Geometric Error Modeling of 3-DOF Planar Parallel Manipulators Using Conformal Geometric Algebra

This paper proposes a geometrically intuitive error modeling method for planar parallel mechanisms (PPMs) based on conformal geometric algebra (CGA). First, the end point of each limb is determined through rotational transformations in geometric algebra. Using this point as the center, the kinematic geometry body (KGB) of each limb is constructed. The end-effector position of the parallel mechanism is then obtained via intersection operations in CGA, while its orientation is derived by constructing the motion plane from the end points. Finally, the error model of the parallel mechanism is established through differential operations. To validate the proposed method, a kinematic calibration simulation was performed using a 3-RPR planar parallel mechanism as an example. The simulation results demonstrate a significant reduction in both position and orientation errors after calibration, indicating a substantial improvement in accuracy and verifying the correctness of the approach.