Parallel mechanisms frequently contain an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. By altering the mechanism through, for example, additional kinematic linkages, the singularity can be modified or even removed. Another approach is to actuate certain unactuated degrees of freedom. The manipulability is guaranteed to improve over the original mechanism, but the mechanism is now over-actuated. By studying a recently proposed parallel machining center, we examine the effectiveness of singularity modification through redundant actuation. As a metric, we use the condition number of the recently developed manipulability ellipsoid for general parallel mechanisms.