  In this paper we consider the equiform motion of a helix in Euclidean space
$\mathbf{E}^7$. We study and analyze the corresponding kinematic three
dimensional surface under the hypothesis that its scalar curvature $\mathbf{K}$
is constant. Under this assumption, we prove that if the scalar curvature
$\mathbf{K}$ is constant, then $\mathbf{K}$ must equal zero.
