Sylvester-Kempe Inversor, Kinematic Model by Martin Schilling, series 24, model 12, number 351
date: label: date made
content: ca 1900
name: label: maker
content: Schilling, Martin
notes: label: Description
content: Around 1900, American mathematicians introduced ideas to their students using physical models like this one. This model is the twelfth in a series of kinematic models sold by the German firm of Schilling to show a mechanical method for generating mathematical curves.
label: Description
content: Linkages are joined rods that move freely about pivot points. A pair of fireplace pincers is an example of a very simple linkage. Producing straight-line motion was an important component of many machines. But producing true linear motion is very difficult and one area of research during the 19th century was to use linkages to produce linear motion from circular motion. In this context, “Inverse” is a geometric term that refers to the process of using algebra and trigonometry to convert or invert one geometric shape into another. In this case, the inverse of the circle will be a straight line. So an “inversor” is a device that finds the inverse of a geometrical object: the conversion of a circle to a straight line in the case of this model.
label: Description
content: A generalization of Hart’s Inversor, the Sylvester-Kempe Inversor is also known as a Quadruplane inversor and creates linear motion from circular motion. English mathematicians James Sylvester (1814-1897) and Alfred Kempe (1849-1922) developed the geometric theory behind these linkages in the 1870s. Kempe proved that every algebraic curve can be generated by a linkage using a Watt’s curve, after Scottish engineer James Watt (1736-1819).
label: Description
content: Unlike the other Schilling linkages in the collection, this one is not made of armatures. It consists of linked triangular metal plates (two large and two small). The smallest triangle is attached to the baseplate at a stationary pivot point. The triangles are linked together at the vertices to form a chain of triangles (small-large-small-large). As with the other linkages, this model has an armature that is attached to a small hand crank on the underside of the baseplate and attached to the vertex of one of the larger triangles that allows the linkage to rotate. It can also be moved by using one of two fingerholds attached to the top of two of the triangles at a vertex.
label: Description
content: As the linkage is rotated, a pin where the armature attaches to the large triangle traces out a circle, visible in the image. At the same time, a pin under the fingerhold on the opposite large triangle traces a straight line from left to right across the baseplate, also seen in the image. The German title of this model is: Inversor von Sylvester und Kempe. The nameplate on the model gives a date of 1875 for this model, most likely the date of discovery by Sylvester and Kempe.
label: Description
content: Reference:
label: Description
content: Schilling, Martin, <i>Catalog Mathematischer Modelle für den höheren mathatischen Unterricht</i>, Halle a.s., Germany, 1911, pp. 56-57. Series 24, group IV, model 12.
label: Location
content: Currently not on view
place: label: place made
content: Germany
topic: label: Subject
content: Mathematics
label: Subject
content: Engineering
setName: label: See more items in
content: Medicine and Science: Mathematics
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content: Science & Mathematics
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content: Kinematic Models
creditLine: label: Credit Line
content: Gift of the Department of Mathematics, The University of Michigan
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 1982.0795.09
label: catalog number
content: 1982.0795.09
label: accession number
content: 1982.0795
objectType: label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: metal (overall material)
label: Physical Description
content: paper (overall material)
label: Physical Description
content: leather (overall material)
label: Measurements
content: overall: 5 cm x 25 cm x 20 cm; 1 31/32 in x 9 27/32 in x 7 7/8 in