Closed-form solutions were developed to optimize kinematics design of a 2-degree-of-freedom (2-DOF) planar parallel manipulator. The optimum design based on the workspace was presented. Meanwhile, a global, comprehensive conditioning index was introduced to evaluate the kinematic designs. The optimal parallel manipulator is incorporated into a 5-DOF hybrid machine tool which includes a 2-DOF rotational milling head and a long movement worktable. The results show that the planar parallel manipulator-based machine tool can be successfully used to machine blades and guide vanes for a hydraulic turbine.

General QR decomposition of the observation matrix is used to solve identification functions to evaluate identification results of every parameter in parallel mechanism calibrations. A relationship between measured information and identification results is obtained by analyzing numerous matrix transforms and QR decompositions. When distributions of measurement error are determined, random distributions of identification result disturbances (IRDs) can be obtained from this relationship as a function of measurement errors. Then the ranges of the IRDs can be effectively estimated, even if true parameter values are unknown. An optimization index based on IRD estimate is presented to select measurement configurations to achieve smaller IRDs. Two simulation examples were carried out with different modes and calibration methods. The results show that the method is effective and that the optimization index is useful. Some regular parameter identification problems can be explained by the IRD estimates.