【正文】 X and Y). However, surface cuts in the nonorthogonal RMT require simultaneous motion of all three axes. Therefore, in addition to the contour error, this motion creates another error, called the indepth error, which is in the Z direction. This error affects the surface finish quality of the workpiece. While contouring, the tool tip of the RMT has not only to follow the predetermi ned path, but also to control continuously the depth of cut. The simultaneous control of both errors, the conventional contour error and the indepth error, requires a new control strategy since the standard CCC algorithms cannot be directly applied. In other words, the RMT control design problem requires a new control approach that is able to correct simultaneously two types of cutting errors. This problem has not been addressed in the literature. In this paper, we describe three types of controllers aimed at reducing the contour and indepth error simultaneously. First we investigate a symmetrical crosscoupling (SCC) controller, which unfortunately does not show good performance in reducing both errors. The poor performance is due to the conflicting demands in reducing the two errors and the lack of information sharing between the two pairs of axes (XY and YZ), which are responsible for error pensation. To overe this problem, the required motion information of one pair of axes is fed forward to the other. This idea results in two new controller types, symmetrical crosscoupling feedforward (SCCFF) controller and nonsymmetrical crosscoupling feedforward (NSCCFF) controller. Finally, the influence of the reconfigurable angular position of the cutting tool on system stability is investigated. 2 Machine Characteristics and the Control Problem In this section we explain the economic advantage of the RMT, and develop the mathematical representation of the contour error and the indepth error. a Machine Characteristics Typical CNC machine tools are built as generalpurpose machines. The part to be machined has to be adapted to a given machine by utilizing process planning methodologies. This design process may create a capital waste: Since the CNC machine is designed at the outset to machine any part (within a given envelope), it must be built with general flexibility, but not all this flexibility is utilized for machining a specific part. The concept of RMTs reverses this design order: The machine is designed around a known part family. This design process creates a less plex, although less flexible machine, but a machine that contains all the functionality and flexibility needed to produce a certain part family. The RMT may contain, for example, a smaller number of axes, which reduces cost and enhances the machine reliability. Therefore, in principle, a RMT with customized flexibility would be less expensive than a parable CNC that has general flexibility. A conceptual example of a RMT designed to machine a part with inclined surfaces of 45 deg is shown in Fig. 1. If a conventional CNC is used to machine this inclined surface, a 4 or 5axis machine is needed. In this example, however, only three axes are needed on a new type of 3axis nonorthogonal machine tool. Nevertheless, one may argue that it39。s not economical to build as product nonorthogonal machine tools for 45 deg. Therefore, we developed a 3axis nonorthogonal machine in which the angle of the Zaxis is adjustable during reconfiguration periods, as shown in Fig. 2. The simple adjusting mechanism is not servocontrolled and does not have the requirements of a regular moving axis of motion. The designed RMT may be reconfigured into six angular positions of the spindle axis, between –15 and 60 deg with steps of 15 deg. The main axes of the machine are Xaxis (table drive horizontal motion), Yaxis (column drive vertical motion) and Zaxis (spindle drive inclined motion) . The two extreme positions of the machine spindle axis (–15 and 60 deg) . The XYZ machine axes prise a nonorthogonal system of coordinates, except for the case when the spindle is in a horizontal position. Two orthogonal auxiliary systems of coordinates are used to describe the machine, XSZ and XYZ , where S is an axis parallel to the part surface and Z is an axis perpendicular to both X and Yaxis. The machine is designed to drill and mill on an inclined surface in such a way that the tool is perpendicular to the surface. In milling at least two axes of motion participate in the cut. For example, the upward motion on the inclined surface in the Saxis direction requires that the machine drive move in the positive Y direction (upward) and in the positive Z direction (downward). When milling a nonlinear contour (., a circle) on the inclined surface of the RMT, we may expect to get the traditional contour error. This error is measured on the workpiece surface (XS plane) relative to the predetermined required path of the tool. However, in our machine, we get additional cutting error at the same time. This error is created due to the fluctuations in the depth of cut as result of the bined motion in the Y and Zaxis and therefore we call it indepth error. This bined motion is required in order to move the tool up and down along the inclined surface. Figure 4 describes three systems of coordinates. XYZ is the machine tool nonorthogonal system of coordinates where the table moves in X direction, Y is the motion along the column and Z is in the direction of the spindle and the cutting tool. XSZ is an auxiliary orthogonal system of coordinates where S is the direction of the inclined surface of the workpiece, which is perpendicular to the tool axis. XYZ is another auxiliary orthogonal system of coordinates where Z is horizontal. b Contouring and InDepth Errors To overe the bined error, we de