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Schleifengleichung

English translation: loop equation

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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)

German term or phrase:	Schleifengleichung
English translation:	loop equation

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08:16 Jul 12, 2011

The asker opted for community grading. The question was closed on 2011-07-16 08:54:22 based on peer agreement (or, if there were too few peer comments, asker preference.)

German to English translations [PRO]
Tech/Engineering - Mathematics & Statistics / Mechatronik, Werkzeugmaschinen

German term or phrase: Schleifengleichung

Werkzeugmaschinen, Mechatronik

Kontext: "Aufstellung der Schleifengleichung im absoluten Koordinatensystem"
Stichwörter: Berechnung von Sigularitäten, Koordinatensystem, Weltkoordinaten, Antriebskoordinaten

Target: lecture for students of Mechanical Engineering, machine tools, mechatronics

SchindlerS KudoZ activity Questions: 16 (none open) Answers: 0
Local time: 00:58

loop equation

Explanation:
Siehe z. B. http://adcats.et.byu.edu/Publication/97-5/Adv_tol_chap-6_11a...
"9.1. Kinematic Constraint Equations

The mating conditions for 3-D assemblies require a variety of kinematic joints to describe the possible relative motions between mating parts. Fig. 12 shows a set that can handle a wide variety of assembly constraints. The kinematic degrees of freedom vary from zero for the rigid joint to five for the spherical slider and crossed cylinder joints.

The vector loop equations were derived for 2-D assemblies in Section 6. Each vector loop equation for 2-D assemblies resulted in three scalar equations, representing the sum of the x and y projections of the dimension vectors in global coordinates and the sum of the relative rotations.

In 3-D space, the system of equations is more complicated. Each vector loop equation for 3-D assemblies results in six scalar equations, representing the sum of the x, y and z projections of the dimension vectors in global coordinates and the sum of the relative rotations about the three global axes. The projection equations still hold in global x, y, and z, but the rotation constraints can only be expressed in matrix form."