Man, I suck at physics. Probably doesn’t help that I last took it in '98, but I digress.
Pretty much anyone who’s ever lifted a weight has tried out the standard biceps curl, and pretty much anyone who’s ever tried to increase the amount of weight they can curl has found that it’s tough to get the weight past a certain point, where their forearm is perpendicular to their upper arm.
How do you go about analyzing the motion to find the point of greatest exertion?
I had this big post prepaired with physics of rotation and all that good stuff, but I think there might be something else going on. I think when you get past the right angle postion on your bicep curl, your muscle starts to run out of room to contract. That, plus the crushing effect on your elbow joint as more and more of the weight of the dumbell is shunted down the arm bones as the weight is gradually positioned above the elbow.
That is my WAG. Thank you and good night.
Unless you have no tendons, the biceps has more than enough room to contract at the 90[sup]o[/sup] mark, and then some.
There’s no doubt in my mind that the physiology complicates things, but I’m interested in the Newtonian mechanics explanation. Humor me.
Your muscles are applying a moment and the weight is roughly rotating around your elbow. When you get to the 90 degree point the force due to gravity is perpendicular to the distance from your elbow to your arm. This is the point of maximum moment due to the weight i.e. the toughest part of the lift.
I am not sure if you are familiar with moments so I’ll do a quick run down. When you close a door you apply a force a certain distance away from the point of rotation. That is why the further away you push from the hinge the easier it is to open the door. If you pushed on the edge of the door (the edge that becomes part of the wall) the door would not rotate becuase their is no perpendicular force.
Here is my lame attempt at a graphical illustration. The W and downward arrow is the force due to gravity. The lines are your arm and the '.'s are just there for spacing.
…|
…|
…/
…/
…/
W
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/
If you break down the weight force into perpendicular and parallel components you find that only a portion of the force is causing a moment.
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…W____/
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…/
As you can see now the entire weight force is causing a moment. Thusly your arm must apply the largest moment at your elbow to counteract it.
If you wanted to do a numerical analysis you find that the moment equation is M=Wsin(theta) where theta is the angle your elbow makes. Take the derivitive of that and you get dM=Wcos(theta). Setting dM=0 gets you either a local max, min or plateau point. In this case it gives us our max.
I’m not sure I understand what you mean by analyzing the motion.
If you decompose the weight as a force vector on a suitable xOy graph (for example one where the origin is centered on the weight, the x axis run along the fore arm and the y axis is perpendicular to the x axis) you’ll see that the y-component is greatest when the forearm is at a 90 degree angle with the upper arm, That is the force that the biceps has to to overcome so that is the point of greatest exertion.
Outside of the 90 degree angle the x-component is not zero. That force is trying to compress or extend the bone of the forearm and does not demand any work from the bicep, hence less exertion.
treis talk funny smart talk. The words are so shiney. Shiney pretty.
Damn you treis! That post snicked in while I wrote mine. 
You explained it better than me. Just a small comment, not a correction: I didn’t mention momentos because in this case the lever of the moment, or torque, is contant (the lenght of the forearm) so the only thing that affects how much force your bicep needs to apply to hold the weight stationary at a given angle is the component of the weight perpendicular to the forearm (depends on mass and angle). That is obviously greatest when at 90 degrees. If you could shorten the lenght of your forearm you would find it easier to lift the weight.
Wouldn’t this only work if the point of attachement for the bicep remained the same distance from the elbow that it was before the forearm was shortened?
Just trying to remember 10 weeks of physics classes from 4 years ago.
thnx
What matters here is the distance between the point of insertion and the weight. As long as that distance decreases, you could move the tendon around a bit and still get ahead.
That’s what I figured.
kisses.
I don’t understand what you mean by point of attachment, possibly your considering the physiology of muscles, which I know nothing about.
I see that ultrafilter has already provided an answer but anyway you can test my assertion. With the forearm at a 90 degree angle place a heavy weight on top of if and vary the distance to the elbow. You’ll see that the farther it is, the harder it gets. That’s what I meant.
Every muscle consists of a muscle belly, which is the part that actually contracts, and two tendons that attach it to the skeleton. One end is deemed the point of origin, and the other the point of insertion. There’s probably a logic to which is which, but don’t ask me for it.
For the biceps brachii, the point of origin is on the scapula, and the point of insertion is on the radius.
Like Ultrafilter said, the point of attachement for a muscle is litterally the spot on the bone where a particular muscle sticks on. If your biscep attached to your forearm exactly at your elbow, you wouldn’t be able to rotate your forearm because there would be no lever action. Like trying to open a door by pushing on the hinge. Your example of changing the position of a weight along a resting, bent arm is exactly what I was asking clarification on. In your new example, the distance between the point of the weight acting on the arm and the point of the muscle exerting the upward force changed because only one variable was altered. The muscle stayed attached to the arm where it was while the weight moved around. In your first post, you said “if you could shorten the length of the forearm” which doesn’t specifically imply that the distance between the weight and the muscle attachement site was changing. Theoretically, you could shrink the forearm and keep the weight and muscle attachment site the same relative distance from one another. This would not impact the difficulty of moving the weight very much because the crucial thing in this situation is how far apart the relative forces are acting from each other along the lever arm, as Ultrafilter said.
My question was not ment as a nit-pick on you. I simply wanted to solidify my understanding of the underlying concepts. Please do not think that I am being snarky.
I have nothing to add to the physics of the matter, but biceps is both plural and singular. Bicep may seem right, but it isn’t. The logic of it might be grounded in Latin. I don’t speak Latin, so I can’t explain it.
I crush you with my bicep! Or, if you neck is big, with both Biceps! Take that!
Not a lot to add, just a different way to explain it.
Watch your arm moving as you do a biceps curl.
While your knuckle moves the first two inches, the weight moves the same, but lifts only a fraction of an inch. While it moves the next few inches, the weight moves only a little bit higher for each inch of movement. {insert trigonometry here} Now you certainly don’t let your form slip so far as to allow inertia to assist you in your lifts, right? So, now look at the motion of your knuckle as you pass through the part of the lift where your forearm is level. Every bit of movement is lift. Then it starts to turn into horizontal motion again.
From the point of view of your biceps, muscle movement is the same at every point of the lift, but the amount of work done is greatest when all of the motion of the weight is upward. In a free weight lift, that will be the third quarter of the lift, with good form. (you don’t do a full half circle.)
In fact, if you alter the angle of your upper arm, and support it, you can isolate different points of the arms motion to be at the point of greatest effort. That can affect the nature of the work out. Working the muscle hard at extension or hard at full compression are different effects. Try it and see, but be careful, using less than normal weights until you have a feel for it.
Tris
The best way to approach this sort of problem, of course, is with a free body diagram of the arm curling the weight. For a biceps curl, your problem is to solve for the arm angle that produces the greatest force on the bicep. This may seem like an easy thing to do. It is not.
This type of problem is tricky since you the more realistic you make it (a curl also depends on the brachioradialis and other muscles, not just the bicep; is close to but not strictly in one plane; the elbow may move slightly during the movement), the less likely you are to have enough data to solve the equations.
How can you set up these equations? Some clues can be found here. This is how to draw a free-body diagram, then set up equations, for an arm holding a weight using a straight arm, which is not moving.
http://www.engin.umich.edu/class/bme456/muscleforce/static1.htm
This site covers similar ground.
In practice, this problem should first be approached by drawing a free-body diagram of a bent arm (at elbow angle theta) holding a weight, assuming motion is in one plane, minimizing the number of muscles involved, etc. These assumptions are not always trivial – but without them there is usually insufficent data to go ahead (see http://www.jneurosci.org/cgi/content/full/17/6/2128 for an example of a more complex approach).
Muscle attachment points can be used to determine the moment arms, as shown in the first site. The weight of the arm and forearm can be estimated from anatomic data, if desired, and these forces (mg) applied at their centres of mass. Rotation occurs around the elbow with an angular acceleration alpha, which is zero if the weight is lifted with a constant angular velocity. The sum of the moments around the centre of mass of the system is Icm*alpha, where Icm is the moment of inertia of the system. While there are papers that estimate I for the elbow joint (q.v. Kearney et al., J. of Biomechanics), things are made much easier by assuming that the angular acceleration about the centre of mass of the system is zero. In practice, the position of the system centre of mass is NOT constant, nor is the angular acceleration about the centre of mass is not zero, nor is the position of the system centre of mass the same as the point of rotation around the elbow.
“Hold on a freakin’ minute”, you say. I’m not trying to build an artificial elbow. I just want to do a rough-and-ready calculation. Back to our static diagram. We draw a bent arm at angle theta, similar to the “line diagram” in the first website cited, except the forces are functions of theta. If we ignore a couple muscles, we can find the biceps force as a function of theta and see where it is maximized.
This paper would imply more muscles than the biceps are involved in the curl (duh)
http://asb-biomech.org/onlineabs/NACOB98/57/
This article gives an interesting overview, but skimps on the math. (A lot of bodybuilding articles, as I’m sure you know, discuss results of biceps strength based on EMG studies. EMG is hard to do well, and minor variations in placement do make a big difference. Measuring biceps action during a curl with an EMG while going through the angles is certainly the “easiest” way to experimentally determine which angle has the maximum recruitment – and I trust you are now more aware that the math can be very daunting. Using a Cybex dynamometer is just easier than going through the math; and also realizing that the math produces very weird answers when you end up trying to rob data from twenty different studies; measurements can be very different from study to study.)
http://www.abcbodybuilding.com/magazine03/wrench/musclesofelbowpart2.htm
A couple interesting articles appear on the web in the journal Medicine & Science in Sports and Exercise, (e.g. www.acsm-msse.org/pt/re/msse/ fulltext.00005768-200101000-00005.htm, www.acsm-msse.org/pt/re/msse/ fulltext.00005768-200009000-00010.htm) but I’m not about to pay to see them and I no longer live in a university town.
Interesting, but a definite sidebar (role of genetics in biceps curl strength): http://www.blackwell-synergy.com/links/doi/10.1046%2Fj.1365-201x.1998.00344.x
Especially if you curl like the average gym-goer, with more pelvic thrust than a baboon in heat.
Seriously, I know a fair amount about the physiological issues associated with this sort of problem. I was just curious to see the second-semester mechanics answer.
The second semester mechanics answer makes so many assumptions to get an answer that it doesn’t match the experimental answers. The abcbodybuilding link gives the best summary, but as I said skimps on the math.