  We study projections onto non-degenerate one-dimensional families of lines
and planes in $\mathbb{R}^{3}$. Using the classical potential theoretic
approach of R. Kaufman, one can show that the Hausdorff dimension of at most
$1/2$-dimensional sets $B \subset \mathbb{R}^{3}$ is typically preserved under
one-dimensional families of projections onto lines. We improve the result by an
$\varepsilon$, proving that if $\dim_{\mathrm{H}} B = s > 1/2$, then the
packing dimension of the projections is almost surely at least $\sigma(s) >
1/2$. For projections onto planes, we obtain a similar bound, with the
threshold $1/2$ replaced by $1$. In the special case of self-similar sets $K
\subset \mathbb{R}^{3}$ without rotations, we obtain a full Marstrand type
projection theorem for one-parameter families of projections onto lines. The
$\dim_{\mathrm{H}} K \leq 1$ case of the result follows from recent work of M.
Hochman, but the $\dim_{\mathrm{H}} K > 1$ part is new: with this assumption,
we prove that the projections have positive length almost surely.
