheat' themselves by rushing, jerking etc.. For genuine muscle improvement you need proper effort over whole cycles; slow and steady - except when there's the word 'jerk' in the description of the lift.

But then Mr Iskiplegday cannot load as much on the machine and brag about it! /s

Sometimes the jerk is also in the machine …

 

[sophiecentaur]

Ok, so easiest/best to just compare the work done by the difference in distance the person moves (squat to standing) vs. the distance the weight moves, which is much smaller?

Of course, MA estimation has to include any 'dead weight' and that can include the effect of the body of the user. If you raise your body as well as moving the weights then the force that your legs supply will include your weight. The effect on the body of a number of reps will include the controlling force, letting you down slowly.
Overall, I'd think that it's best not to try to get involved with what exactly the weights involved are doing but to note how much you mange to lift after a course of training on the machine. Animal bodies are really too complicated to try to tame them with Engineering and Physics experiments. Those machines make you stronger and they make you sweat - good value.