Geodesic
Special motions of robot-manipulators
Applications of Mathematics, Tome 39 (1994) no. 2, pp. 127-136.

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There exist many examples of closed kinematical chains which have a freedom of motion, but there are very few systematical results in this direction. This paper is devoted to the systematical treatment of 4-parametric closed kinematical chains and we show that the so called Bennet’s mechanism is essentially the only 4-parametric closed kinematical chain which has the freedom of motion. According to [3] this question is connected with the problem of existence of asymptotic geodesic lines on robot-manipulators considered as submanifolds of a pseudo-Riemannian space. All computations were performed by the help of a formal manipulation system on a PC-computer.
DOI : 10.21136/AM.1994.134249
Classification : 53A17, 70B15, 93C85
Keywords: kinematics; robotics; kinematical chains; Bennet’s mechanism; freedom of motion; robot- manipulators 
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Karger, Adolf. Special motions of robot-manipulators. Applications of Mathematics, Tome 39 (1994) no. 2, pp. 127-136. doi : 10.21136/AM.1994.134249. http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134249/

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