【正文】 Sakamoto and Inasaki, 1992). However, automatic tool changerswere not considered. The system that automatically performs tool changes between the spindle and the tool magazine of a machining center is called automatic tool changer (ATC). ATC plays an important role in reducing the machine idle time and therefore increases productivity in machining propose of this paper is to present a design methodology for the systematic generation of all possible configurations of machining centers with automatic tool changer, that are opentype spatial mechanisms subject to topology and motion constraints Existing Mechanisms The first step of the design process is to study existing mechanisms and conclude their topology and motion characteristics, A machining center is a machine tool consisting of four basic ponents: a spindle, a tool magazine, a tool change mechanism, and a machine tool structure including motion of power axes. The machine tool structure largely determines the accuracy of machined surface, stiffness, and dynamic quality. The spindle rotates the tool to machine the workpiece to the desired surface. The tool magazine stores the tools and moves them to suitable positions for use in machining operations. The tool change mechanism executes tool changes between the tool magazine and the spindle. The simplest ATC is a design without a tool change mechanism, and the relative motions between the tool magazine and the spindle achieve tool change motions. Figures 3(a) and (b) show two 3axis horizontal machining centers with drum type and linear type tool magazines, respectively. To represent and analyze the topological structures and motion characteristics of machining centers, a coordinate system is defined to describe the allocation of each motion axis of the machining centers based on International Organization for Standardization (ISO, 1974) nomenclature. This standard coordinate system is righthanded rectangular Cartesian one, related to a workpiece mounted in a machine and aligned with the principal linear sideways of that machine. The positive direction of movement of a ponent of a machine is that which causes an increasing positive dimension of the workpiece. The schematic drawings of horizontal machining centers appended to ISO standard are shown in Fig. 3. By analyzing available existing 3axis horizontal machining centers without tool change mechanism, we conclude their topology and motion characteristics (Yan and Chen, 1995) as follows. Topology Requirements Topology requirements are concluded according to the topology characteristics of existing mechanisms. For our example, the design requirements of links and joints of the 3axis horizontal machining centers in their corresponding tree graphs are: 1. There must be a pendant vertex as the spindle. 2. There must be a vertex, where the length of path to the spindleis four, as the working table. 3. There must be a root, which is located on the path from the spindle head to the working table, as the frame. 4. There must be a vertex, which is a pendant vertex branching from the branch vertex located on the path from the frame tothe spindle head, as the tool magazine. 5. The edge incident with the spindle must be assigned as arevolute pair. 6. The edges between the spindle head and the working tablemust be assigned as prismatic pairs. 7. The edges between the tool magazine and the branch vertexmust be assigned as revolute, prismatic, or cylindrical , if there is a revolute pair or a cylindrical pair, it must beincident with the tool magazine. Based on the topological requirements of existing mechanisms,the assignment rules of links and joints are concluded as follows. Link assignment rules 1. Select a pendant vertex as the spindle. 2. Select a vertex, where the length of path to the spindle is four, as the working table. If this vertex does not exist, delete this graph and go to step 6. 3. Select a vertex, which is located on the path from the spindle head to the working table, as the frame. 4. Select a vertex, which is the pendant vertex branching from the branch vertex located on the path from the spindle head to the frame, as the tool magazine. If this vertex does not exist, delete this graph and go to step 6. 5. The other unassigned vertices are assigned as links L. 6. Complete the link assignment. Joint assignment rules 1. The edge incident with the spindle is assigned as a revolute pair. 2. The edges on the path from the spindle head to the working table are assigned as prismatic pairs. 3. Based on the length of path from the branch vertex to tool magazine, the edges can be assigned according to the joint permutations of R, P, and C. After specialization, we must identify these specialized tree graphs subject to topology constraints of the mechanisms of machining centers we would like to create. For our example, the topology constraints are listed as follows: 1. The pendant vertices must be the spindle, the tool magazine, or the working table. 2. The vertex of tool magazine is located on the branch from the spindle head to the frame. 3. The revolute pair must be incident with the spindle or the tool magazine, and the cylindrical pair must be incident with the tool magazine. According to the link and joint assignment rules, we can specialize the atlas of tree graphs to obtain the specialized tree graphs. The process of specialization can be puterized by inputting adjacent matrices of the tree graphs into the program and resulting with desired link adjacent matrices and the numbers of topological structures.