The Stiffness of 3-PRS PM Across Parasitic and Orientational Workspace

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.

Unveiling the Complete Variant of Spherical Robots

This study presents a systematic enumeration of spherical ($SO(3)$) type parallel robots' variants using an analytical velocity-level approach. These robots are known for their ability to perform arbitrary rotations around a fixed point, making them suitable for numerous applications. Despite their architectural diversity, existing research has predominantly approached them on a case-by-case basis. This approach hinders the exploration of all possible variants, thereby limiting the benefits derived from architectural diversity. By employing a generalized analytical approach through the reciprocal screw method, we systematically explore all the kinematic conditions for limbs yielding $SO(3)$ motion.Consequently, all 73 possible types of non-redundant limbs suitable for generating the target $SO(3)$ motion are identified. The approach involves performing an in-depth algebraic motion-constraint analysis and identifying common characteristics among different variants. This leads us to systematically explore all 73 symmetric and 5256 asymmetric variants, which in turn become a total of 5329, each potentially having different workspace capability, stiffness performance, and dynamics. Hence, having all these variants can facilitate the innovation of novel spherical robots and help us easily find the best and optimal ones for our specific applications.