Damped Least Square (DLS) method has been widely used as an on-line algorithm for manipulator path tracking near and at singular configurations. Wampler (1986) formulated the framework of DLS method applied to velocity control and addressed the applicability of DLS method to acceleration control. The purpose of this paper is to demonstrate the differences in the joint paths generated by damped velocity and damped acceleration control algorithms in non-redundant manipulators. We examine these joint paths, find the cause of the differences, and demonstrate the features of damped acceleration control in non-redundant manipulator dynamics. Simulation results on a planar 2R and a spatial 6R manipulator moving through and near singular configurations verify the phenomena analyzed.