10/8/2019 Three Pendulum Rotary Harmonograph Math
Simulating Harmonographs. Well the motion of a single damped pendulum along the x axis can be described by the parametric equation where t denotes time, p is a phase factor between 0 and 2.pi and d is the strength of the damping term. The larger you make d, the more quickly the pendulum oscillations will decay.
A harmonographA harmonograph is a mechanical apparatus that employs to create a geometric image. The drawings created typically are, or related drawings of greater complexity. The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890s, cannot be conclusively attributed to a single person, although, a professor of at the, is commonly believed to be the official inventor.A simple, so-called 'lateral' harmonograph uses two pendulums to control the movement of a relative to a drawing surface. One pendulum moves the pen back and forth along one axis and the other pendulum moves the drawing surface back and forth along a axis. By varying the and phase of the pendulums relative to one another, different patterns are created. Even a simple harmonograph as described can create, and other Lissajous figures.More complex harmonographs incorporate three or more pendulums or linked pendulums together (for example hanging one pendulum off another), or involve rotary motion in which one or more pendulums is mounted on to allow movement in any direction.A particular type of harmonograph, a pintograph, is based on the relative motion of two rotating disks, as illustrated in the links below (as opposed to a, a mechanical device used to enlarge figures). Turner, Steven (February 1997).
'Demonstrating Harmony: Some of the Many Devices Used To Produce Lissajous Curves Before the Oscilloscope'. 11 (42): 41. L.P.
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'Understanding Pendulums: A Brief Introduction'. Cite journal requires journal=. Gregory L. Baker and James A. Blackburn (2005). 'The Pendulum: a case study in physics'. Cite journal requires journal=.
and Mark W. Zemansky: University Physics, Third Edition, Addison-Wesley Publishing Company, 1964.External links.
Situation ProblemThe company “Blueworks” designscustomized displays for museums that are both interactive and educational. Wehave been contracted to assist the Ontario Science centre in the process of updatingits old exhibits and introducing new exhibits that will interest museum-goers.One of the new exhibits we have been contracted to design is a harmonographtable which displays the concepts of resonance and momentum in a visual manner.The participants in the exhibit will be able to use the harmonograph to producea drawing on a sheet of letter size paper. This drawing can then be removed andtaken as a souvenir, enhancing the interactivity of the exhibit. Theharmonograph exhibit will be primarily designed with durability andinteractivity in mind.
And will be composed of primarily maple hardwood whichwill benefit the durability and appearance of the exhibit. The production ofthis harmonograph will aid the museum by introducing a new interactive exhibitthat will interest museum-goers of all ages. Design BriefTheharmonograph will be designed with the use of AutoCAD software. After adetailed parts drawing has been produced, the amount of material needed will beassessed and purchased. Once the stock arrives, time will be spent squaring thestock and preparing the correct portions needed for part production. It is onlyafter the base parts have been manufactured that other secondary parts will bemanufactured. After all the parts have been checked for accuracy, assembly ofthe harmonograph will commence.
Once the harmonograph is fully assembled, afinish may be applied to help ensure the longevity of the exhibit. Research Internet Sites- How tomake a 3 pendulum harmonograph - Harmonographs- How tomake a 3 pendulum harmonograph- TheHarmonograph - VirtualHarmonograph - TheAmazing Harmonograph.
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