Hinge square

Rocker arm (Engl. Crank rocker). The base, whichcarriesthe two fixed bearings , is also known as the frame and counts as a member of the articulated polygon . See also the basic sketches in the figure below.

A four-bar linkage (English: four-bar linkage ) is an articulated quadrilateral, consisting of four members (e.g., rods ), which by hinges at their corners together to form a quadrangle are connected. Other designations are (closed) four-bar chain or four-membered kinematic chain .

Gearboxes formed from a four-bar linkage are called four-bar gearboxes .

The quadrangular joint can also be used for the mechanical representation of mathematical functions or movement assignments that have been empirically obtained from series of measurements.

Flat joint polygons, which are connected to one another exclusively via swivel joints , are movable when they

are connected via at most as many swivel joints as they have links and
none of its members are connected to form a triangle.

They then have a degree of movement ( degree of freedom ) greater than or equal to zero and are statically underdetermined . In contrast, an ideal framework is composed of statically determined link chains.

The four-bar linkage is the kinematic chain with the smallest number of links and only one driven link that executes a positive movement when one of the other links is a stationary frame . That is, if a link is fixed and one of the other links is rotated around one of its end points, then the third and fourth inevitably move with it in a fixed movement . Two drive movements are required from the pentagon.

Such mechanisms are used as coupling gear or, more precisely as a crank mechanism : (English crank-rocker linkage hereinafter).

The attached (frame) side is called the bridge, the two adjacent sides are called arms, the fourth side is the coupling (rod). All with the coupling points directly and indirectly fixed to hot crosspoints , their movements describe coupling curves (English: coupler curve ).

In order to determine whether one of the links can perform a complete rotation, one applies Grashof's rule , which states that in a flat quadrilateral joint, a continuous relative movement between two links is only possible if the sum of the lengths of the shortest and the longest link is smaller than the sum of the lengths of the other two links.

Articulated quadrilaterals (English: four-bar linkage). In the first and last figure two arms can rotate, in the second figure only the right arm and in the third figure none at all. Rotating arms are also known as cranks .

Many mechanisms in everyday life as well as in technology can be traced back to quadrilateral joints.

literature

Mareike Mink: Everywhere articulated quadrilaterals, in: Discovering geometry in technical applications; Learning environments for STEM lessons with everyday relevance . ISBN 978-3-658-19413-0

Individual evidence

↑ Kurt Rauh , Leo Hagedorn: Practical gear theory: first volume . Springer-Verlag, 1931, p. 11 ( full text in Google Book Search).
↑ Rudolf Beyer: Kinematic gear synthesis: Fundamentals of a quantitative gear theory of plane gears. For the designer, for lectures and self-study.
↑ Kurt Hain: Link gear construction: with small computers HP series 40 (HP 41C / CV) and HP series 80 (HP-83, HP-85, HP-86, HP-87) . Springer-Verlag, 2013, ISBN 978-3-663-14113-6 , pp. 14 ( google.de [accessed on January 21, 2019]).
↑ Hanfried Kerle, Burkhard Corves, Mathias Hüsing: Gear technology: Fundamentals, development and application of unevenly translating gear . Springer-Verlag, 2015, ISBN 978-3-658-10057-5 , pp. 33–43 ( google.de [accessed January 17, 2019]).
↑ Leo Hagedorn, Wolfgang Thonfeld, Adrian rankers: Constructive Getriebelehre . Springer-Verlag, 2013, ISBN 978-3-662-08167-9 , pp. 15 ( google.de [accessed on January 12, 2019]).
↑ Mareike MINT: Articulated Quadrilaterals - Recognizing Elementary Geometry in Everyday Technology. In: www.mathematik.uni-dortmund.de. Retrieved January 11, 2019 .
↑ Ahmed A. Shabana: Introduction to multi-body simulation . John Wiley & Sons, 2017, ISBN 978-3-527-67809-9 , pp. 130 ( google.de [accessed on January 12, 2019]).
^ Dubbel paperback for mechanical engineering . 16th, corrected and supplemented edition. Springer Berlin Heidelberg, 1987, ISBN 978-3-662-06778-9 , pp. 22 .

[1] Kurt Rauh , Leo Hagedorn: Practical gear theory: first volume . Springer-Verlag, 1931, p. 11 ( full text in Google Book Search).

[2] Rudolf Beyer: Kinematic gear synthesis: Fundamentals of a quantitative gear theory of plane gears. For the designer, for lectures and self-study.

[3] Kurt Hain: Link gear construction: with small computers HP series 40 (HP 41C / CV) and HP series 80 (HP-83, HP-85, HP-86, HP-87) . Springer-Verlag, 2013, ISBN 978-3-663-14113-6 , pp. 14 ( google.de [accessed on January 21, 2019]).

[4] Hanfried Kerle, Burkhard Corves, Mathias Hüsing: Gear technology: Fundamentals, development and application of unevenly translating gear . Springer-Verlag, 2015, ISBN 978-3-658-10057-5 , pp. 33–43 ( google.de [accessed January 17, 2019]).

[5] Leo Hagedorn, Wolfgang Thonfeld, Adrian rankers: Constructive Getriebelehre . Springer-Verlag, 2013, ISBN 978-3-662-08167-9 , pp. 15 ( google.de [accessed on January 12, 2019]).

[6] Mareike MINT: Articulated Quadrilaterals - Recognizing Elementary Geometry in Everyday Technology. In: www.mathematik.uni-dortmund.de. Retrieved January 11, 2019 .

[7] Ahmed A. Shabana: Introduction to multi-body simulation . John Wiley & Sons, 2017, ISBN 978-3-527-67809-9 , pp. 130 ( google.de [accessed on January 12, 2019]).

[8] Dubbel paperback for mechanical engineering . 16th, corrected and supplemented edition. Springer Berlin Heidelberg, 1987, ISBN 978-3-662-06778-9 , pp. 22 .