Low Cost Competition

A Double Pendulum Constructed From Inline Roller Skate Wheels


The 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" deep
  • Requires electrical power? No.
  • Is this apparatus intended for use with an overhead projector? No.
  • 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 new $14.99.
  • 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). Cost $8.98.
  • 3 2 x 2 x 1 thick wood pieces to be used with C-Clamps. Nominal cost.
  • 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: --
  • Safety Concerns

  • 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 fast.
  • 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.
  • Assembly

    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 chaos.

    Reference: "Chaos in a double pendulum," Troy Shinbrot, Celso Grebogi, Jack Wisdom, and James A. Yorke, Am.J.Phys. 60, 491-499 (June 1992).