  We provide a complete classification of paradoxical closed-loop $n$-linkages,
where $n\geq6$, of mobility $n-4$ or higher, containing revolute, prismatic or
helical joints. We also explicitly write down strong necessary conditions for
$nR$-linkages of mobility $n-5$. Our main new tool is a geometric relation
between a linkage $L$ and another linkage $L'$ resulting from adding equations
to the configuration space of $L$. We then lift known classification results
for $L'$ to $L$ using this relation.
