I believe there is some incorrect information presented
on your website (see below). Resistance arm and force arm should
be defined as the perpendicular distance from axis
to point of force application. When you are considering forces
applied to levers, you are dealing with torques. T= f X perpendicular
distance. The physical distance and the perpendicular distance
can be the same, or they can be different, depending on whether
or not the force is being applied at a right angle (perpendicular)
to the lever. Perpendicular distance can be calculated by multiplying
the physical distance X the sine of the angle of force application.
In the diagram of the variable resistance machines, the
perpendicular distance (shortest distance from line of force
to axis) from resistance force to axis does not change. The physical
distance from axis to resistant force point of application does
change. But the perpendicular distance does not change. Therefore,
the resistant torque does not change. However, the effort torque
(force X perpendicular distance) does change. The effort torque
decreases thus making the movement more difficult. The resistant
torque remains constant.
Using the diagram below, simply extend the line of force
for the resistance and the force. Then simply draw a line from
the axis to the extended line, making sure to create a right
angle __I__. You will see that the resistant arm remains
the same while the force arm shortens.
Dr. Robert Koslow
Resistive force (R) is initially relatively short [close to fulcrum
As motive force (F) acts on lever, resistive arm becomes longer
requiring progressively greater motive forces throughout movement.
Thank you for your insightful comments. This is what I am considering
placing on this page based on your first recommendation:
When calculating forces applied to levers, torque loads must
be considered. Torque = Force x Perpendicular Distance. The physical
distance and the perpendicular distance are the same only when
force is being applied at a right angle (perpendicular) to the
lever. Perpendicular distance can be calculated by multiplying
the physical distance x sine of the angle of force application.
Now let me try to understand what you are telling me in the
case of the Variable Resistance Lever. In the first figure, forces
are perpendicular (90°). In the second figure, both the resistive
and motive forces are acting on the lever at approximately 35°,
so there are no relative differences between the resistive and
motive forces based on that fact alone. However the physical
distance the resistive force increases from the fulcrum is approximately
2 fold requiring greater motive force as the weight is lifted.
Your argument is that even though the physical distance between
the resistive force and fulcrum increase, perpendicular distance
is the same. I can certainly see that from drawing vertical lines
down the mentioned points as you suggest, so perpendicular distance
is the same, therefore you say the resistive torque remains constant.
I don't believe I had made any erroneous statements on this section,
it's just stating 'resistive arm becomes longer' may be a bit
misleading with no further explanation and clarification? I understand
you are just urging me to add these comments so it is clearer
how these forces are interacting. Is that correct?
I see you are the Head of Health Sciences at James Madison University.
That's nice you took the time to offer your advice. I appreciate
James Griffing, ExRx.net
The error is in the statement As motive force (F)
acts on lever, resistive arm becomes longer requiring progressively
greater motive forces throughout movement.
The resistant arm is longer. But the angle of resistant
force has changed, thus keeping the resistant torque consistent
throughout the movement. So, why is more force needed if the
resistant torque does not change? The answer is that the motive
force physical distance has not changed, but the motive force
angle of application has changed. The user is no longer applying
a force in an efficient manner. But the difference is that the
physical distance of the motive force has not changed. If the
resistant force = 10 lbs. and the perpendicular distance = 10
T= 10 X 10= 100 in-lbs. This is true for both diagrams.
In order to hold the bar in a steady state, the motive torque
in diagram #1= T= 10 lbs. X 10 in.= 100in-lbs. In diagram 2 the
motive torque will be reduced, not because of the lengthening
of the resistant physical distance, but because of the shortened
perpendicular distance of the motive arm. If we kept the effort
force at 10 lbs, our overall motive torque will be decreased
due to the shortened perpendicular distance of the effort force.
We need to apply more than 10 lbs of force because our motive
perpendicular distance has decreased.
So, why is progressively greater motive force needed when
the resistant torque has not changed? Because the motive force
perpendicular distance has shortened.
Hope this makes sense.
Thank you for this clarification. I will make these changes
on our next site update.
James Griffing, ExRx.net