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Date: 1959

Inventory Number: 1990-5-0030

Classification: Mathematical Model

Subject:

Maker: Walter Balcke

Cultural Region:

Place of Origin:

City of Use:

Dimensions:

1.7 x 20.8 x 13.3 cm (11/16 x 8 3/16 x 5 1/4 in.)

Material:

Accessories: in library folder (Lib 4927):
-twenty-one letters from Joseph L. Walsh, mathematics professor at Harvard University, to Walter Balcke, dated between 27 May 1957 and 24 January 1964 (letters thank Balcke for the many mathematical models he gifted to the Mathematics Department, praise his skill and ingenuity, many invite him to faculty and personal luncheons, and one letter provides an analytic solution to the "13-point problem" behind one of Balcke's models)
- one letter from J.L. Walsh pertains directly to this object, dated April 21, 1959
-three letters from Garret Birkhoff (then Chairman of the Harvard Mathematics Department) dated 3 March 1954, 4 January 1955, and 10 January 1955, each expressing gratitude (and in one case, an official department thank you) for the many mathematical models he gifted to the mathematics department
-photocopy of original envelope in which correspondence between mathematics department and Walter Balcke was stored (original was destroyed on 13 July 1997)
-photocopy of instructional card for object 1997-1-1671
- seven instructional cards that accompany the following Balcke models: Pascal's Theorem, Brianchon's Concurrent Lines, Trisector, Twelve Point Ellipse, Rolling Parabola, unknown, Equation Solution with a 'Constant' Variable and Thread
- photograph of the display case containing Balcke's models in the Harvard Mathematics department

DescriptionThe model is mounted in a rectangular mahogany frame. The frame is backed by a rectangular black plastic panel. A panel of plexiglass is mounted on the front of the frame. The model itself is constituted of partly transparent, white plastic parts. There is a track along the top edge of the model frame, with rounded edges and a thin slit cut the full length. A small red pin slides horizontally along the track. It is attached to a hole in a short arm with three other holes. Two holes have cross beams fitted in them that attach this arm to another, parallel and identical arm. One hole in each of these arms, that does not serve to attach them together, attaches to another arm that begins thin and becomes thicker towards the bottom of the model. Each of these arms ends with a half-circle hook fixed to a pivot near the bottom edge of the frame. The final, fourth hole of the second parallel straight arm is attached to a circular component with a second tier circle of slightly less diameter and with geared teeth.

Signedunsigned

Inscribedtyped in black ink on an off-white label in bottom left-hand corner of model frame: PEAUCELLIER'S STRAIGHT LINE / 1864

FunctionThe Peaucellier-Lipkin linkage was originally invented independently by Charles-Nicolas Peaucellier, a French Army Officer and Engineer and Yom Tov Lipman Lipkin, a Lithuanian applied mathematician. The linkage was designed to create perfect straight linear motion without the need for guides or tracks. The friction generated by guides and tracks in industrial machines produced short life-spans, fatigue, and erosion of machine components. This demonstration apparatus is a modification of the linkage design, producing linear motion along the track at the top edge through motion transfer among the arms below. The geared circular component is the origin of the circular motion: users manually turn the circle and that motion is transferred through the arms and joints into linear motion along the top.

Walter Balcke built and gifted many mathematical models to the Harvard Mathematics department at Harvard University. According to substantial correspondence between mathematics professors and Balcke, the models were sometimes used in classes, circulated around the department for observation, and eventually put on display in the mathematics library.

A discussion of the history and functioning of the Peaucellier-Lipkin linkage, including a helpful animation, is available here.

Walter Balcke built and gifted many mathematical models to the Harvard Mathematics department at Harvard University. According to substantial correspondence between mathematics professors and Balcke, the models were sometimes used in classes, circulated around the department for observation, and eventually put on display in the mathematics library.

A discussion of the history and functioning of the Peaucellier-Lipkin linkage, including a helpful animation, is available here.

Curatorial RemarksThis object is clearly visible in a Polaroid photograph taken in August 1961. The photograph is labeled "Exhibit of mathematical models and devices designed and constructed by Mr. Walter H. Balcke of Winchester, Mass. Department of Mathematics, Harvard University. August 1961" (in Lib. 4927). The display was set up in the Harvard Mathematics Department Library.

ProvenanceFrom the Department of Mathematics, Harvard University.

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