Special motions of robot-manipulators.

*(English)*Zbl 0805.53009Summary: 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 [the author, Math. Pannonica 4, No. 2, 235-247 (1993; Zbl 0793.53011)], 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.

##### MSC:

53A17 | Differential geometric aspects in kinematics |

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\textit{A. Karger}, Appl. Math., Praha 39, No. 2, 127--136 (1994; Zbl 0805.53009)

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##### References:

[1] | Karger A.: Geometry of the motion of robot-manipulators. Manuscr. Math. 62 (1988), 115-126. · Zbl 0653.53007 · doi:10.1007/BF01258270 · eudml:155334 |

[2] | Karger A.: Classification of singular robot-manipulators. Submitted to Mech. Mach. Theory. · Zbl 0653.53007 |

[3] | Karger A.: Robot-manipulators as submanifolds. Submitted to Mathematica Pannonica. · Zbl 0793.53011 · eudml:229159 |

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