# Author Archives: kristian morse

MArch student at McGill University

# Exercise 3: Drawing machine – deconstructing a 2-D image

Our initial research focused on several drawing machines from the Renaissance such as Jacopo Barozzi da Vignola’s Bi-Dimensional perspectograph (developed between 1527-1545), Jacques Besson’s Drawing Machine from Theatrum instrumentorum et machinarum (1578), Albrecht Dürer’s perspectograph (Dürer’s Door – 1525) and other machines that have since been reiterated by people such as JH Lambert in 1752 and recently for purposes of abstract art by Eske Rex.

Inspired in most part by a machine developed by an unknown artist we saw on the internet, we became interested in developing a drawing machine that would generate the cams that could produce a 2-D drawing.

A cam changes the input motion, which is usually rotary, to a reciprocating motion of the follower. Cams can be shaped to change the way the follower moves. The shape of the cam is called the profile. If a cam rotates clockwise, the movement of the follower in 1 would be a gradual rise and fall motion for each rotation; the follower in 2 would rise and fall twice for each rotation; in 3, the follower would be motionless for half the cycle and then rise and fall; and the follower in 4 would rise gradually and then fall suddenly. Note that 1, 2 and 3 would have the same result if the cam was rotating anticlockwise; 3 would jam. These aren’t the only shapes you can use. Anything goes…depending on what sort of motion you want…though there are practical limitations to making these things out of wood.

Our drawing machine, thus, acts to develop a shape (not necessarily circular) that would deconstruct a drawing into horizontal and vertical data. Theoretically, this data could in turn be plugged back into the process to generate the original drawing.

Next we decided to fabricate a machine that would automate step two. For this to occur, a series of gears would navigate two arms vertically and horizontally. These arms are connected to the “master” pen that traces a 2-dimensional drawing. The veritcal and horixzontal arms hold pens to record data on a moving canvas. We decided to deconstruct Henri Matisse’s “Blue Nude” (1952). Matisse’s painting is a rather simple outline of 2-Dimensional figure, one that would be fairly easy to trace with our machine. Furthermore, we were intrigued to see the outcome that would occur by deconstructing an already semi-abstract painting.

# Research and preliminary proposal

For my project I have narrowed my research to two main fields of interest:

1/ In researching ancient drawing machines, I came across a website that contains replications from an exhibition that belongs to the collection “Theatrum Machinarum” at the University of Modena and Reggio Emilia, Mathematics department. All the models, also the ones reproducing machines that have been largely used in the past (since the 15th century) to carry out a number of different activities (painting, architecture, design, cartography, military art, etc), have been constructed with a “didactical intention, in order to introduce a historical discourse about perspective constructions and the mathematics of central projections”

The perspectograph, in particular, is a famous instrument that allows one to obtain a correct perspective drawing of a threedimensional object. Painters and architects including Leon Battista Alberti in the 16th and 17th centuries used Perspectographs. Some types of perspectographs are very simple (as these reproduced in Dürer’s perspectograph), some types are rather complex.

Jacopo Barozzi da Vignola’s Bi-Dimensional perspectograph (developed between 1527-1545) uses two rulers, one fixed in the vanishing point and the other one in the point at a distance (both on the horizon line), many dead lines (to be deleted after the drawing is finished), which would appear if following the Second Rule, will not be needed. The premise for this device has been reiterated by JH Lambert in 1752 and recently employed for purposes of abstract art rather than perspective by Eske Rex.

2/ Gimbal: I find this device intriguing because it is not clear who invented the object but it has been used countless times in navigational devices, in telescopes, lighting devices, etc.

Drawing of a compass supported by gimbals (1570)

The Gimbal is essentially a pivoted support that allows the rotation of an object about a single axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of the rotation of its support.

The device is beautiful in its construction, as it seems to enact the rotation of the cosmos while allowing itself to be useful in numerous, everyday tasks.

Research and Bibliography

http://www.rarebookroom.org/

http://archiviomacmat.unimore.it/PAWeb/Sito/Inglese/Templatei.htm

Sawday, Jonathan. Engines of the Imagination: renaissance culture and the rise of the machine. New York: Routledge, 2007.

# The Horizon: Alberti’s Delineation of Rome

Alberti’s survey of Rome records the passage and lineamenta (outline) of certain features in the city of Rome including: walls, rivers, streets, hills, and buildings, as well as the locations of temples, public works, gates, and monuments.
The device is made up of two main components: the Horizon and the Spoke.
The Horizon is the circle within which the depiction of the city is enclosed. The Horizon is divided into equal degrees (up to 48) and then subdivided into four parts called minutes. The north will be marked at degree 0, the eastern equinox will be at 12, south at 24, and the west equinox at 36.
The Spoke is a straight rod much like an hour hand that is set at the centre of the horizon and extends to its outer circumference. The spoke is divided into 50 equal parts, similarly called degrees.
Once the device is made, the process of tracing the map involves identifying the degrees and minutes in the accompanying table that correspond with a title. These numbers will be used to guide the horizon and the spoke simultaneously to find the titles coordinates.
For example, if we start in the table labeled “Walls of Litium”, under “Horizon” we read: “43 degrees, 2 minutes”. Therefore we position the spoke at this number on the horizon. Next, under “Spoke” we read: “31 degrees, ½ minute”. Therefore, we locate this number on the spoke and we draw a dot at this coordinate. At the end we connect all the coordinates with a straight line, giving us the passage or lineamenta of the wall of Litium.

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