Compliance Analysis of a 3-DOF Spindle Head by Considering Gravitational Effects

The compliance modeling is one of the most significant issues in the stage of preliminary design for parallel kinematic machine（PKM）. The gravity ignored in traditional compliance analysis has a significant effect on pose accuracy of tool center point（TCP） when a PKM is horizontally placed. By taking gravity into account, this paper presents a semi-analytical approach for compliance analysis of a 3-DOF spindle head named the A3 head. The architecture behind the A3 head is a 3-RPS parallel mechanism having one translational and two rotational movement capabilities, which can be employed to form the main body of a 5-DOF hybrid kinematic machine especially designed for high-speed machining of large aircraft components. The force analysis is carried out by considering both the externally applied wrench imposed upon the platform as well as gravity of all moving components. Then, the deflection analysis is investigated to establish the relationship between the deflection twist and compliances of all joints and links using semi-analytical method. The merits of this approach lie in that platform deflection twist throughout the entire task workspace can be evaluated in a very efficient manner. The effectiveness of the proposed approach is verified by the FEA and experiment at different configurations and the results show that the discrepancy of the compliances is less than 0.04 μm/N^-1 and that of the deformations is less than 10μm. The computational and experimental results show that the deflection twist induced by gravity forces of the moving components has significant bearings on pose accuracy of the platform, providing an informative guidance for the improvement of the current design. The proposed approach can be easily applied to the compliance analysis of PKM by considering gravitational effects and to evaluate the deformation caused by gravity throughout the entire workspace.