Using Nega'tor Springs as a Source of Constant Force

Using Nega’tor Springs as a
Source of Constant Force
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G.R. Reich and Adam Bradshaw, Physics Department, Union College, Schenectady,
NY 12308; reichg@union.edu
The constant force “Neg’ator B” spring
motor, 1 developed in the 1950s, is a
rather interesting piece of apparatus
having a number of useful applications in
physics teaching. Yet it seems that few physics
teachers are familiar with the device. We’ve explored
the possibility of using the Neg’ator
spring motor as an alternative to the batterypowered
fan cart in constant-acceleration experiments.
In this note we describe the operation of
this interesting device and present some of our
test measurements and conclusions.
The Neg’ator B spring motor consists of a coil
of flat spring metal wound around two drums, as
shown in Fig. 1. The spring material is manufactured
so that in its unstressed state the coil has
a natural radius similar to that of the takeup
drum in the figure. As the drums turn, the material
is first straightened and then backward
wound so that energy is stored in the stressed
material on the output drum. As long as the
spring metal is much thinner than the radii of
the drums (the thickness is greatly exaggerated in
the spirals in the figure), the energy E stored will
be proportional to the length of winding on the
output drum. That is, the energy stored in the
stressed spring is given by E = k�, where � is the
angle through which the output drum has been
turned and k is a constant. The torque developed
on the output drum � = dE/d� is thus constant.
Typically, a pulley of radius R is mounted
on top of the output drum (see Fig. 2), and
string is wound onto it to form a reel. The tension
force T = �/R tending to retract the string is
then also constant, independent of how much
string has been played out. Spools of different
radii can, of course, be easily mounted so that
the same spring motor can be adapted to yield
Fig. 1. Constant torque Neg’ator B spring motor.
Fig. 2. A small constant-force spring motor with a
spool mounted on the output drum.
Fig. 3. A constant-force spring motor attached to a
low-friction cart.
THE PHYSICS TEACHER ◆ Vol. 40, March 2002

Fig. 4. Position-time graph for a low-friction cart
moving under the influence of a constant-force
spring motor (solid line) and a similar motion of a
PASCO fan cart.
different tensions.
For testing purposes we mounted a spool of
2.5-cm radius on the output drum of a spring
motor 2 whose nominal advertised torque was
0.01 N-m, producing a string tension of about
0.35 N, similar to the thrust of a PASCO fan
cart. 3 The string was then attached to a low-friction
cart rolling on an aluminum track (see Fig.
3), and an ultasonic range finder (not shown),
mounted at the opposite end of the track, was
used to follow the motion. The cart was projected
away from the spring end, it slowed as the
string played out about 1.0 m, and then it sped
up as it returned. Figures 4 and 5 show the position-
and velocity-time graphs of the cart (solid
line) in comparison with a similar motion of a
PASCO fan cart. While the spring-motor motion
produced less noise in the motion sensor
than the fan cart, its velocity-time graph had a
greater change of slope on reversal than the fan
cart. In the case of the fan cart, the change of
slope of about 20% seems to be due mainly to
friction in the wheel bearings; in the case of the
spring motor, an additional 20% change seems
to arise from internal losses in the spring motor
itself. It is not known to what extent that effect
can be reduced by changes to manufacture or design,
for example, by improving the bearings.
The spring-motor pulley can also be used as a
handheld puller. Students in laboratory are
THE PHYSICS TEACHER ◆ Vol. 40, March 2002
Fig. 5. Velocity-time graph for a low-friction cart
moving under the influence of a constant-force
spring motor (solid line) and a similar motion of a
PASCO fan cart.
sometimes asked to pull on an object with constant
force by keeping a rubber band stretched to
a constant length as the object moves or by keeping
a spring scale at a constant setting. It is always
an awkward procedure, and, especially for
the initial motion, the motion is usually quite
jerky. Spring motors work more successfully at
this since the force they exert does not depend
on keeping a fixed amount of string played out.
With a little practice, it is possible to keep increasing
the string length even while the object
reverses direction, thus avoiding the hysteresis
effect mentioned above and maintaining a quite
constant acceleration. It appears that Neg’ator B
motors can be a useful alternative means of providing
constant forces to moving objects.
Acknowledgments
The authors would like to thank S. Lepp for
bringing these devices to our attention and for
helpful discussions.
References
1. F. A. Votta, Jr., “Theory and design of long-deflection
constant force spring elements,” Trans.
ASME 74, 439 (1952).
2. Available from McMaster-Carr, New Brunswick,
NJ, Part # 61115A1 ($59.); http://www.
mcmaster.com.
3. PASCO catalog # ME-9485.
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