###### Abstract  
The article presents a novel strategy for enhancing the efficiency of machines that are used for complex structure machining. It proposes a low-cost five-axis four-linkage milling system as an alternative to the more expensive five-axis five-linkage system. Kinematic analysis of the machine tool is conducted to establish a correlation between the tool location data and the displacement of kinematic axes. An interpolation algorithm is then devised to determine a four-axis linkage milling strategy. The theoretical errors of the interpolation trajectory are observed to be reduced following the transformation. The research employs impeller processing as a case study, wherein the five-axis linkage machining path is translated into a more efficient five-axis four-linkage path using the interpolation algorithm. The practical application of this novel milling strategy confirms its effectiveness in processing the integral impeller within acceptable efficiency parameters. The results provide a theoretical foundation for the practical application of the low-cost five-axis four-linkage machining strategy in high-precision five-axis five-linkage machine tools. five-axis machine tool; continuous machining strategy; tool path; interpolation algorithm; cost-effective +
Footnote †: journal: Medical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China  
multi-axis linkage numerical control systems continue to hold the sway in mainstream surface processing, which poses a predicament regarding their exorbitant pricing [5]. To reduce costs and attain comparable machining accuracy to conventional multi-axis simultaneous machining systems, there is growing interest in cost-effective multi-axis CNC systems [6]. Such systems typically encompass five or more independent axes; however, their control systems only allow simultaneous four-axis machining. Also acknowledged as 4 + 1 or 4 + 2 axis machining, this pertains to the coordinated movement of four motion axes on a five-axis or six-axis CNC machine tool, while the remaining one or two motion axes intermittently move or remain fixed at a predetermined position. This paper takes the five-axis four-linkage numerical control system as an example. Compared to the five-axis linkage system, the four-axis linkage system is 30% more cost-effective, and four-axis machining technology has found broader application in factory production. At present, many scholars have studied the application of the four-axis linkage system in surface machining [7; 8]. For the complex surface machining of the integral impeller, the four-axis linkage machining strategy of Power MILL and the corresponding transformation techniques are used to process the impeller [9]. A four-axis trochoidal tool path planning algorithm utilizing a ball-end milling tool is suggested to successfully process complex curves. However, the four-axis machining in the aforementioned curved surfaces is typically specific to some particular curved surface instances and entails a certain level of skill, which hinders the practical application of cost-effective curved surface parts processing. So, it is imperative to delve into the cost-effective and high-precision four-linkage processing method using five-axis machine tools. However, conventional CAM software is incapable of producing a four-axis tool path directly for a five-axis CNC system. The approach in this paper involves designing the tool path for traditional five-axis continuous machining in standard CAM software. We then use the method outlined in this paper for translation into a five-axis four-linkage continuous machining trajectory that the device can leverage, thus accomplishing the objective of five-axis five-linkage machining. This reduction in the production cost of high-end parts carries immense significance for the low-end machine tool industry as it allows for the full potential of cost-effective five-axis CNC machine tools.