  We introduce six families of three-dimensional space-periodic steady
solenoidal flows, whose kinetic helicity density is zero at any point. Four
families are analytically defined. Flows in four families have zero helicity
spectrum. Sample flows from five families are used to demonstrate numerically
that neither zero kinetic helicity density, nor zero helicity spectrum prohibit
generation of large-scale magnetic field by the two most prominent dynamo
mechanisms: the magnetic $\alpha$-effect and negative eddy diffusivity. Our
computations also attest that such flows often generate small-scale field for
sufficiently small magnetic molecular diffusivity. These findings indicate that
kinetic helicity and helicity spectrum are not the quantities controlling the
dynamo properties of a flow regardless of whether scale separation is present
or not.
