Let $SE\left(3\right)$ be the Lie group of all Euclidean motions in the Euclidean space $E_3$, let $se\left(3\right)$ be its Lie algebra and $s{e}^{*}\left(3\right)$ the space dual to $se\left(3\right)$. This paper deals with structures of the subspaces of $s{e}^{*}\left(3\right)$ which are formed by all the forces whose power exerted on the robot effector is zero.