Abstract: Based on the requirements of machining, a structural scheme for a cutting robot is proposed, and the machining motion of the cutting robot is analyzed. Keywords: cutting robot, structural scheme, motion analysis 1 Introduction When people think of industrial robots, they think of manipulators in factories that can handle materials, workpieces, or hold tools. However, this concept has changed. For example, Japan uses existing industrial robots to complete machining operations such as grinding, scraping, polishing, and deburring [1][2][3][4][5]. Due to the use of traditional robot structures, their rigidity is poor and their precision is low. Recently, the author developed an SCR6-1 cutting robot, which has the characteristics of high flexibility, large machining range, high rigidity and precision. Based on the introduction of the structure of the SCR6-1 cutting robot, this paper analyzes and studies the machining motion of the cutting robot. 2 Structural Analysis of Cutting Robot The cutting robot is different from the general industrial robot for handling and grasping. Its basic function is to provide the motion and power necessary for metal cutting. The basic working principle is as follows: through the relative movement between the tool and the workpiece, the tool removes excess metal material from the workpiece surface, forming the geometric shape and size of the machined surface and achieving its required precision. Generally, industrial robots primarily require high flexibility (like a human arm) and have lower requirements for rigidity and precision. Therefore, most robot movements are completed by the robot's manipulator (host), with the workpiece side only performing auxiliary movements such as orientation and rotation. The function of a cutting robot differs from that of a regular robot; it is used for cutting operations. Its motion allocation principle should simultaneously consider rigidity, precision, and flexibility. Therefore, the cutting robot developed in this research adopts a motion function allocation scheme where the motion function is shared by both the tool side and the workpiece side, avoiding a decrease in rigidity due to excessive arm length. Based on the motion function allocation scheme of the cutting robot, the SCR6-1 cutting robot was developed, as shown in Figure 1. This robot adopts a modular structure, which can be configured into various structural layouts as needed. For situations where there is interference between the tool holder and the non-machined surface of the workpiece, or between the tool and the machined surface, the SCR-1 cutting robot exhibits unique flexibility compared to Cartesian coordinate machine tools. [IMG=Machining Robot]/uploadpic/THESIS/2007/11/2007111512211119013L.jpg[/IMG] Figure 1 Machining Robot 3 Motion Analysis of Machining Robot A machining robot can be modeled using a closed-loop joint chain, which consists of several elastic bodies acting as actuators to drive rotating or moving joints in series. The start and end points of the chain are the cutting points (i.e., the contact points between the workpiece's machining surface and the cutting tool). The workpiece is mounted at one end of the chain (on a fixture), and the cutting tool is mounted at the other end to complete the machining task. In reality, the machining process consists of a robot, fixture, workpiece, and cutting tool forming a process system. In this system, the cutting edge of the cutting tool contacts the workpiece's machined surface, and the relative motion between them achieves the machining of the part's surface. Therefore, we consider the robot, fixture, cutting tool, workpiece, and machined surface as a closed loop, as shown in Figure 2. In this study, a computational model as shown in Figure 3 was established based on the structure of the SCR6-1 cutting robot, and the coordinates of each joint are shown in Figure 4. The machining system in Figure 3 can be divided into two parts: one part is from one part of the robot to another part, i.e., from o1 through o2, o3, o4, o5 to o6. This part is fixed for a given robot, and the coordinate transformation from o1 to o6 is denoted as [1T6]. The other part is from one part of the robot through the workpiece and the tool to another part of the robot, i.e., o1→ow→os→op→o6, and the coordinate transformation from o1 to o6 is denoted as [1T6]. Wherein, oi—xiyizi (i=1,2,…,6) is the robot joint coordinate system, ow—xwywzw is the workpiece coordinate system, Os—xsyszs is the coordinate system of the cutting point on the cutting surface, and op—xpypzp is the tool coordinate system. For the cutting robot, the direction of motion of each joint is defined as the zj direction of the local coordinate system. When machining different curved surfaces and using different cutting tools, [1T6]' changes, while [1T6] remains constant. Therefore, the machining correlation diagram shown in Figure 4 can be used to represent it. [IMG=Machining System Chain Diagram]/uploadpic/THESIS/2007/11/20071115122150478361V.jpg[/IMG] Figure 2 Machining System Chain Diagram [IMG=Surface Machining Motion Connection Diagram]/uploadpic/THESIS/2007/11/2007111512222558093C.jpg[/IMG] Figure 3 Surface Machining Motion Connection Diagram [IMG=Machining Association Diagram]/uploadpic/THESIS/2007/11/2007111512225994738F.jpg[/IMG] Figure 4 Machining Association Diagram According to the principle of homogeneous coordinate transformation, we can obtain 〔1T6〕=〔1T6〕＇ （1） In the formula, [1T6] is the homogeneous coordinate transformation matrix between the o6 and o1 coordinate systems of the robot joints, which can be expressed as [IMG=homogeneous coordinate transformation matrix]/uploadpic/THESIS/2007/11/2007111512233696583F.jpg[/IMG] Where: A11=-s3-2s4c6-c3-2s5s6-s3-2c4c5s6 A12=s3-2s4s6-c3-2s5c6-s3-2c4c5c6 A13=c3-2c5-c3-2c4s5 A21=c3-2s4c6-s3-2s5s6+c3-2c4c5c6 A22=-c3-2s4s6-s3-2s5c6+c3-2c4c5c6 A23=s3-2c5+c3-2c4s5 A31=-c4c6+s4c5s6 A32=c4s6+s4c5c6 A33=s4s5 a6x=a6（c3c5-s3c4s5）+b6（-s3c4c5-c3s5）+c6s3s4-a5s3s4-b5s3c4+c5c3+a4c3-b4s3-a2c2-b2s2-a1 b6y=a6（s3c5-c3c4s5）+b6（c3c4c5-s3s5）-c6c3s4+a5c3s4+b5c3c4+c5s3+a4s3+b4c3+a2s2-b2c2-b1 c6z=a6s4s5+b6s4c5+c6c4-a5c4+b5s4+c5+c4-c2-c1-dz1 In the formula, si=sinθi, ci=cosθi, s3-2=sin(θ3-θ2), c3-2=cos(θ3-θ2). [1T6]' is the homogeneous coordinate transformation matrix between the workpiece, fixture, tool, and robot coordinate systems o6 and o1, which can be expressed as [1T6]' = [1Tw].[wTs].[sTp].[pT6] where [1Tw] is the homogeneous coordinate transformation matrix between the workpiece coordinate system ow and the robot joint coordinate system o1; [wTs] is the homogeneous coordinate transformation matrix between the workpiece machining surface machining point coordinate system os and coordinate system ow; [sTp] is the homogeneous coordinate transformation matrix between the tool coordinate system op and coordinate system os; and [pT6] is the homogeneous coordinate transformation matrix between the robot joint coordinate system o6 and coordinate system op. For different workpieces and tools, formula (3) varies. Therefore, as long as the workpiece, tool, and machining feed method are determined, the above matrix will also be determined. Formula (1) is the basic relational expression for the machining motion analysis of the cutting robot. By solving this formula, the joint variables required to realize the relative motion between the tool and the workpiece can be obtained. Due to space limitations, the solution process is omitted. By controlling the obtained joint variables, the desired machined surface can be obtained. 4. Conclusion This paper develops a novel cutting robot based on the requirements of metal cutting, featuring high flexibility, a large machining range, and high rigidity and precision. Based on the introduction of the SCR6-1 cutting robot's structure, the machining motion problem of the cutting robot is analyzed and studied. This robot can machine any curved surface. When machining the inner surface of a cavity, the SCR6-1 cutting robot exhibits unique flexibility compared to Cartesian coordinate machine tools, especially in situations where there is interference between the tool holder and the workpiece's non-machined surface, and between the tool and the machined surface.