Heavy-load Nonapod: A novel flexible redundant parallel kinematic machine for multi-DoF forming process

The high-performance multi-DoF forming process (MDFP) necessitates a 6-DoF forming machine tool with high normal and lateral stiffness to bear large normal and lateral forming force of millions of Newton (MN). However, the payload of parallel kinematic machine (PKM) is generally limited to thousands of Newton (kN), which restricts its application in MDFP. Therefore, this paper aims to develop a novel heavy load PKM with high stiffness for MDFP. To maximise the normal stiffness, a 6-PSS PKM with zero base angle and horizontal driver is proposed. Further, the inner force transfer model of 6-PSS PKM is established, indicating that the normal stiffness will be maximised when the link force approaches to be vertical. Consequently, a design criterion for maximising normal stiffness, i.e., the root mean square error (RMSE) for horizontal projection of all links should be minimised, is established. To maximise the lateral stiffness, general force balance equations of 6-PSS PKM are derived, indicating that lateral force can cause unintended negative force of links, significantly reducing the lateral stiffness. Thus, a novel auxiliary 3-SPS configuration is employed to provide additional force system to mitigate this negative force via hydraulic links. Correspondingly, a design criterion for maximising lateral stiffness, i.e., all link force should remain positive, is proposed. By combining aforementioned design criterion and kinetostatic models, a near-singular 6-PSS PKM with maximising normal stiffness is achieved, and dimension parameters of 3SPS PKM with maximising lateral stiffness are optimised. On this basis, a novel flexible redundant 6-PSS/3-SPS PKM with both high normal and lateral stiffness is proposed, and a novel heavy load Nonapod with payload of 8 MN and payload-mass ratio of 40 is developed, showing good stiffness performance. The plastic deformation mechanisms of multi-DoF formed aviation bevel gear are revealed, and experimentally formed aviation bevel gear in the new Nonapod achieves good accuracy, microstructure and mechanical performance. This work provides a new methodology for synthesis of heavy load PKM with high normal and lateral stiffness, and has significant application prospect in PKM under heavy load working condition.