  A major challenge in the study of active systems is to harness their
non-equilibrium dynamics into useful work. We address this by showing how to
design colloids with controllable spontaneous propulsion or rotation when
immersed in active nematics. This is illustrated for discs with tilted
anchoring and chiral cogs, for which we determine the nematic director through
conformal mappings. Our analysis identifies two regimes of behaviour for chiral
cogs: orientation-dependent handedness and persistent active rotation. Finally,
we provide design principles for active nematic colloids to achieve desired
rotational dynamics.
