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Special motions of robot-manipulators. (English) Zbl 0805.53009
Summary: 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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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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