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Neutral wrenches of 3-parametric robot-manipulators of the spherical rank 1. (English) Zbl 1240.70009
Summary: Let \(SE(3)\) be the Lie group of all Euclidean motions in the Euclidean space \(E_3\), let \(se(3)\) be its Lie algebra and \(se^{*} (3)\) the space dual to \(se(3)\). This paper deals with structures of the subspaces of \(se^{*} (3)\) which are formed by all the forces whose power exerted on the robot effector is zero.
MSC:
70E60 Robot dynamics and control of rigid bodies
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References:
[1] J. Bakša: Three-parametric robot manipulator with parallel rotational axes. Appl. Math. 52 (2007), 303–319. · Zbl 1164.53310 · doi:10.1007/s10492-007-0016-3
[2] A. Dekrét, J. Bakša: Applications of line objects in robotics. Acta Univ. M. Belii, Ser. Math. 9 (2001), 29–42. · Zbl 1046.70004
[3] M. Fecko: Differential Geometry and Lie Groups for Physicists. Cambridge University Press, Cambridge, 2006. · Zbl 1121.53001
[4] A. Karger: Robot-manipulators as submanifolds. Math. Pannonica 4 (1993), 235–247. · Zbl 0793.53011
[5] J.M. Selig: Geometrical Methods in Robotics. Springer, New York, 1996. · Zbl 0861.93001
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