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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.

The external derivative $d$ on differential manifolds inspires graded operators on complexes of spaces ${\Lambda }^r{g}^{*}$, ${\Lambda }^r{g}^{*}\otimes g$, ${\Lambda }^r{g}^{*}\otimes g^{*}$ stated by $g^{*}$ dual to a Lie algebra $g$. Cohomological properties of these operators are studied in the case of the Lie algebra $g=se\left(3\right)$ of the Lie group of Euclidean motions.