A Mid Century Modern Harmonograph

this is a furniture quality harmonograph designed to be good company for mid-century modern furniture the design is characterized by simplicity smooth lines and shapes and no ornamentation it was inspired by an article in the may 1964 issue of scientific american it was built in about 1975 using black walnut that came from a mature tree in the backyard of a friend the wood was destined to become firewood so i was able to trade some cut and split firewood for the two large logs from the trunk and a couple of the larger limbs i was able to make a living room and dining room chair set from the logs and some smaller projects with the scraps this is my favorite harmonograph configuration because it takes up little space and it fits nicely in a corner it's a good conversation piece most people want to see it work and are willing to start it swinging to make personalized drawings there are two pendulums and each are free to swing in two dimensions the bottom pendulum hangs from the upper pendulum so the two pendulums are strongly coupled and don't really move independently there are two modes of motion in the prairie mode the top and bottom pendulums move relatively slowly in the same path like a single pendulum with a joint in the middle in the secondary mode the top and bottom pendulums move relatively quickly in opposite directions to make drawings that don't look like scribbles the period of the primary mode must be a rational multiple of the period of the secondary mode for example two to one three to two four to three and so on these periods depend on the positions of the upper and lower weights on the pendulum bars since the pendulums are strongly coupled both weight positions affect both periods so it's a little tricky to get the positions correct adjusting the weights for a 2 1 ratio is the easiest and in my opinion make the best drawings the weights were each shaped from one solid piece of walnut cut from a large limb of the tree they are cylinders about 7 inches in diameter and 10 inches high with a one and a quarter inch hole drilled through the center in keeping with the idea of simple design the clamp to hold the weight in position was hidden worm gear radiator hose clamp was buried inside the center hole a dremel tool was used to reach inside and grind away wood to make room for the hose clamp a 3 8 inch hole was drilled from outside into the space so that a screwdriver could access the worm screw to adjust the clamp the weight rests on the worm screw bump on the clamp there are two basic configurations for this type of harmonograph fixed pen with moving paper or fixed paper with moving pen this harmonograph has moving paper attached to a 13 inch diameter table that swings with the pendulums the pin is attached to an arm that can only move up and down constrained by a pivot connected to the back wall with the other configuration the pin arm is connected to the pendulum so that it is constrained to move with the pendulum as well as move up and down a fixed table is mounted to the wall to hold the paper i've made both configurations and prefer the fixed pin with moving paper version because it's easier to hold the pen up while starting the pendulum swinging then slowly lowering the pen onto the moving paper with the other configuration it's difficult to hold the swinging pin without stressing the pen arm stress on the pin arm when the pin is lowered causes a few initial squiggles in the drawing it takes practice to do it well a disadvantage of the moving paper configuration is the pendulum structure needs to provide clearance for the pen as well as center line support for the lower pendulum in this case a single hook shaped curve was carved from a single piece of wood trying to make it as smooth and simple as possible the pen arm and wall mount were curved and shaped to look simple and smooth the wall mount has a hidden hole in the underside so it can be fastened to the wall in this case the wall is unsupported sheetrock so a sheetrock molly was used two headless brads were inserted into the back of the wall mount to keep it from rotating about the single anchor screw the two arms of the wall mount are about 12 inches long and thin enough so they can flex about a quarter of an inch at the end of each of these arms there is a quarter inch square piece of sheet brass glued to their insides the center punch was used to make dimples in these to provide a mating point for the pivots on the pen arm the pin arm pivot points are small headless nails pushed into the pin arm these pivots are adjusted so that the arms must be spread about one quarter inch to fit the distance between the pivot points the pin arm needs an adjustable counterweight to compensate for different pins and pin positions the counterweight is a wood cylinder about two inches in diameter and three inches long with a bent hole through its center this bent hole was made by drilling slightly off axis from each end so the bend can match the curve of the pin arm when properly aligned the weight can be easily moved to any position on the pin arm when in the proper position the weight can be rotated so that the bent hole interferes with the armband so the weight is held in place the pin is held in position on the pen arm by a clamp that was shaped from a piece of walnut the clamp has a horizontal hole that slides easily over the pin arm it also has a vertical pin hole that slightly intersects the armhole so that there is about a 3 8 inch opening where the holes intersect a threaded hole opposite this opening fits a plastic thumb screw when the clamp with the pin is properly positioned on the arm the thumb screw is tightened to hold everything in place the pendulum pivots were also designed to appear as simple as possible the upper and the lower pivots are identical the visible part of the pivot is a two and a quarter inch length of one inch inside diameter brass tubing the outside diameter is about one and an eighth inch which matches the diameter of the pendulum bars two pair of 1 8 inch holes were drilled in the tubing passing through its center axis one pair was 3 8 inch from the top the other pair was 3 8 inch from the bottom and perpendicular to the top pair a one and a half inch by .078 inch roll pin through a pair of holes are the pivot contact surfaces a one and a half inch by one quarter inch lag screw was used to connect the roll pin to the pendulum bar a 7 8 inch outside diameter washer held in place by the roll pin keeps the lag bolt centered the roll pins have bent because of use and the heavy load fortunately this bending also helps keep the lag bolts centered the lag bolts were screwed into holes drilled in the ends of the pendulum bars since the pivots are spaced about one and a half inches apart the left right period will be slightly different from the towards a weight period this causes the basic drawing shape to rotate with each cycle which usually causes the final drawings to have more depth and folds compared to pendulums with equal periods the harmonic graph was designed for an eight-foot ceiling the top pendulum bar is 52 inches long from top to bottom with the table about seven inches above its bottom the bottom pendulum is about 33 inches long the total height is about seven feet seven inches it is now installed in a house with nine foot ceilings so i made a new ceiling mount about 12 inches long the harmonograph weighs about 50 pounds too much for unsupported sheetrock fortunately there is a stud such that the harmonograph could be located 23 inches from the back wall and 21 inches from the sidewall a double ended lag screw was used to connect the ceiling mount to the ceiling joist over the years at least 100 people have made drawings with this hermonograph some of the best have been inspired by weekend water

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Length: 8min 23sec (503 seconds)

Published: Thu Apr 28 2022