Effect of Spherical Joint Symmetry Axis Orientation on the Kinematic Performance of Lower Mobility Parallel Manipulators

Parallel manipulators (PMs) are often used as parallel kinematic machines (PKMs), which are more accurate and have more payload capacity compared to their serial counterparts. Spherical joints are frequently used in the construction of PKMs; however, spherical joints have a unique physical constraint, known as cone angle limit, around their axis of symmetry. The present work investigates the effect of changing the orientation of the spherical joint symmetry axis (SJSA) on the kinematic performance of PMs. Workspace index, global conditioning index, kinematic conditioning index and global stiffness index are chosen as performance indices. It is found that changing the orientation of SJSA has a remarkable impact on the kinematic performance of PMs. Also, it is shown that considering the cone angle limits considerably affect the kinematic performance of PMs. To demonstrate the results, two PMs, namely 3-PRS (P, R, and S denote prismatic, revolute, and spherical joints, respectively) and 3-RPS manipulators with spherical joints with adjustable axis of symmetry orientation, are used. The effect of changing SJSA orientation on various performance indices is carried out, and optimal orientation values are determined. Genetic algorithm (GA) optimization technique and traditional method are used. The results obtained using the two methods matched very well. It is found that orientation of the SJSA is one of the important PMs optimization parameters that should be considered during the design process.