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kinematics; robotics; kinematical chains; Bennet’s mechanism; freedom of motion; robot- manipulators
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.
[1] Karger A.: Geometry of the motion of robot-manipulators. Manuscr. Math. 62 (1988), 115–126. DOI 10.1007/BF01258270 | MR 0958256 | Zbl 0653.53007
[2] Karger A.: Classification of singular robot-manipulators. Submitted to Mech. Mach. Theory.
[3] Karger A.: Robot-manipulators as submanifolds. Submitted to Mathematica Pannonica. Zbl 0793.53011
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