Previous |  Up |  Next


robotics; Lie algebra; twist; wrench
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.
[1] Bakša, J.: Three-parametric robot manipulator with parallel rotational axes. Appl. Math. 52 (2007), 303-319. DOI 10.1007/s10492-007-0016-3 | MR 2324729
[2] Dekrét, A., Bakša, J.: Applications of line objects in robotics. Acta Univ. M. Belii, Ser. Math. 9 (2001), 29-42. MR 1935681 | Zbl 1046.70004
[3] Fecko, M.: Differential Geometry and Lie Groups for Physicists. Cambridge University Press Cambridge (2006). MR 2260667 | Zbl 1121.53001
[4] Karger, A.: Robot-manipulators as submanifolds. Math. Pannonica 4 (1993), 235-247. MR 1258929 | Zbl 0793.53011
[5] Selig, J. M.: Geometrical Methods in Robotics. Springer New York (1996). MR 1411680 | Zbl 0861.93001
Partner of
EuDML logo