A numerical error modeling method for parallel kinematic machines and its applications

Error model is the basis for accuracy-related computations and analyses for parallel kinematic machines (PKMs). Traditional error modeling methods are usually based on differentiation of kinematic solutions, but the solving process is often complex and has limitations for certain specialized PKMs. A concise numerical error modeling method with the inverse kinematic solution as its only requirement is presented in this paper. To avoid complex Jacobian matrix computations, the difference matrix that can be quickly calculated by kinematic solutions was used to replace the differential matrix. The quasi-Newton method, which has high speed and high precision, was introduced to solve the numerical forward kinematic problem. To verify the efficiency of this numerical error modeling method, three applications in error transformation matrix (ETM) modeling, error analysis, and kinematic calibration were simulated on a 4RRR PKM. A comparison with the results obtained by the traditional method shows that the numerical method is accurate, convenient, and has lower requirements and wider applicability, especially for certain specialized and manufactured PKMs.