Machining, Measurement, and Control Laboratory

2 0 0 0    C o n f e r e n c e    P a p e r

Kinematic Calibration of a Hexapod Machine Tool by Using Circular Test
Yukitoshi Ihara (Kyoto University)
Takahiro Ishida (Kyoto University)
Yoshiaki Kakino (Kyoto University)
Zire Li (Joetsu University of Education)
Tetsuya Matsushita (Okuma Corp.)
Masao Nakagawa (Okuma Corp.)

Recently, the application of machine tools with parallel mechanism becomes popular. Ideally, this type of machines has the advantage of higher stiffness and higher accuracy. In real case, however, it is very difficult to obtain them by designing a machine. Another existing problem is the difficulty to calibrate the kinematic errors since any machine movement, no matter in linear or circular shape, needs the motion of more than one actuator, thus the motion error source is uncertain.

Circular test is one of the best methods to measure and calibrate the motion accuracy of orthogonal type machine tools such as machining centers. By programming the machine to move in a circular shape, the motion accuracy can be obtained according to the circularity of the trace (profile of the motion). Kinematic calibration for articulated serial mechanism robots by using circular test was tried and some success was achieved. However, for a parallel mechanism machine, characteristic trace measured by circular test is difficult to be extended to individual error pattern because the error sources resemble each other. More precisely, almost all trace patterns of individual element error are offset circles and ellipses. When these trace patterns are combined, they will be also offset circle and ellipse. Therefore, it is very difficult to identify the individual error sources.

In this study, a Stewart platform type machine tool and static error source are dealt with. The machine has 6 actuators and 12 joints. Parameters to be considered are length of actuator (6) and position deviation of joints (12~3 DOFs). A Double Ball Bar (DBB) device is used for circular test. First, all 42 trace patterns of an individual element's error with circular test are calculated. Second, these trace patterns are transformed by Fourier transformation in order to know the mathematical information of these trace patterns and the possibility to separate them. Third, with these information, the type (position, radius) of circular test suitable for the purpose of separating each parameter error is discussed. The result shows that it is difficult to separate error sources if DBB measurements are done only on a center position. Fourth, a measurement sequence is proposed, sensitivity coefficients of each parameter error are calculated and the method to calculate individual parameter error by solving simultaneous equations is shown. Finally, on a real hexapod machine tool, DBB measurements are done and the effectiveness of this method is proved.

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