Ludwig Ernst Hans Burmester (5 May 1840 – 20 April 1927) was a German kinematician and

geometer A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * ...

. His doctoral thesis (from

German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...

: ''About the elements of a theory of

isophote In geometry, an isophote is a curve on an illuminated surface that connects points of equal brightness. One supposes that the illumination is done by parallel light and the brightness is measured by the following scalar product: :b(P)= \vec n(P) ...

s'') concerned lines on a surface defined by light direction. After a period as a teacher in

Łódź Łódź, also rendered in English as Lodz, is a city in central Poland and a former industrial centre. It is the capital of Łódź Voivodeship, and is located approximately south-west of Warsaw. The city's coat of arms is an example of canti ...

he became professor of synthetic geometry at

Dresden Dresden (, ; Upper Saxon: ''Dräsdn''; wen, label=Upper Sorbian, Drježdźany) is the capital city of the German state of Saxony and its second most populous city, after Leipzig. It is the 12th most populous city of Germany, the fourth larg ...

where his growing interest in kinematics culminated in his (''Textbook of Kinematics, First Volume, Planar Motion'') of 1888, developing the approach to the theory of

linkage Linkage may refer to: * ''Linkage'' (album), by J-pop singer Mami Kawada, released in 2010 *Linkage (graph theory), the maximum min-degree of any of its subgraphs *Linkage (horse), an American Thoroughbred racehorse * Linkage (hierarchical cluster ...

s introduced by

Franz Reuleaux Franz Reuleaux (; ; 30 September 1829 – 20 August 1905), was a German mechanical engineer and a lecturer of the Berlin Royal Technical Academy, later appointed as the President of the Academy. He was often called the father of kinematics. He wa ...

, whereby a

planar mechanism In engineering, a mechanism is a device that transforms input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components which may include: * Gears and gear trains; * Belts and chain ...

was understood as a collection of Euclidean planes in relative motion with one

degree of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...

. Burmester considered both the theory of planar kinematics and practically all actual mechanisms known in his time. In doing so, Burmester developed

Burmester theory In kinematics, Burmester theory comprises geometric techniques for synthesis of linkages. It was introduced in the late 19th century by Ludwig Burmester (1840–1927). His approach was to compute the geometric constraints of the linkage direct ...

which applies

projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pro ...

to the loci of points on planes moving in straight lines and in circles, where any motion may be understood in relation to four Burmester points. The Burmester linkage of 1888 is a four bar linkage part of whose coupler curve is an approximately straight line (see also

Watt's linkage In kinematics, Watt's linkage (also known as the parallel linkage) is a type of mechanical linkage invented by James Watt in which the central moving point of the linkage is constrained to travel on a nearly straight line. It was described in W ...

). Burmester is also known for his focal linkage, which is a highly over-constrained but movable linkage related to Kempe's focal linkage and Hart's straight line linkages. Burmester is the inventor of the

French curve A French curve is a template usually made from metal, wood or plastic composed of many different segments of the Euler spiral (aka the clothoid curve). It is used in manual drafting and in fashion design to draw smooth curves of varying radii. ...

; as such, a French curve may also be called a Burmester curve.

References

External links

*
Burmester linkage (see figure 12)
{{DEFAULTSORT:Burmester, Ludwig 1840 births 1927 deaths Geometers 19th-century German mathematicians 20th-century German mathematicians University of Göttingen alumni Technical University of Munich faculty