adaptive  control  approach ， which  is  used  to  adjust  the  instantaneous    contact

relationship between cutter and the workpiece, exhibits a certain effect on controlling the cutting force and protecting the cutting tools during machining. Because the cutting force and vibration may increase almost instantaneously at a sharp corner or a narrow

slot, the adaptive control approach could help to reduce to a certain degree but not completely avoid the negative influences.

The second approach is the treatment of the trajectory by changing the track form. Zhao et al. (2007) demonstrated that residual materials at the corner can be effectively removed by inserting a biarc curve. Through the technique, the tool may be subjected to high cutting loads because the tool enters the corner in a direct manner. Choy and Chan (2003) inserted bow-like tool path segments at a corner and concluded that the improved tool path can clear the accumulated material and reduce the cutting load at pocket corners; this progressive cutting method can effectively control the milling load. Elber et al. (2004) considered the need for C1 continuous tool paths and presented a pocket tool path containing a series of circular arcs; this method mainly focuses on the geometrical analysis and discussion. Ibaraki and Yamaji (2010) proposed that the materials of the medial axis areas of the pocket should be removed by trochoidal grooving to effectively control the tool load during the late milling stage. Ferreira and Ochoa presented a method to generate trochoidal tool paths for pocket milling process with multiple tools and concluded that the method can avoid the momentary increments in the radial depth of cut. The second method is more effective in decreasing the load variation and protecting the milling tool; however, few papers have comprehensively considered the milling force, cutting tool, and processing.

Trochoidal machining for high-speed milling pockets can be categorized as the second method. It is a method of progressively cutting away material and is very suitable for milling narrow areas or sharp corners, where the cutting load changes considerably (Fig. 1). In recent years, certain commercial CAM software has included trochoidal machining methods. Several scholars have also launched corresponding studies on

trochoidal machining. Through process experiments, Uhlmann et al. (2013) holds that a trochoidal milling strategy for TiAl6V4 workpieces offers considerable potential to improve energy consumption and process time during production. For difficult-to- machine materials such as Nickel-based superalloys, Pleta et al. (2014) provided a comparison of trochoidal milling with a traditional milling technique. They believe that the process of trochoidal machining can result in improved productivity and efficiency. Aiming at the workpiece surface with holes and bosses, Otkur and Lazoglu (2007) proposed an approach to model the milling force for trochoidal milling. The experimental results demonstrated the good agreement between the predicted forces and the measured forces. Rauch et al. (2009) investigated the trochoidal model which infers curvature and tangency continuity, and concluded that the cutting time and tool life can be effectively improved in a high dynamics machining tool. Rauch and Hascoet (2007) developed algorithms that can be used to generate trochoidal and plunge cutting trajectories for pocket milling. The results of this study lead to a better definition of the strengths and weaknesses of trochoidal milling and plunge cutting strategies in rough machining of aluminium alloys with a focus on optimizing the choice of strategies. In these trochoidal models, the trochoidal circles normally present equal diameters.

In this paper, the trochoidal definition is expanded to include two types of trochoidal machining: isometric circle trochoid (Fig. 1b) and variable circle trochoid (Fig. 1c). Ibaraki and Yamaji (2010) reported that the medial axis areas of a pocket should be removed by trochoidal tool paths prior to high-speed contour-parallel cutting. The experiments demonstrated improved machining efficiency and tool wear. In the study, the machining parameters, such as the size or distance of trochoidal circles, are specified based on experience. Unsuitable parameters may cause reduced efficiency or