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.

This paper presents a consistent analytic kinematic formulation of the 3-PRS parallel manipulator (PM) with a parasitic motion by embedding the velocity level structural constraint equation into the motion expression. Inverse rate kinematics (IRK) is solved with a simple constraint compatible velocity profile, which is obtained by projecting the instantaneous restriction space onto the motion space. Moreover, the systematic method to reveal the parasitic motion is introduced. Thus, the parasitic terms are automatically identified from the main motions. Unlike the usual approach, this study does not consider any explicit parasitic motion expression. Consequently, the derivation of constraint compatible input velocity, which comprises the parasitic term, is simplified. To incorporate the parasitic motion into the task velocity, constraint Jacobian of the manipulator is analytically obtained first. The manipulator Jacobian is extended to incorporate the passive joint’s information apart from the active joints and structural constraint. Hence, the dimension of the Jacobian matrix used to solve IRK is 9 × 6. The validity of the IRK is proved by the Bordered Gramian based forward rate kinematics (FRK). Then, an accurate numerical integration, RK4, is applied to the joint velocity of IRK to obtain the manipulator’s joint values. Consequently, the moving plate’s pose is obtained via forward position kinematics computed using integrated active and passive joint values for validation. The projection matrix used to get compatible constraint motion adjusts our input velocity and makes it compatible with the structural constraint policy, and the parasitic motion is embedded easily. Thus, an explicit formulation of the parasitic motion equation is not required, as the usual practice. Finally, the study presented numerical simulations to show the validity of the outlined resolutions. This paper’s result and analysis can be uniformly applied to other parallel manipulators with less than 6 DoFs.

Optimizing high-degree-of-freedom robotic manipulators requires searching complex, high-dimensional configuration spaces, a task that is computationally challenging for classical methods. This letter introduces a quantum-native framework that integrates Quantum Machine Learning (QML) with Grover's algorithm to solve kinematic optimization problems efficiently. A parameterized quantum circuit is trained to approximate the forward kinematics model, which then constructs an oracle to identify optimal configurations. Grover's algorithm leverages this oracle to provide a quadratic reduction in search complexity. Demonstrated on simulated 1-DoF, 2-DoF, and dual-arm manipulator tasks, the method achieves significant speedups—up to 93x over classical optimizers like Nelder-Mead—as problem dimensionality increases. This work establishes a foundational, quantum-native framework for robot kinematic optimization, effectively bridging quantum computing and robotics problems.