【正文】 uces Ex (the axial position error along the X direction) and another input from the crosscoupling controller to reduce rx (the X ponent of the contour error). Similarly, the Yaxis plant receives two inputs. The additional inputs to each axis are used to decrease the contour error in the normal direction represented by r The objective of this paper is to suggest a suitable crosscoupling control strategy for both the contour and indepth errors. Three controllers are examined: a symmetric crosscoupling (SCC) controller, the symmetric crosscoupling controller with additional feedforward (SCCFF), and a nonsymmetric crosscoupling controller with feedforward (NSCCFF). a Controllers Structures. The detailed structure of the three controllers is illustrated The basic structure is to have two standard crosscoupling (CC) controllers, one for the contour error in the XYsubsystem with a gain Gr and the other for the indepth error in the YZsubsystem with a gain Gz. Section 4b includes a discussion on the values of Gr and Gz. The indepth crosscoupling controller has the same basic control structure as the contour crosscoupling controller. In addition, a feedforward term may be used to inform the Zaxis about the additional Yaxis input caused by the contour crosscoupling controller. Knowing this information in advance, the Zaxis can pensate for the movement of the Yaxis in order to reduce the indepth error. The differences among the three proposed controllers are: (a) the presence or absence of a feedforward term (In the SCC controller, the Kff block does not exist), and (b) a difference in the direction of the controlling error (in the NSCCFF controller, Czy is zero). If the feedforward term exists, Kff in Figure 6 can be expressed as follows The tracing error estimation gains, Crx, Cry, Czy, Czz are given in Equations (1) and (2). The symmetric crosscoupling (SCC) controller uses the contour crosscoupling controller between the X and Yaxis and the indepth crosscoupling controller between the Y and Zaxis. The contour crosscoupling controller decreases the contour error by coupling the X and Yaxis movements while the indepth crosscoupling controller pensates the indepth error by coupling the Y and Zaxis movements. The Yaxis receives one output from each crosscoupling controller。 This machine allows ERC researchers to validate many of the new concepts and machine tool design methodologies that have been already developed in the center. There are many types of RMTs. This paper describes an archtype nonorthogonal multiaxis RMT machine 。2020 ASME Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division January 3, 2020。附錄 Control of a NonOrthogonal Reconfigurable Machine Tool Reuven KatzJohn YookYoram Koren Received: January 3, 2020。 revised: September 16, 2020 Abstract Computerized control systems for machine tools must generate coordinated movements of the separately driven axes of motion in order to trace accurately a predetermined path of the cutting tool relative to the workpiece. However, since the dynamic properties of the individual machine axes are not exactly equal, undesired contour errors are generated. The contour error is defined as the distance between the predetermined and actual path of the cutting tool. The crosscoupling controller (CCC) strategy was introduced to effectively decrease the contour errors in conventional, orthogonal machine tools. This paper, however, deals with a new class of machines that have nonorthogonal axes of motion and called reconfigurable machine tools (RMTs). These machines may be included in largescale reconfigurable machining systems (RMSs). When the axes of the machine are nonorthogonal, the movement between the axes is tightly coupled and the importance of coordinated movement among the axes bees even greater. In the case of a nonorthogonal RMT, in addition to the contour error, another machining error called indepth error is also generated due to the nonorthogonal nature of the machine. The focus of this study is on the conceptual design of a new type of crosscoupling controller for a nonorthogonal machine tool that decreases both the contour and the indepth machining errors. Various types of crosscoupling controllers, symmetric and nonsymmetric, with and without feedforward, are suggested and studied. The stability of the control system is investigated, and simulation is used to pare the different types of controllers. We show that by using crosscoupling controllers the reduction of machining errors are significantly reduced in parison with the conventional decoupled controller. Furthermore, it is shown that the nonsymmetric crosscoupling feedforward (NSCCFF) controller demonstrates the best results and is the leading concept for nonorthogonal machine tools. 169。 final revision September 16, 2020. Associate Editor: J. Tu. Keywords:machine tool, crosscoupling controller, nonorthogonal, RMT 1 Introduction Currently manufacturing industries have two primary methods for producing medium and high volume machined parts: dedicated machining systems (DMSs) and flexible manufacturing systems (FMSs) that include CNC machines. The DMS is an ideal solution when the part design is fixed and mass production is required to reduce cost. On the other hand, the FMS is ideal when the required quantities are not so high and many modifications in the part design are foreseen. In contrast to these two extremes, Koren describes an innovative approach of customized manufacturing called reconfigurable manufacturing systems (RMS). The main advanta