Drawing Board…..7/1/09 1 Don Rathjen....Exploratorium Teacher Institute....3601 Lyon St., San Francisco, CA 94123...donr@exploratorium.edu © 2009 Exploratorium, www.exploratorium.edu

Drawing Board A pendulum moving in two directions creates beautiful designs.

Introduction The Drawing Board consists of a marking pen that remains stationary and a platform that swings beneath the pen, acting as a pendulum. As the platform swings, the pen marks a sheet of paper that is fastened to the platform, generating beautiful repetitive patterns, which grow smaller with each repetition. These colorful designs contain hidden lessons in physics.

Materials about 15 ft of ½" PVC pipe, Schedule 40 -- lengths of pieces into which you will cut the pipe are noted in the Assembly section, as is their location in the device shown in the photo above -- lengths of representative pieces are also labeled in the photo 8 ½" PVC 90 degree elbow 3 ½" PVC T 2 ½" PVC cross wood dowel, 3/16", 6 in long 10" x 10" platform board (particle board, plywood, etc. -- see Assembly section for platform comments 4 screw eyes (size #12 works well) drill 5 binder clips, large drill bit, 13/64" 2 binder clips, mini or micro 8 ½" x 11" copier paper (can use blank side of used paper) marking pens (Sharpie fine point markers, or similar), assorted colors 4 pieces of string, each approximately 2 ft long (cut off extra after assembly if necessary) ruler or measuring tape PVC cutter, hacksaw blade, or other way to cut PVC pipe

18 in

2 in

18 in

18 in

5 in 21 i n

7 in 5 in 4 in

2 in 2 in

2 in

Drawing Board…..7/1/09 2 Don Rathjen....Exploratorium Teacher Institute....3601 Lyon St., San Francisco, CA 94123...donr@exploratorium.edu © 2009 Exploratorium, www.exploratorium.edu

Assembly Cut the PVC pipe into the following pieces (see photo of assembled device on first page for location of pieces noted below) 4 pieces each 5 long (for attaching the hanging platform to the upright frame) 2 pieces each 7 inches long (for the left and right top portions of the upright frame) 1 piece 4 inches long (for the center top portion of the upright frame) 4 pieces each 5 inches long (for the short sides of the base) 2 pieces each 21 inches long (for the long sides of the base) 3 pieces each 18 inches long (two for the legs of the upright frame; one for the swinging arm of the penholder) 3 pieces each about 2 inches (5 cm) long (two for the hand-hold on the swinging arm of the penholder; one to insert in the penholder PVC T itself, so that the pen fits snugly inside) Rather than attempting to give detailed instructions for assembling the device once the PVC pieces have been cut, we have chosen instead to supply some photos and helpful hints. The rest is left to the dedicated experimenter.

Using binder clips allows you to adjust the four pieces of string so that the drawing platform hangs level.

A standard Sharpie marking pen will fit into the half-inch The wooden dowel for the drawing arm pivot is PVC T pipe, but you can modify the holder to suit any held in place with two mini or micro binder clips. size felt-tip marker.You can fit the pen by wrapping it with masking tape. The platform must have sufficient mass so that its motion does not die down too quickly. The platform shown in the photos is a 10 in x 10 in piece of ¾ in particle board, which has a significant mass. If a lighter platform is used, a mass can be affixed to the platform; if the location of the mass is adjustable, you may find that its location will affect the pattern obtained. One old commercial version of this toy used a Tupperware-type container filled with sand for the platform.

Drawing Board…..7/1/09 3 Don Rathjen....Exploratorium Teacher Institute....3601 Lyon St., San Francisco, CA 94123...donr@exploratorium.edu © 2009 Exploratorium, www.exploratorium.edu

The penholder must be counterbalanced so that the pen exerts minimum pressure on the moving board while maintaining constant contact with the writing surface. The size and orientation of the pieces at the back end of the pen assembly can be adjusted to achieve a suitable balance. For the pen assembly shown in the photos, the pivot hole was drilled about 10 in from the pen end. If the hole is drilled at a different location, the size and location of the mass at the far end of the arm should be adjusted accordingly The Drawing Board should produce a pattern that repeats the same basic shape over and over again, with each cycle getting smaller. If the pattern is not consistent from one cycle to the next, try adjusting the counterbalance weight on the penholder. To Do and Notice Once the Drawing Board is adjusted, you can create wonderfully intricate designs. Push the board to start rotational as well as translational motion; lower the pen to start drawing and raise it to stop. Try drawing one to four patterns on the same paper using pens of different colors, changing the direction and force of the push with each new color.

Drawing Board…..7/1/09 4 Don Rathjen....Exploratorium Teacher Institute....3601 Lyon St., San Francisco, CA 94123...donr@exploratorium.edu © 2009 Exploratorium, www.exploratorium.edu

What’s Going On When the platform is displaced from its rest position, the four suspending strings exert forces on it to bring it back. You can think of these forces as acting in two directions perpendicular to each other: "north-south" and "east-west," for example. The combination of these two simultaneous motions can produce a variety of curved forms, in the same way that proper simultaneous manipulation of the two knobs on an Etch-a-Sketch toy allows you to draw curves. The diminishing size of each successive repetition of the pattern is a graphic demonstration of how friction steadily dissipates the energy of a moving object. Etcetera Some of the shapes you will produce with the Drawing Board are known as harmonograms or Lissajous figures. An oscilloscope can easily produce these figures, since the pattern on the scope face is generated by a single electron beam simultaneously moving vertically and horizontally on the screen. An oscilloscope can be thought of as an electronic Etch-a-Sketch. One of our teachers had this Snack set up and running during an aftershock of the 1989 Loma Prieta earthquake. The pen traced the pattern of motion generated by the aftershock. The operating principle behind the Drawing Board—a pen directly attached to the earth with a paper only loosely attached to the earth—is the operating principle behind a seismograph.