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I do not know where to put this one mods, please move to where it suits...
Do the total home gym packages with the weights being lifted on a series of cables and pullies, weigh true to their numbered weight stampings ??...
Lets say the user has a total plate weight of 150 pounds pinned in. The weights are being lifted basically by a system of block and tackle , which to me makes the object lifted lighter. What say you engineers ?
Pulleys and cables will not reduce the weight unless the cable is doubled (or tripled) at some point, and the weight being lifted moves 1/2 (or 1/3) the distance you are moving your arms/legs. If you look closely at the picture, you will see that the pulleys and cables merely re-arrange the forces so that pulling out on the bar causes the weights to move up.
It has been my experience (with the equipment at health club gyms) that the weights move the same distance as your arms/legs, which means there's no leverage or mechanical advantage and the weights pinned in are approximately the amount you are lifting.
The operative word is "approximately". You can't rely on the "weight rating" as anything more than a relative effort for that particular machine. It isn't very accurate for the amount of actual mechanical force required -- no better than +/- 30 percent.
On some machines, the weight of the carriage is significant, and not counted in the amount of the weight stack. On others, there is a "Nautilus" style cam arrangement, such that the lever arm does change during the range of motion, easier at first and harder towards the end, or harder at first and easier at the end, in much the same fashion as a compound bow.
So don't be using the weight stack to attempt to calibrate your torque wrench..
Free weights are more difficult to lift because you have to control X, Y and Z axis, on say, a bench press machine, you provide movement in only one axis.
Like furball said, you have to have more control over free weights than a machine. That's why you'll hear some people who swear by free weights-they'll strengthen your "stabilizer" muscles, instead of focusing on just the core group.
At 6'0" tall (not overly tall by any means), I find that many non-free-weight systems have poor range-of-motion for me. For example, curling machines may have the pivot offset from where my elbow rests, so the machine doesn't follow the swing of my arm, but introduces a "cam-like" motion instead--not good for joints. Or, on a bench-press machine, the carriage motion is perfectly straight up, whereas your arms can't quite do that motion, so somewhere in the stroke, you introduce some extra weight through friction when your stroke causes the carriage to push against one side of the guides or the other. Plus, free weights cause you to use other muscles to stabilize the motion, so one exercise works several muscle groups for a more efficient workout, where machines tend to over-isolate certain muscles and totally ignore others, often leading to increased risk of injury. It's kind of like someone who uses steroids--their muscle mass grows quicker than their bone mass can accomodate, leading to joint injuries--your quads may be able to allow you to squat 500 lbs, but your knees might not handle it and blow at the first rep.
I did the free weights back when I was 27 and I loved them. Your point is dead on about their advantage over cabled weights. ...
But back then I took some bad advice to get bulked up fast and end up hurting myself and had to give up free weights. I still have that bulk under some loose skin and fatty tissue though...
At 54 y.o. now, I need a different kind of exercise program.
My main concern is I am losing my leg power. I had torn menicus surgery on both knees in the last two years and now I have to pull myself up out of a chair. I am getting a bit of Mr. Arthur in them also. ....
When I drive for a hour I have to roll out of the truck and stand still for a bit to get my knees unkinked. So, I thought the home gym with a leg press/curl attachment would help me. Matter of fact, I am picking one up that resembles the one in the link this wed night . ( they would not send a young lady like the one in the link pic to train me though. Rats )