Modeling of Position and Pose Error of Stewart Machine Tool Based on D-H Transforming Matrix

Abstract

The kinematical equation of the moving platform of Stewart parallel machine tool is established with D-H transformation matrix,the equation contains the pose parameters of hinge joints and the D-H parameters of component parts in all branches of parallel mechanism. Based on the equation,an new computation model of position-pose error of parallel machine tool is set up by means of the differential method of matrix. It is demonstrated that not only the effects of all geometrical parameter errors on the accuracy of machine tool are reflected in the model,but also the linear,explicit formula are derived approximately from the nonlinear,implicit correlation between machine position-pose error and all geometric errors. To verify the linear model,another model is derived from the length formula of branches of mechanism,which can reflect much exactly the nonlinear correlation between machine position-pose error and all geometric errors. A simulation demonstrates the effectiveness of linear model because its results approximate satisfactorily those of nonlinear model. Therefore the linear model can be applied to Stewart type parallel machine tool in accuracy analysis or integration,and kinematical identification due to its advantages in analysis. The simulation also demonstrates that the influence of all D-H geometric errors on the machine tool position and pose should be considered when high accuracy of the position and pose is required.