 Solution

A holonomic constraint can be written as an equation $f(q_1,\dots ,q_n,t)=0$ involving coordinates and possibly time, without an irreducible dependence on velocities. For example a particle confined to a fixed sphere obeys $x^2+y^2+z^2-a^2=0$. A general rolling without slipping constraint in three dimensions need not be integrable into such a coordinate equation.