Biomechanics of the Forelimb of Mammals
(revised Jan 2010)
While doing this exercise, please do not mix the bones of one box with those of another.
When the triceps muscle of the upper forelimb contracts it can cause the ulna to rotate
around the distal end (the end away from the body) of the humerus. The ulna then exerts a force
at its distal end. In most mammals, the application of the force of the ulna is against the ground.
Use the freeze-dried limbs and the articulated mammalian skeletons to familiarize yourself with
the action of the triceps muscle and the movement of the forelimb resulting from its contraction.
In this exercise, we wish to analyze this action of the ulna as a lever. The pivot
(=fulcrum) point of this lever is the center of the axis of rotation of the ulna within the prominent
trochlear notch near the proximal end of the bone. The actual center of the axis of rotation is
within the notch and not on the ulna itself. The distance from this pivot to the point of attachment
of the triceps muscle is the in-lever (li) and the distance from the pivot to the point of application
of force at the distal end of the ulna is the out-lever (lo). The force of contraction of the triceps
muscle is the force-in (fi) of the system and the force exerted at the distal end of the ulna is the
out-force (fo). At equilibrium the following simple relationship exists in any lever:
fi x li = fo x lo
In this exercise, we are more interested in the force that is exerted at the distal end of the ulna that
is expressed as follows:
fo = fi x li
lo
We are not taking any measurements of forces (the appropriate unit for this force is the Newton)
and we are only interested in the relationship of the in-lever to the out-lever. We will ignore the
force component of the equation and focus on the li/lo ratio. It is not difficult to see that when
this value is great we get a magnification of the value of the force-in without a change in the
muscle itself. When the value of li/lo is small, this magnification is absent.
The triceps contracts with a given speed (=velocity Vi), and the distal end of the ulna
moves with a resultant speed (Vo) according to the following relationship:
Vo x li = Vi x lo
or solving for the velocity out (distal end of the ulna),
Vo = Vi x lo
li
Notice that the lever ratio is the inverse of the relationship for force: fo = fi x li.
lo
Therefore velocity will be sacrificed for force and vice versa. Lever arms are a compromise for
the requirements for enhancing force and velocity.
Assignment: Make measurements in groups. Indicate the number of the specimen box you
used on the assignment you submit. There are some specimens that all groups will measure (seal,
cow, horse (#327), tiger, bear, wombat, cheetah, human, and pronghorn). Include the
measurements from an Asian elephant (Li= 197 mm, Lo= 673 mm). Type the table and answers
(The Figure can be done by hand) and turn in as individual effort. (15 points)
1) Measure the li and lo from the center of the semicircular trochlear notch to the appropriate
end of the bone.
2) Prepare a table listing the specimens in ranked order from highest to lowest ratio. Include the
ratio value. Use an appropriate number of significant figures. Add a caption to your table.
3) Plot the data in a Figure from #2 on a horizontal axis with the specimen name at the
appropriate place on the line. (See Example) The values on the line should be the numerical
li/lo ratios with accurate incremental separation. Add a figure caption.
4) Which three specimens (by name) have the li/lo ratio most suited for the greatest force
application at the distal end of the ulna? What is this good for?
5) Which two specimens have the lowest li/lo ratio? For what do you think they are suited?
6) Before the next lab meeting, read the information you can about the adaptations of the limbs
of the cheetah, rabbit, hippopotamus, pronghorn, and wombat (on-line is fine). In particular,
for what is the forelimb used? I assume you do not need to research the uses of the human
forelimb. 6b). Where do you predict the ulnar ratios for these six mammals will be located on
your plot (#3 above)? Measure the ulnas of the human, cheetah, rabbit, hippopotamus,
pronghorn, and wombat to test your hypotheses. The measurements for the hippopotamus are:
Li= 165 mm, Lo= 387 mm.
7) Would you expect all ulnas in a given species to have identical values? Determine the Li/Lo
ratios of the seven deer ulnas to test your hypothesis. Report your values in a table. If you
found differences, what might account for them?
Recalculate these values for the deer. Are the values reproducible? What does this suggest
regarding the use of significant figures (#2 above)?
8) Do you think that differences in human athletic performance might have their basis in
differences in the lever mechanics of human bodies? Explain how you would test for
differences in a specific lever system for a specific human activity. Please be precise,