A New Theoretical Method for Solving Forward Kinematics of the Parallel Mechanisms Based on Transfer Matrix

The flexible parallel mechanism is widely utilized in precision instruments, thanks to its numerous advantages, such as high precision, frictionless operation, and seamless movements. The establishment of the motion equations for this mechanism is crucial for designing, analyzing, controlling, and simulating parallel mechanisms. While the existing inverse kinematics solution theory is comprehensive, developing a forward solution model is challenging due to the nonlinear nature of the attitude equation. To address this issue, a new method based on the transfer matrix approach is proposed in this research to calculate the forward kinematics of parallel mechanisms. The proposed method is applied to analyze the forward kinematics and workspace of both planar and spatial flexible mechanisms. Simulation calculations and experiments are conducted to verify the method’s effectiveness. The results demonstrate that the error is approximately 2%, indicating the feasibility and accuracy of the calculation method.