Optimization of 3-DoF Manipulators' Parasitic Motion with the Instantaneous Restriction Space-Based Analytic Coupling Relation

This paper presents a velocity-level approach to optimizing the parasitic motion of 3-degrees of freedom (DoFs) parallel manipulators. To achieve this objective, we first systematically derive an analytical velocity-level parasitic motion equation as a primary step for the optimization. The paper utilizes an analytic structural constraint equation that describes the manipulator’s restriction space to formulate the parasitic motion equation via the task variable coupling relation. Then, the relevant geometric variables are identified from the analytic coupling equation. The Quasi-Newton method is used for the direction-specific minimization, i.e., optimizing either the x-axis or y-axis parasitic motion. The pattern-search algorithm is applied to optimize all parasitic terms from the workspace. The proposed approach equivalently describes the 3-PhRS, 3-PvRS, 3RPS manipulators. Moreover, other manipulators within a similar category can be equivalently expressed by the proposed method. Finally, the paper presents the resulting optimum configurations and numerical simulations to demonstrate the approach