  This study investigates the stiffness characteristics of the Sprint Z3 head,
also known as 3-PRS Parallel Kinematics Machines, which are among the most
extensively researched and viably successful manipulators for precision
machining applications. Despite the wealth of research on these robotic
manipulators, no previous work has demonstrated their stiffness performance
within the parasitic motion space. Such an undesired motion influences their
stiffness properties, as stiffness is configuration-dependent. Addressing this
gap, this paper develops a stiffness model that accounts for both the
velocity-level parasitic motion space and the regular workspace. Numerical
simulations are provided to illustrate the stiffness characteristics of the
manipulator across all considered spaces. The results indicate that the
stiffness profile within the parasitic motion space is both shallower and the
values are smaller when compared to the stiffness distribution across the
orientation workspace. This implies that evaluating a manipulator's performance
adequately requires assessing its ability to resist external loads during
parasitic motion. Therefore, comprehending this aspect is crucial for
redesigning components to enhance overall stiffness.
