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.

翻译：本文研究了Sprint Z3主轴头（亦称3-PRS并联运动机构）的刚度特性，该机构是精密加工应用领域研究最深入且成功应用最广泛的机械臂之一。尽管针对此类机器人机构已有大量研究成果，但尚无文献揭示其在寄生运动空间内的刚度性能。由于刚度具有构型依赖性，这种非期望运动会对其刚度特性产生影响。为填补这一研究空白，本文构建了同时包含速度级寄生运动空间与常规工作空间的刚度模型。通过数值仿真展示了该机械臂在所有考虑空间内的刚度特性。结果表明：与定向工作空间内的刚度分布相比，寄生运动空间内的刚度曲线更为平缓且幅值更小。这意味着充分评估机械臂性能需要考察其在寄生运动过程中抵抗外载荷的能力。因此，理解该特性对于重新设计零部件以提升整体刚度至关重要。