Finally the Forces explained

By Tom Black   

      Those who train with heavy duty torsion spring grippers have always be curious as to how much force it takes to close a particular gripper.  These numbers are important not only for ones own personal edification but for purposes of comparison to others.  After all, with weightlifting one usually can easily compare their lifts even if they have never met.  While gym weights are not always consistent, they don't vary enough to make that much of a difference.  In competition the weights, if calibrated, should be fairly close.  Grippers, on the other hand, are stated by the manufactures to vary and in reality vary even more than most would want to admit.

        Richard Sorin was asked by Ironmind to estimate the forces to close each of a series of their grippers.  He estimated the force needed to close a gripper at the center of the handle.  The numbers estimated are all very familiar to those who train with Ironmind's grippers, 100-pounds for the Trainer, 140-pounds for the #1, 195-pounds for the #2, 280-pounds for the #3 and 365-pounds for the #4.

      Now when most of us are curious about the strength of a gripper one of the easiest methods is to push the gripper down on a bathroom scale.  I do this by taking a washcloth, folding it up and pressing the gripper down on the washcloth.  This reading can best be described as the force needed to close the gripper from the end, or for purposes of calculation below F_end.  There are other methods, one of which is to use a weight stack placed above the gripper.    In 2001 PDA created a machine which purportedly measured the same force the near the end of the handle.   PDA then used this number to determine the torque at the center of the handle.  This, of course, is a different number than the Ironmind number.  This created confusion that continues to this day regarding both the Ironmind numbers and the PDA numbers.

      I believed that the machine used by PDA accurate, but I only had one reference point to compare, that being a PDA361 gripper made long after many other grippers were tested and people started commenting on grippers tested by PDA being incorrectly measured.  I also was never comfortable with the method that PDA used to calculate the torque.  They multiplied the end of the handle force reading (F_end) by 2.375, which is their approximation of the center of the handle (although it's also my understanding that they didn't apply the force on the end, which would further elevate their numbers).  Now grippers vary in length, but most are closer to 4.625" (4 5/8") from center of spring to end of the handle (all the way to the stamped end).  This is known as the moment arm length when calculating torque.  So right from the start I

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 thought that the number should have been 2.3125, which is one half of 4.625".  Nevertheless, since this number was consistently applied I thought it didn't really matter in the end.   Also, it really is a minor difference between 2.375" and 2.3125" and this is not the reason for the major differences in the final PDA calculations compared to Ironminds.  PDA noted that "The torque arm was offset 0.375" to account for differences in grippers and to prevent coil bind."

      Now, after great reflection (two years worth), I can't accept the multiplication of 2.375 by the force measured at the end of the handle for the following reason.  Torque is defined as Force times Distance.  The distance being also known as the moment arm being from the center of the spring to the point at which the force is applied, which was the end of the handle on PDA's measurements.  It seems as though PDA used this formula, taking the force at the end multiplied by the distance that everyone agreed was the distance that the true force was felt by the hand while closing (i.e., the center of the handle).  But their force measurement was taken from the end, not the center.  My feeling back then that PDA should have calculated as follows the torque at the end of the handle:

F_end  * D_end = Torque at end of handle

     So why didn't PDA use these numbers?  Well, do the math for a second, using actual numbers from a typical older #2 gripper that I have.  This gripper measures 119-pounds on the bathroom scale, and it's harder than some #2's I've seen, a little weaker than others.  It is about as "average" as they get, based on about seven #2's that I've tried.   Torque at the end of the handle would thus be:

Torque= 119 * 4.625" = 550.375 Pounds-Inch.

    Frankly, I can immediately see why PDA did not use a number in the 536.5 inch-pound range, his being a mere #2 gripper with a Torque of 550.375 Pounds-Inch!  Talk about confusion between the old estimated numbers and the new numbers.  But of course, they aren't really the same thing, one being a force and the other a torque.  

     Now the reason I'm writing this article now is due to a revelation I had recently. In order understand the revelation I will explain how I envisioned it.  Imagine cutting off the handle of the above gripper to the point where the ring encircles the handle.  This is the "center" everyone refers too.  Is it really in the center of the moment arm?  Well, no, but it's the accepted "average" point of the force, and it makes sense too most people. More importantly, it was the point that Richard was taking about in his estimate, as we will see later in this article.  Now, what is the torque required to close the gripper at that point?  It's Force * Distance, but here the Force is much higher than before because the lever arm is so short.  Also, the distance is much shorter than before the handles were cut.  But, you see, the torque mentioned above is the torque as the spring sees it, that is, the mechanical advantage of the hand on the gripper is exerting 550.375-Inch-pounds of rotation around the center of the spring.  The revelation is that the Torque to move the spring a certain angle never changes, regardless of the length of the gripper handle, short or long.  Another way of looking at it is that the spring does not know that the handles have been cut short, it moves the same angle to the same force, it's just the hands ability to apply that torque has been lessened by the shorter moment arm.  While the Force required to close a gripper is going up, the distance the force is applied from is going down proportionately, and hence:

                F_center * D_center = F_end  * D_end 

This formula reflects the statement above that the torque is the same.   Solving for the Force at the center of the handle we get:

                F_center = ( F_end  *  D_end) / D_center

The distance measured from the center of the spring to the ring on most of my grippers is 2.75".   

Taking the old #2 gripper measured by PDA we get the following:

               F_center = (119 * 4.625)/ 2.75

                F_center = 200.13-pounds 

This number should look very familiar.  It is very close to Richard Sorin's 195-pound estimate of a #2 gripper that was then used by Ironmind.  As we all know, grippers vary quite a bit, and for my gripper to be 200-pounds at the center, and another to be 195 is a very reasonable difference.

      Moving on, I'm going to use the 4.625" total length and the 2.75" center of handle length for the remaining calculations, but before I do let me point out that subtle differences in handle lengths were, in fact, not taken into account by PDA and I now believe this was another cause of the discrepancies noted by people when they actually compared "hand-to-hand" PDA tested grippers.  My calculation would have had PDA measure all the handle lengths and use that in the force calculation, this would then bring in handle length (and thus handle set into the spring) into the force calculation.  I do this adjustment later in the article. 

      Next let's first look at Sorin's/Ironmind's force number of 280-pounds for the #3 gripper.  What we would like to see is a force at the center of the handle to be 280-pounds, like in the following formula:

                     280 = F_center = ( F_end * 4.625)/ 2.75

Solving for the measured Force on the end, F_end would be 166.5-pounds.  Now, many grip trainers have pushed grippers down on their scales.  Many have found numbers in the low 100's for #2 grippers and mid 100's for #3 grippers.  I have a #3 that only measures about 145 on the scale and it is my easiest.  I have another double stamped #3 which is much hard and it measured 165-pounds.  It's tough to measure a gripper with that kind of poundage reading!  I have yet another gripper which I really can't press down all the way and it seemed to read 181 before I gave up.  This gripper was made prior to 1997 and is very wide. My point is that it is very reasonable that a #3 gripper that is 4.625" long could have a closing force on the end of 166.5-pounds and thus a center of handle force of 280-pounds, exactly as Richard Sorin observed (and probably measured or calculated himself).

     The following table shows all of the measurements if taken at the end of a "typical" gripper measuring 4.625" that would yield the Sorin/Ironmind numbers:

     The F_end numbers above are very common for the gripper listed using the bathroom scale method described above.   I personally have tested many grippers on the scale that have fallen very close to the F_end force numbers.  I have also tested a series of Trainers and #1 grippers (about 6 different grippers were tested).  These grippers are very easy to test on the scale, and very easy to determine how they fall in a strength range relative to each other.  There were no surprises when testing these grippers, all calculated with the formula to a strength level the same as they felt.

Center of the Handle   

      I did all of the above with the ring on the center of the handle as the center point of force.  For my hand 4" wide hand, however, this really isn't the "center of force" in my opinion.  I only bring this up to illustrate how the size of your hand can make a difference in leverage.  For me the "center" is about 1/2" further up the handle.  This would yield a F_center force of 237-pounds for a #3 gripper given the 166.5 reading from the end.  I am not so keen on changing the nomenclature of where the center of force applied is, especially since it is different depending the size of your hand.  2.75" from the center of the spring is as good as any length in this area.  Nevertheless, I bring this up to illustrate another discontinuity as I see it.  This is the difference between the "accepted" force numbers on torsion spring grippers and those measured with a dynamometer.  

  On Robert Baraban's new dynamometer Nathan Holle currently holds the record with 125 kilos, which is 275.5 pounds.  It must be stated that Nathan is well beyond the #3 gripper and is approaching the #4.  Thus, his force reading should be much higher than the 280-pounds noted for the #3, and yet it does not appear to be based on his dynamometer reading.  The F_center of the "typical" #4 gripper using my hand (3.25" from the center of spring, rather than 2.75") would yield 309-pounds as opposed to the Ironmind 365-pound number.  I think this 309-pounds compares much more favorably with the 275.5-pounds that Nathan shows on the dynamometer, which is a "straight pull" that can be calibrated with weight.  It also may show where Nathan is compared to a #4 gripper, and of course, there still is the variance of #4's so he may even have a #4 in the 280 or 290-pound range with the F_center measure at 3.25" and is thus "knocking at the door."

     I predict that using the above calculations that someday someone can do the following test:

-Just close a particular gripper with a carefully measured F_end reading.

-After resting, test themselves on a dynamometer.

-Using the dynamometer reading to solve for the true D_center of the gripper. 

They would use the same formula as above, but solve for D_center instead:  

                        D_center = ( F_end  * D_end) / F_center 

Using my PDA361 for example, lets say I train someone to just be able to close this  gripper.  I've measured it on the scale and it's 139.5-pounds.  This gripper is standard length of 4.625".   Then if the person squeezes the dynamometer to 178-pounds then this would be used for the value of F_center.  Solving for D_center would yield 3.25".   Keep in mind I'm not predicting that the D_center number will be 3.25", but that the person will find the true number based on their hand size.  

Differences in Feel

     It was recognized fairly quickly that PDA calibrated grippers of the same Pounds-Inch readings felt different.  As was stated correctly then by members of the gripboard, the length of the grippers was not properly taken into account with the PDA results.  You see, the length from spring center to handle end of a "typical" gripper is very close to the 4 5/8" (4.625") number I have used above, but they definitely do vary.  I've seen grippers that are clearly 4.5", 1/8" shorter than "normal."  It is also very common to have a gripper 1/16" longer than "normal" and no doubt there are some that are 1/8" longer, although I do not seem to have one myself.  I thus varied the length in my equation and found the numbers in the following chart:

      Do these differences account for the differences in "feel" noted by those that own PDA calibrated grippers?  I don't know really.  I only have one PDA gripper, a 361, and it feels exactly "right" to me.  Note on the #3 grippers above that the difference is 10-Pounds-Inch, and this strikes me to be large enough to account for the difference.

Placing a Number Rating on your Gripper

     The calculation now enables us also to place a number rating on a particular tested gripper.  If you have a gripper that tests at 116-pounds you know that it is exactly a "#2" gripper.  But what if it tests at 121-pounds?  Or what if you've shorted it by +1/4" and it tests at 122-pounds, what it is then?  

Here is the complete formula:

     Rating =2+  (85- (280-F_center) )/85

Because the difference between the #3 and #4 is also 85-pounds the formula works without changing the 2 to a 3 and the 280 to 385 (you subtract off a negative number in the equation, which is a positive).  The following chart shows various gripper ratings given the hypothetical numbers I noted above.  Also, if anyone wants to make a #5 gripper with an 85-pound F_center increase in force, I've put it on the chart.

     I have also created a handy spreadsheet that calculates your gripper forces and ratings.  Click HERE.

Modified Grippers

     If you've read the above and don't agree I submit another interesting test, and an idea for using the formula in gripper length modifications.  The "typical #3" I noted above has been modified to attach an extended handle.  It is extended 1/2" and when I push it down on my digital scale it reads 149 pounds.  Now I've been training on this gripper for awhile now and at its current length it felt identical to the PDA361 when closed, as  a matter of fact I wrote that many times in my workout log that they were the same and over many days and closings they "felt" the same at closing.  I wasn't even making this comparison for purposes of validating my formula, it was just a training observation.  When I tested the extended #3 it was 149-pounds.  At first I thought that something was wrong, shouldn't  it be 139.5?  I almost was dejected about it, but then remembered that the length makes a difference in leverage.  That is, the scale doesn't know it's longer so the formula must be used to calculate its true closing force.  I wasn't sure if the 1/2" would make that much of a difference, but when I plugged the numbers into the formula it read 234.96 for the extended gripper.
     
      Here it is again:
     
      Extended #3=234.96  and 149 from end
      PDA361  =   234.61   and 139.5 from end

   This number can be used to make estimates of a gripper before modification, thus giving the owner of the gripper an idea on the final strength after modification.

Conclusion

       Ironmind makes a gripper that they never claimed to have been "calibrated," but their numbers now appear to be around what they stated they were.  This being for the simple reason that Richard Sorin probably measured his grippers years ago with a weight stack.    The torque calculations at the spring at the "typical" length of 4.625" and the Ironmind force at the center ring  would be:

      Personally, the Torque (T_spring) numbers have little meaning to me in how they relate to the grippers, and looking at the #3 for example, the 770 Pounds-Inch is really the torque at the spring center, given the leverage of the hand on the long handle.

     Finally, in summary, I offer the following chart to show the forces using both the force at the center ring and at a point another 1/2" up the handle, which for my somewhat "average" hand width of 4" is the center point of my applied force.  I submit that the F_{1 3/8" from end} number given below may more accurately reflect the applied force for most people and may be closer to their actual readings on a dynamometer if they have the strength to close a gripper with the F_end number as shown.  Most dynamometers only go to 100kg or 220.46-pounds.  Most guys who can close a #3 can peg these meters no problem.   Based on some of the results I've seen on the gripboard regarding dynamometers, even people well beyond the #3 gripper can "only" do around 270-pounds on a dynamometer.  This, of course, does not correlate well with the 280-pound number, but does with the 236.94-pound number below.

Further Reading;

Torque measurement:  "The measure of a force's tendency to produce a rotation about an axis is called torque."

From "Engineers Edge":  k= P * M/Deg, where k=spring constant (inch-pounds/Deg), Deg=Deflection in degrees, M= Moment arm in Inches, P=Force exerted on spring in pounds.  Note also that P = k * Deg/M.  Thus, as the spring is compressed a higher angle in degrees, the Force increases proportionately.  k and M are constant throughout the range of motion of the gripper.  

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Copyright April 2003