A Most Unusual Harmonograph

this harmonograph is the result of a self-challenge to design and make the most unusual configuration i could think of i also wanted it to be a display piece that was as amusing and interesting as i could make it i was willing to challenge my woodworking skills and try some new techniques i like the modern aesthetic of a simple and unadorned structure with smooth curves and a minimum of straight lines and corners appearance was the primary goal withdrawing quality a low priority it is constructed mostly from thick walnut stock walnut veneered quarter inch plywood and about 200 pounds of lead and steel for weight it hangs from a wall mounted structure that sticks out about 7 inches from the wall it has four pendulums that move parallel to the wall two pendulums move vertically up and down like a seesaw the two other pendulums move horizontally left and right like a swing a 16 inch diameter weight wheel 3.5 inches deep is connected to the right end of the pendulum bar of the first vertical pendulum the left end of this bar supports the pivot for the first horizontal pendulum the first vertical pendulum pivots on a knife edge that mace with a v-shaped groove in the brass bar that is part of the wall mounted structure top end of the first horizontal pendulum bar is connected to a second weight wheel its pivot is in the middle at the bottom end of this bar is the pivot for the second vertical pendulum the left end of the second vertical pendulum bar is connected to a third weight wheel its pivot is in the middle at the right end of this bar is the pivot for the second horizontal pendulum at the top of the second horizontal pendulum bar is a fourth weight wheel 16 inches in diameter and one and three quarter inches deep this wheel also has the paper holder and drawing surface at the bottom of this bar is a fifth weight wheel same size as the paper wheel each pendulum provides the pivot location for the next pendulum the movements of each pendulum combine to produce the movement of the drawing surface on the second vertical pendulum viewed from the side the first three pendulums move in a plane parallel to the wall about eight inches away the second horizontal pendulum bar is slanted so that the drawing surface moves on a plane about 11 inches from the wall so it clears the pivot of the first vertical pendulum this slanted bar causes the bottom weight wheel to move in a plane about 5 inches from the wall this configuration of pendulums was tricky to balance and tune since the pendulums are tightly coupled once built adjustments could only be made inside the weight wheels by changing the amount of weight and the height of the weight during the design phase i built a roof prototype to determine the pendulum links pivot locations weights and their heights relative to their pivots i discovered steel was not dense enough to provide the needed weight so lead was used for some of the weights most of the space in the first vertical pendulum weight wheel was needed to hold the necessary weight so not much vertical adjustment was possible there was more adjustment room in the other weight wheels for example this is the first horizontal pendulum based on my previous experiences i wanted the periods of the first two pendulums to be twice as long as the periods of the last two pendulums i also wanted the pendulums to swing slower than might be expected considering the relatively short links of the pendulum bars the design targets were a 5 second period for the first two pendulums and a 2.5 second period for the last two pendulums since the pendulums are tightly coupled energy is transferred between them if any one of the pendulums is moved the other three will soon be moving when all of the pendulums are moving energy is continually transferred between them this tight coupling also makes all of the periods unstable for ratios other than one to one i initially used the stopwatch to measure the periods while tuning this took a long time to get accurate measurements and these were not reproducible i finally mounted an accelerometer on each pendulum to precisely measure its period this verified the instability of the system all of the drawings have similar shapes from one cycle to the next but these change significantly each cycle so there is a lot of irregular space between the lines all of the drawings look more chaotic than those from other homanographs that are well tuned i spent a lot of time trying to make the harmonograph look like a sculpture with applying high quality furniture finish for example the paper holding wheel has a lever connected to a hidden mechanism that allows the paper to be easily inserted into a slot in the side of the wheel moving the lever then locks the paper in place the paper access slot in the side of the wheel has a veneer edge to hide the end grain of the plywood the weight wheels are constructed to minimize exposed end grain and to make the glue joints thin and tight eight mitered pieces of two by three and three-quarter inch walnut stock were glued together to form an octagon about 17 inches across three of these were used to make the first three weight wheels two by two inch stock was used to make two more octagons for the paper pendulum wheels lathe was not large enough to turn these octagons into cylinders i made some templates and jigs so a router could be used these have water stains and rot after spending about 20 years in the crawl space the first template made with the sides of the octagon and guided the router to make a 15 inch diameter hole inside of the octagon this hole was made about 5 16 inch deep so one quarter inch plywood disk could be inserted to make the side of the wheels these octagons were then shaped into cylinders using a jig that held the router while the octagon was rotated under the router bit two three-quarter inch plywood discs were cut to tightly fit into the holes cut in the octagon side a long axle passed through the center of these discs one under the axle was a one-half inch by 13 threaded rod about six inches long the other end of the axle was a smooth one-half inch rod about 10 inches long these discs were held in place by wood screws that went through one disc and screwed into the other this assembly of the octagon discs and axle fit into the jig the router was adjusted so the end of the cutting bit was 8 inches from the center axis this assembly moved 1 13 inch per rotation along its axis which fed the octagon into the router bit the joint between the weight wheel and the expanded end of a pendulum bar needed to be tight for both strength and appearance i made a 16 inch drum sander for my multi-function shop tool to quickly make this joint i used the wheel jig to make the drama so it exactly matched the weight wheels the pin holder was the most complex and difficult to make i wanted it to look like it was a single piece of bent wood and steam bending is a way to achieve this however one inch walnut is difficult to bend to a radius of about three inches the bending was even more difficult because there were two different convex bends my research and experiment showed that the thickest board that could be bent to the desired shape was about one quarter inch thick the pen holder starting shape was made using four pieces of one-quarter inch walnut five inches wide and 54 inches long these pieces were cut from a single piece of half inch thick stock and kept in order so the end grain matched when reassembled each piece was bent separately using this custom jig the piece of mdf is about the same size as the walnut pieces used the jig constrains the length so all bending is accomplished by compressing the wood fibers otherwise the wood would tear and fray after steaming for about 30 minutes the board was placed in the bending jig and the constraining sheets adjusted so the end stops were tight against the board ends then the wood was bent by moving the straight end pieces around the curved forms and clamping the ends in place here the mdf was not stained so it broke when bent the bent piece was left in the jig for about 24 hours to dry all four pieces were bent the same way using bolts and cross pieces as clamps the same jig was used to glue the four pieces together after thorough drying this piece was shaped and cut to make the pen arm and arm holder this piece also functions as a brace for the beam that connects the wall mount to the stationary part of the pivot for the first vertical pendulum this beam was actually two pieces made to look like a single piece that pierces the arm holder these pieces were held together by a long leg screw that went through holes in the wall mount the first beam piece the arm holder and finally screwed into the second beam piece the moving parts of the pivot were a one and a quarter inch wide piece of hard steel knife edge on one part that set into a v-shaped groove in brass on the other part the pivot hardware for the first vertical pendulum was shaped from pieces of 1 8 inch polished brass stock the vertical part of the pivot was one and a half inch wide and epoxied into a mortise in the end of the wall mount bar the other part of the pivot was two inches wide and recessed flat into the center of the pendulum bar held in place by four wood screws a volume under the slot in this plate was removed to make room for the moving parts plates at the ends of the pendulum bars are epoxied into mortises and have the v-groove part of the pivot when these plates are vertical a three-eighths inch long piece of plate stock is soldered to the bottom end to make a shelf and the v-groove cut into its top recessed plates at the middle of the pendulum bars have steel knife edges attached with high temperature solder the plates are attached to the bars using two wood screws during the six months after construction two separate failures caused all the pendulums to fall to the floor first the pivot in the middle of the first vertical pendulum pulled out of the mortise in the wall mount apparently the epoxy did not set up properly because it was contaminated or too old it was fairly easy to repair everything and reassemble the harmonograph then a few months later the first vertical pendulum bar broke in half at the pivot the wood failed because too much wood was removed fitting the recessed plate and making room for the pivot parts the bar was completely rebuilt using new wood the recessed plate also was redesigned to strengthen the bar at this pivot i spent about 300 hours designing constructing tuning and repairing this harmonograph it was a significant effort but fulfilled my original goals i'm committed to believing it was worth it i optimistically kept all the jigs i used to build it but now that they're documented i'm going to throw them away i don't want to build another one and i would not encourage anyone else unless they are masochistic or very very easily amused

Channel: gyrogearjammed

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Id: 7Dp-S770wYw

Length: 11min 24sec (684 seconds)

Published: Thu May 05 2022