This paper analyzes the possible contribution of actuation redundancy in obtaining very high acceleration with Parallel Kinematic Machines (PKM). This study is based on redundant and non-redundant Delta/Par4-like robots (frequently used for pick-and-place applications). The dynamic model, valid for both redundant and non-redundant robots, is used to analyze the traveling plate acceleration capabilities: (i) at zero speed and in any directions, (ii) at zero speed in the "best" direction. The results show that actuation redundancy allows to homogenize the dynamic capabilities throughout the workspace and to increase the traveling plate acceleration capability. Finally, the design of a redundant Delta/Par4-like robot optimized for typical pick-and-place trajectories is presented.