Kinematic error modeling and identification of the over-constrained parallel kinematic machine

•The kinematic errors of the PKM are classified into four groups according to their property, which gives a more clear insight into the PKM's kinematic characteristics and contributes to the systematic kinematic error modeling.•The deformations of the parts and the static equilibrium condition are considered in the kinematic error modeling of the over-constrained PKM.•The least square method together with Regularization method has been utilized to identify the kinematic errors of the over-constrained PKM with the consideration of the kinematic chain's deformations.

Kinematic calibration has proved to be an effective method in improving the kinematic accuracy of the parallel kinematic machine (PKM). Though the PKM's kinematic calibration method has achieved substantial progress, its application is limited and can be only utilized in non-redundant PKM. Over-constrained PKM parts are forced to deform under redundant constraint forces to satisfy the assembly condition, which does not meet the assumptions made in the present PKM's kinematic calibration method in which all the parts are rigid. To deal with this issue, the present study investigates the kinematic error modeling and identification of the over-constrained PKM considering the deformations of the parts. A 2-DOF over-constrained PKM is taken as the object of study and its kinematic error model is derived based on the analyses of the link's deformations and the machine's static equilibrium condition. The method of least squares and the Regularization method are adopted to identify the kinematic errors of the over-constrained PKM. Finally, simulation analyses are carried out to verify the feasibility and effectiveness of the proposed method.