- Name: Tom DeFayette and Gene Clark
- Address: Trinity University, Department of Physics
- Phone 210-999-7380 Fax is 210-999-7423
- email: firstname.lastname@example.org email@example.com
Low Cost Competition
A Double Pendulum Constructed From Inline Roller Skate
double pendulum is a popular device for demonstration of deterministic
chaos. It is mechanically simple and has visually impressive dynamics.
However, it must have low friction in order to sustain undriven oscillations
long enough to make the chaotic character of the motion obvious. A design
for a very low friction double pendulum that is large enough for class
demonstrations has been published. However, this design requires machinist
skills and access to a machine shop. This note presents a design that has
the properties of low friction and large size required for a successful
classroom demonstration and the advantage that it can be constructed entirely
from in-line roller skate wheels and common wooden and metal rod stock.
No machining or skill is required for construction.
Approximate Size: 24" tall, 12" wide, 6"
Requires electrical power? No.
Is this apparatus intended for use with an overhead projector?
Will you be present to set up your apparatus? No.
Parts List for One Inline Roller Skate Double Pendulum
Quantity Item (all units in inches, unless noted otherwise)
1 1/4 - 20 x10 long threaded steel rod. Cost $3.29.
1 1/4 - 20 x 4 long threaded steel rod. Cost $3.29
2 3/8 - 16 x 6 long hardwood dowel. Cost $1.99
1 5/16 - 18 x 61/2 long threaded steel rod. Cost $3.29
6 1/4 hex nut (nominal cost)
1 ( or more) 5/16 hex nut (nominal cost)
10 1/4 flat nylon washers (nominal cost)
5 Inline roller skate wheels (new or used) with axles
and bearings (ABEC 7 rated). Wheels should be indoor-rated if possible.
Check garage sales and flea markets for used skates. Cost if purchased
1 .08 FL. Oz. Bottle Loctite 242 Thread Locker (alternative
is one roll of Teflon pipe thread tap used by plumbers). Cost $2.99.
2 5 inch C-Clamp (for attaching pendulum to sturdy object).
3 2 x 2 x 1 thick wood pieces to be used with C-Clamps.
1 Pint - Mineral Spirits. Cost $0.89
Total cost $39.71
Note. All items except inline roller skate wheels
can be purchased at a hardware store. Dowels and threaded rods are normally
sold in 2 or 3 foot lengths. Use the wood saw to trim dowels and a hacksaw
with a 24 tooth blade to cut the threaded rod.
Inline Roller Skate Double Pendulum Tool List
Portable hand drill or drill press with the following
drill bits: --
- Use a 11/32 drill bit to drill holes into four wheels
for the wooden dowel --
- Use a 27/64 drill bit to drill hole into the wheel for
the 5/16-18 x 6 1/2 long threaded rod (lower pendulum arm)
- Vise to hold wheels when drilling holes for dowels and
- Wood crosscut saw.
- Hacksaw with 24 tooth blade
- Tape measure or ruler.
- 1/4"Flat tip screwdriver
1. Use Loctite 242 Thread Locker to keep nuts from becoming
loose on the threaded rod. These nuts should not be tightly compressed
against the wheel bearings. Hand tighten nuts only. Examine the position
of these nuts each time the pendulum completes a complete series of rotations
(start to stop). These nuts should remain in a fixed position and not loosen
on the threaded rod axle. Use thread locker before you apply any lubricant
(lubrication is not necessary). Thread locker will not hold the hex nuts
in position if the threaded rod has been oiled.
2. Ensure the C-clamps are capable of holding the top
pendulum axle securely. The bottom arm of the double pendulum rotates very
3. Do not allow anyone to stand in the pendulum's plane
of rotation. Observers should view the pendulum rotation by standing perpendicular
to the plane of rotation. If the pendulum becomes unattached from the C-clamps
during rotation, it will fly forward or backward - not sideways.
4. Wear safety glasses during assembly.
5. Observe required safety practices when using portable
hand tools and mineral spirits.
- 1. Assemble all materials from the Parts List before
- 2. If using used skate wheels, remove bearings and unthreaded
axles from wheels by pressing the bearing out by hand or with a screw driver.
These bearings are easily removed and inserted. New bearings and axles
are sold separately from the wheels.
- 3. Clean bearings, old or new, by soaking in mineral
spirits. If the bearing has a dust/dirt cap, remove cap with a small screwdriver.
New and used inline roller skate bearings are packed with white lithium
grease. This grease hinders rotation of the bearing and therefore movement
of the pendulum. Soak the bearings in mineral spirits for approximately
one hour. You may need to use a cotton swap to remove the grease after
soaking. If compressed air is available it can be used to blow out the
grease. It is especially important to wear safety glasses during this procedure
since the bearing will spin rapidly in the race while you are holding onto
it. It will not be necessary to replace the dust/dirt cap. Place the bearings
and the unthreaded axles off to the side. You will use them latter.
- 4. Drill holes in wheels. Before inserting or reinserting
the bearings and axles, drill required holes in the five wheels. Four wheels
will be drilled with the 11/32" drill bit. One wheel will be drilled
with a 27/64" drill bit. Drill holes as deep as possible, but do not
drill into the plastic wheel hub where the bearing will be located. Ensure
you drill your hole perpendicular to the hub and not at an angle. If you
do not do this correctly, turn the wheel over and try drilling a hole correctly
on the other side of the wheel.
- 5. Insert bearing and unthreaded axle into each wheel.
This is a simple process and done without tools. Reverse procedure you
used for removing the bearings from old wheels or follow the instructions
which came with new wheels.
- 6. Insert wooden dowels. Insert hardwood dowels into
the holes of the four wheels having a 11/32" hole. This is a simple
press fit. Using only your hands, press the dowel into the hole as deep
as possible. Two wheels will be connected together by a dowel. Glue is
not required to hold the dowel in the wheel. Do not use any lubricant on
the dowel or in the wheel hole. You can add a small amount of rubber glue
or a poly-acrylic resin (sold as a "clear sealant" at hardware
stores) in each hole before inserting the dowel. However, you may not be
able to latter remove the dowels from the wheels if you use an adhesive.
Using an adhesive may interfere with your ability to conduct such experiments
as the affect of pendulum arm length on oscillations.
- 7. Insert the 5/16 -18 threaded rod. Insert the 5/16
- 18 x 61/2 threaded rod into the wheel having the 27/64" hole. This
rod should be hand screwed into the wheel hole. Screw the rod into the
hole as far as possible. No abrasives or lubricants are necessary. The
threaded rod will tap threads in the wheel hole. This wheel and threaded
rod comprises the bottom arm of your double pendulum.
- 8. Assemble the top axle. The 1/4 -20 x 10" threaded
rod is the axle for the top pendulum arm. Insert this rod through two of
the skate wheels having a 11/32" hole. Use four of the hex nuts and
four nylon washers to position the wheels on this axle. Hand-tighten the
hex nuts. The wheels should be separated approximately 2 inches as measured
from the center of each wheel; not the side edges of the wheels. These
dimensions are not critical. Experiment and see what happens. After completing
this step, you have two skate wheels skewed on a threaded rod. Fasten the
top axle with wheels to a sturdy object using the c-clamps and wood pieces.
The wood pieces grip the threaded rod between the c-clamps and the sturdy
- 9. Assemble the lower axle. The 1/4 - 20 x 4" threaded
rod is the axle for the lower pendulum arm. This lower axle connects the
two wheels hanging on wooden dowels from the top pendulum. Placed in between
these two wheels is the wheel having the 5/16 - 18 x 61/2 " threaded
rod. Place two nylon washers between each wheel to separate the wheels
on the axle. Use the hex nuts to secure all the wheels by placing one hex
nut on each end of the threaded rod lower axle. Hand-tighten only. The
axle should protrude from the hex nut by approximately 1/2 inch. Do not
use thread locker at this time on your hex nuts.
- 10. Test your double pendulum. Carefully swing the pendulum.
The pendulum should move smoothly, not make noises, and not come apart
or loosen at the joints. Look for any unstable joint or connection and
any erratic movements during the swings. Check the c-clamps holding the
top axle to ensure they stay tight. When you are satisfied that the movement
of the double pendulum is smooth and that the apparatus is safe, loosen
each hex nut and place one drop of the thread locker on the threaded rod
where the hex nut will be located. Hand tighten the hex nut to where it
was located before adding the thread locker. The thread locker will keep
the hex nut from loosening on the threaded rod. The thread locker will
"lock" the hex nut in position in about 6 hours. As an alternative
to using thread locker, you can use teflon pipe thread tape. Wrap a small
piece of teflon pipe thread tape around the threaded rod and hand tighten
the hex nut over the tape.
Optimizing the design
There are several ways to optimize the oscillation of
your double pendulum. The double pendulum shown in our picture has sections
cut from the lower wheels in order to reduce the mass at the lower axis
of rotation. Use a hacksaw blade to trim pieces of the wheel. The oscillations
are affected by many variables which impact on the pendulum's movement.
We attempted to increase the amplitude, frequency, and period of the oscillation
by screwing nuts of different masses onto the lower pendulum arm. Since
the wooden dowels are easily disconnected from the wheels, you can experiment
with various lengths of dowels. As with all pendulums, your double pendulum's
oscillations are affected by friction and the moment of inertia of the
components. The design presented here has the advantage of producing many
chaotic oscillations of the lower pendulum. If the lower pendulum has a
smaller moment of inertia it will swing at a much larger angular velocity
and so will lose energy to friction at a faster rate.
How long should the lower pendulum continue to swing over
the top? When constructed using these plans the lower pendulum will produce
about 30 chaotic oscillations when dropped from the point of unstable equilibrium
above the support point for the upper pendulum.
How can you record quantitative data from this pendulum?
You can record quantitative data from the double pendulum by attaching
a magnet to any point whose positions you want to record. Use a Hall effect
sensor to detect the position. A time series of the Hall probe output with
a magnet on the end of the lower pendulum is usually sufficient to diagnose
Reference: "Chaos in a double pendulum,"
Troy Shinbrot, Celso Grebogi, Jack Wisdom, and James A. Yorke, Am.J.Phys.
60, 491-499 (June 1992).