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Pergamon MACHINE TOOLS & MANUFACTURE DESIGN, RESEARCH AND APPLICATION International Journal of Machine Tools & Manufacture 42 (2002) 505-520 Five-axis milling machine tool kinematic chain design and analysis E.L.J. Bohez * Department of Design and Manufacturing Engineering, Asian Institute of Technology, P.O. Box 4, Klong Luang, 12120 Pathumthani, Thailand Received 23 May 2000; received in revised form 12 September 2001; accepted 13 September 2001 Abstract Five-axis CNC machining centers have become quite common today. The kinematics of most of the machines are based on a rectangular Cartesian coordinate system. This paper classifies the possible conceptual designs and actual existing implementations based on the theoretically possible combinations of the degrees of freedom. Some useful quantitative parameters, such as the workspace utilization factor, machine tool space efficiency, orientation space index and orientation angle index are defined. The advantages and disadvantages of each concept are analyzed. Criteria for selection and design of a machine configuration are given. New concepts based on the Stewart platform have been introduced recently in industry and are also briefly discussed. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Five-axis; Machine tool; Kinematic chain; Workspace; CNC; Rotary axis 0890-6955/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S0890-6955(01)00134-1 1. Introduction The main design specifications of a machine tool can be deduced from the following principles: ? The kinematics should provide sufficient flexibility in orientation and position of tool and part. ? Orientation and positioning with the highest possible speed. ? Orientation and positioning with the highest possible accuracy. ? Fast change of tool and workpiece. ? Save for the environment. ? Highest possible material removal rate. The number of axes of a machine tool normally refers to the number of degrees of freedom or the number of independent controllable motions on the machine slides. The ISO axes nomenclature recommends the use of a right-handed coordinate system, with the tool axis corresponding to the Z-axis. A three-axis milling machine has three linear slides X, Y and Z which can be positioned everywhere within the travel limit of each slide. The tool axis direction stays fixed during machining. This limits * Tel.: +66-2-524-5687; fax: +66-2-524-5697. E-mail address: bohez@ait.ac.th (E.L.J. Bohez). the flexibility of the tool orientation relative to the workpiece and results in a number of different set ups. To increase the flexibility in possible tool workpiece orientations, without need of re-setup, more degrees of freedom must be added. For a conventional three linear axes machine this can be achieved by providing rotational slides. Fig. 1 gives an example of a five-axis milling machine. E.L.J. Bohez /International Journal of Machine Tools & Manufacture 42 (2002) 505-520 511 2. Kinematic chain diagram To analyze the machine it is very useful to make a kinematic diagram of the machine. From this kinematic (chain) diagram two groups of axes can immediately be distinguished: the workpiece carrying axes and the tool carrying axes. Fig. 2 gives the kinematic diagram of the five-axis machine in Fig. 1. As can be seen the workpiece is carried by four axes and the tool only by one axis. The five-axis machine is similar to two cooperating robots, one robot carrying the workpiece and one robot carrying the tool. Five degrees of freedom are the minimum required to obtain maximum flexibility in tool workpiece orientation, this means that the tool and workpiece can be oriented relative to each other under any angle. The minimum required number of axes can also be understood from a rigid body kinematics point of view. To orient two rigid bodies in space relative to each other 6 degrees of freedom are needed for each body (tool and workpiece) or 12 degrees. However any common translation and rotation which does not change the relative orientation is permitted reducing the number of degrees by 6. The distance between the bodies is prescribed by the toolpath and allows elimination of an additional degree of freedom, resulting in a minimum requirement of 5 degrees. 3. Literature review One of the earliest (1970) and still very useful introductions to five-axis milling was given by Baughman [1] clearly stating the applications. The APT language was then the only tool to program five-axis contouring applications. The problems in postprocessing were also Fig. 2. Kinematic chain diagram. clearly stated by Sim [2] in those earlier days of numerical control and most issues are still valid. Boyd in Ref. [3] was also one of the early introductions. Beziers’ book [4] is also still a very useful introduction. Held [5] gives a very brief but enlightening definition of multi-axis machining in his book on pocket milling. A recent paper applicable to the problem of five-axis machine workspace computation is the multiple sweeping using the Denawit-Hartenberg representation method developed by Abdel-Malek and Othman [6]. Many types and design concepts of machine tools which can be applied to five-axis machines are discussed in Ref. [7] but not specifically for the five-axis machine. The number of setups and the optimal orientation of the part on the machine table is discussed in Ref. [8]. A review about the state of the art and new requirements for tool path generation is given by B.K. Choi et al. [9]. Graphic simulation of the interaction of the tool and workpiece is also a very active area of research and a good introduction can be found in Ref. [10]. 4. Classification of five-axis machines9 kinematic structure Starting from Rotary (R) and Translatory (T) axes four main groups can be distinguished: (i) three T axes and two R axes; (ii) two T axes and three R axes; (iii) one T axis and four R axes and (iv) five R axes. Nearly all existing five-axis machine tools are in group (i). Also a number of welding robots, filament winding machines and laser machining centers fall in this group. Only limited instances of five-axis machine tools in group (ii) exist for the machining of ship propellers. Groups (iii) and (iv) are used in the design of robots usually with more degrees of freedom added. The five axes can be distributed between the workpiece or tool in several combinations. A first classification can be made based on the number of workpiece and tool carrying axes and the sequence of each axis in the kinematic chain. Another classification can be based on where the rotary axes are located, on the workpiece side or tool side. The five degrees of freedom in a Cartesian coordinates based machine are: three translatory movements X,Y,Z (in general represented as TTT) and two rotational movements AB, AC or BC (in general represented as RR).Combinations of three rotary axes (RRR) and two linear axes (TT) are rare. If an axis is bearing the workpiece it is the habit of noting it with an additional accent. The five-axis machine in Fig. 1 can be characterized by XfYfAfBfZ. The XYAB axes carry the workpiece and the Z-axis carries the tool. Fig. 3 shows a machine of the type XYZArBr, the three linear axes carry the tool and the two rotary axes carry the workpiece. 4.1. Classification based on the sequence of workpiece and tool carrying axes Theoretically the number of possible configurations is quite large if the order of the axes in the two kinematic chains of the tool and workpiece carrying axes is counted as a different configuration. Also the combinations with only two linear axes and three rotary axes are included. One tool carrying axis and four workpiece carrying axes can be combined in a five-axis machine as follows: for each possible tool carrying axis X,Y,Z,A,B,C the other four workpiece carrying axes can be selected from the five remaining axes. So the number of combinations of four axes out of five with considering different permutation as another configuration is 5x4!=120 for each possible tool axis selection (1 out of 6 or 6 possibilities). So theoretically there are 6x120=720 possible five-axis machines with one tool carrying axis. The same analysis can be done for all other combinations. With t the number of tool carrying axes and w the number of workpiece carrying axes (w+t=5) the total number of combinations is as follows. Ncomb=(t)t!(w )w! t^3,什w=5 ⑴ (6\ (6-w\ Nco^b=\ )w!\ t It! t>3, t+w=5 (2) The value of this equation is always equal to 6! or 720 when w+t=5. Some of these 720 combinations will be containing only two linear axis. If only five-axis machines with three linear axes are considered, only 3x5!=360 combinations are still possible. The set Gt of combinations is characterized by a fixed value of t. This set is identical to the set Gw characterized by a fixed value of w, w=5 —t. Using above definitions following subgroups of five-axis machines exist: (i) Group G0/G'5; (ii) Group G1/G'4; (iii) Group G2/G'3; (iv) Group G3/G'2; (v) Group G4/G'1; (vi) Group G5/G0. 4.1.1. G5/G0f machine All axes carry the tool and the workpiece is fixed on a fixed table. Fig. 4 shows a machine with all the five axes carrying the tool. The kinematic chain is XBYAZ (TRTRT). This machine was one of the earliest models of five-axis machines to handle very heavy workpieces. As there are many links in the tool carrying kinematic chain, there can be a considerable error due to elastic deformations and backlash in the slides. 4.1.2. G0/G5f machine All axes carry the workpiece and the tool is fixed in space. This construction is best used for very small workpieces (see Section 6.3).  4.1.3. G4/G1 machine Four axes carry the tool and one axis carries the workpiece. There are basically two possibilities, the workpiece carrying axis can be R or T. 4.1.4. G1/G4’ machine One axis carries the tool and the other four axes carry the workpiece. There are basically two possibilities, the single axis kinematic chain can be R or T. Fig. 1 is an example of such a machine, with the single tool carrying axis T. 4.1.5. G3/G2f machine Three axes carry the tool and two axes carry the workpiece. There are basically three possibilities, the workpiece carrying axes can be both linear (W) both rotational (R'R') or mixed (T'R'). Fig. 5 gives an example of a machine with the tool carried by two rotary axes and one linear axis. This machine allows processing of large workpieces but the construction of the toolside is complicated. The most common configuration is the workpiece carried by the two rotary axes such as the one given in Figs. 3, 6 and 8. 4.1.6. G2/G3f machine Two axes carry the tool and three axes carry the workpiece. There are basically three possibilities, the tool carrying axis can be both linear (TT) both rotational (RR) or mixed (TR). Fig. 7 shows the mixed construction. Fig. 8 shows two linear axes carrying the tool. 4.2. Classification based on the location of rotary axes Fig. 7. ZrCBY machine. The machines can be classified depending on the place where the rotation axes are implemented. Fig. 5. XZ'CAY machine.  Only machines with two rotary axes and three linear axes will be considered further. The possible configurations are: The number of possible designs is the sum of the following combinations: (i) For the group G0/G5' the tool is fixed in space all the five axes will carry the workpiece. The number of different designs is 10 (NTf=3 and NR =2), (Figs. 15 and 16). (ii) For the group G1/G4r, NT+NR=1, so NT=1 and NR=0, is the only possible choice for the tool kinematic chain. Equation (3) gives NCOMB=6. The combinations are: RfRfTfTfT; TfTfRfRfT; RfTfRfTfT; TRTRT; RTTRT; TRRTT. Fig. 9 shows these six designs. (iii) For the group G2/G3' the tool axes are TT so Nt'=1, Nr =2, Nj=2, Nr=0 and Equation (2) gives Ncomb=3. The three design combinations are: RRTTT; RfTfRfTTand TfRfRfTT. The group G2/G3f contains three instances of the RfRf machine. These instances are represented in Fig. 10. (vi) If the tool axes are TTT the workpiece carrying axes can only be RrRr. So only one design combination is possible. From the above-mentioned findings it can also be concluded that the total number of RfRf five-axis machine configurations is 20. Machines with two axes on the clamping table can be seen in Figs. 1, 3, 6 and 8. The advantages are: (a) rotation axes are implemented on tool spindle; (b) rotation axes are implemented on machine table; (c) combination of both. The sequence of the axes in the tool or workpiece carrying kinematic chain is not important if the axes are of the same type R or T. In general, if there are NT transitory axes and Nr rotary axes in the workpiece carrying kinematic chain and NT translatory axes and NR rotary axes in the tool kinematic chain, then the numbers of combinations is [11]: N JNt+Nr)\(Nt+Nr)\ 以一b- Nt!NR Nt!Nr {) with Nt+Nt=3, Nr+Nr=2 The number of combinations of each group will be given below case by case. The total number of combinations over all groups is 60. From the design point of view this is a more tractable number of alternatives to be considered. 4.2.1. RR machine The two rotary axes carry the workpiece. The tool axis can be fixed or carried by one (T), two (TT) or three (TTT) linear axes. ? In case the spindle is horizontal, optimal chip removal is obtained through the gravitational effect of the chips just dropping. ? The tool axis during machining is always parallel to the Z axis of the machine. So the drilling cycles can be executed along the Z-axis of the machine. Circles under a certain orientation of the workpiece are always executed in the XY plane of the machine. The above-mentioned functions can be executed in the simple three-axis numerical control mode. ? The compensation of the tool length happens all the time in the NC control of the machine, as with three- axis machines. Disadvantages: ? Machines with a rotating table are only for workpieces with limited dimensions. ? The useful workspace is usually much smaller than the product of the travel in X,Y and Z axis. ? The transformation of the Cartesian CAD/CAM coordinate (XYZIJK) of the tool position to the machine axes positions (XYZAB or C) is dependent on the position of the workpiece on the machine table. This means that in case the position of the workpiece on the table is changed this cannot be modified by a translation of the axes system in the NC program. They must be recalculated. In case the control of the NC machine cannot transform Cartesian coordinates to machine coordinates, then a new CNC program must be generated with the postprocessor of the CAD/CAM system every time the position of the workpiece changes. Important applications for this type: ? Five-sided cutting of electrodes for EDM and other workpiece. ? Machining of precision workpieces. ? Turbines and tire profiles with a certain workpiece geometry rotated over a certain angle. The same NC program can be repeated after the zero of the rotation axis has been inclined over a certain angle. 4.2.2. RR-machine The number of possible design combinations (Ncomp=20) is the same as in the case of the R'R' machine because of the symmetry. Five-axis machines with the rotation axes implemented on the tool axis spindle can be seen in Figs. 4 and 5. Advantages: ? These machines can machine very large workpieces. ? The machine axis values of the NC program XYZ, depend on the tool length only. A new clamping position of the workpiece is corrected with a simple translation. This happens with a zero translation in the CNC control of the machine. Disadvantages: ? The drive of the main spindle is very complex. Simple design and construction is only obtained when the whole spindle with the motor itself is rotating. ? There is a lower stiffness because the rotation axis of the spindle is limiting the force transmission. At high revolutions per minute (higher than 5000 rpm) there is also a counter acting moment because of the gyroscopic effect which could be a disadvantage in case the tool spindle is turning very fast. ? Circular interpolation in a random plane and drilling cycles under random orientation are often not implemented. ? A change in the tool length cannot be adjusted by a zero translation in the control unit, often a complete recalculation of the program (or postprocessing) is required. Important applications of this type of machine tool are: ? All types of very large workpieces such as air plane wings. 4.2.3. R’R machine One rotary axis is implemented in the workpiece kinematic chain and the other rotary axes in the tool kinematic chain (e.g. Fig. 7). The groups G4/G1’，G4’/G1, G3’/G2, G3/G2’ cover this design. Nowadays there are many machines on the market with one rotation axis on the tool spindle and (4) Wr = one rotation axis on the table. They are, however, combining most of the disadvantages of both previous types of machines and are often used for the production of smaller workpieces. The application range of this machine is about the same as with machines with two rotation axes implemented on the table. In all possible designs of this machine the NRf=NR=1 and Nt+Nt=3. The total number of possible designs is: ncomb[nt=0,Nt=3]+ncomb[nt= 1,Nt=2]+ncomb[nt =2,Nt=1]+Ncomb[NT=3, NT' = 0] or 4+6+6+4=20 possible designs. (i) For NTr=0 and Nt=3 the four combinations are: RRTTT; RTRTT; RTTRT; RTTTR. (ii) For NT=1 and Nt=2 the six combinations are: TRRTT; TRTRT; TRTTR; R’T’RTT.， R’T’TRT; R’T’TTR. (iii) For NT'=2 and Nt=1 the six combinations are (see Fig. 11): R'T'T'TR; TR'T'TR; T'TR'TR; RT'TRT; TRTRT; T'TRRT. (iv) For NT=3 and Nt=0 the four combinations are: RT'T'TR; TRT'TR; T'TRTR; T'T'TRR. 5. Workspace of a five-axis machine Before defining the workspace of the five-axis machine tool, it is appropriate to define the workspace of the tool and the workspace of the workpiece. The workspace of the tool is the space obtained by sweeping the tool reference point (e.g. tool tip) along the path of the tool carrying axes. The workspace of the workpiece carrying axes is defined in the same way (the center of the machine table can be chosen as reference point). These workspaces can be determined by computing the swept volume [6]. Based on the above-definitions some quantitative parameters can be defined which are useful for comparison, selection and design of different types of machines. 5.1. Workspace utilization factor WR A possible definition for this is the ratio of the Boolean intersection of the workpiece workspace and tool workspace and the union of the tool workspace and workpiece workspace. WSTOOL^ WSWORKPIECE WSTOOL ^ WSWORKPIECE A large value for WR means that the workspace of the tool and the workspace of the workpiece are about equal in size and overlap almost completely. A small value of WR means that the overlap of tool workspace and workpiece workspace is small and that a large part of the workpiece workspace cannot be reached by the tool. The analogy with two cooperating robots can be clearly seen. It is only in the intersection of the two workspaces of each robot that they can ‘shake hands’. For the five-axis machine tool this corresponds to the volume in which the tool and workpiece reference point can meet. However, in the case where all the five axes carry the workpiece and the tool is fixed in space the above definition would give a zero value for the workspace utilization. In the case of cooperating robots it would mean that there is only one point were they can shake hands. In the case of a five-axis machine, the workpiece can still be moved in front of the tool and remove metal. The reason is that many points from the workpiece can serve as reference point on the workpiece. All