  We identify a pseudolocal conserved charge in the Fredkin and Motzkin quantum
spin chains and explore its consequences for the hydrodynamics of systems with
Fredkin- or Motzkin-type kinetic constraints. We use this quantity to formulate
an exact upper bound ${\cal O}(L^{-5/2})$ on the gap of the Fredkin and Motzkin
spin chains. Our results establish that transport in kinetically constrained
dynamical systems with Fredkin or Motzkin constraints is subdiffusive, with
dynamical exponent $z \geq 5/2$.
