The Uncertainty of Parallel Model Coordinate Measuring Machine

The Stewart platform is one of 6-DOF (6 degrees of freedom) parallel mechanism. A parallel mechanism is a mechanism to connect six actuators in parallel between the base and the stage. It is necessary to calibrate the kinematic parameters that compose the mechanism in order to use the parallel mechanism as the coordinate measuring machine. Additionally, it is necessary to estimate the uncertainty about the measurement results. In this study, the kinematics parameters are estimated by using the calibration point in one point, the uncertainty is estimated at several measurement coordinates from kinematic parameters and postures angle. The verification method is shown following; i) The amount of the actuator expansion and contraction in the parallel mechanism is assumed to be a value obtained with the sensor and, the kinematic parameters are estimated from the values by using the least squares method. ii)The coordinates of the stylus are calculated from the estimated kinematic parameters by forward kinematics. The uncertainty is estimated from the coordinates of the stylus. As a result, the influence of the uncertainty is reported when the target coordinates are measured. © Metrology Society of India, All rights reserved 2011. 1. Indroduction Recently, the size and the form of machine parts are required to be measured accurately for its high accuracy. The serial mechanism has been conventionally used for coordinate measuring machines (CMMs), machine tools and industrial robots because of easiness in its structure and control. However, this structure has the problem that the deflection is caused by the weight of itself at each joint. Therefore, a parallel mechanism is expected to be applied to CMM as it has positioning, and more rigid structure. The CMM with parallel mechanism is called parallel model CMM. As for a CMM, more accurate positioning is required. However, it is difficult to manufacture a CMM as exactly as a design value, and the various errors arise. Therefore, the errors should be compensated and the calibration work of a mechanism is important. In this study, the kinematic parameter was estimated by the selfcalibration method using sensor information of actuator on the measuring instrument. As a result, the target coordinates disposed in measuring volume are measured using the kinematic parameters estimated at the only one calibration point. The uncertainty of measurement is reported when the target coordinates are measured. 2. Model of 6 DOF Parallel CMM In this study, the Stewart platform, the representative of six DOF parallel mechanism, is dealt. The model is MAPAN Journal of Metrology Society of India, Vol. 26, No. 1, 2011; pp. 47-53 ORIGINAL ARTICLE Kosuke Iimura, Eiichiro Kataoka , Miyu Ozaki and Ryoshu Furutani 48 shown in Fig. 1 and its top view is shown in Fig. 2. This mechanism consists of the base plate and stage. Both of the base plate and stage have six spherical joints. The base plate and stage are connected with six links which ended at each spherical joint. The links have the actuators and the stage could change the location and orientation in world coordinate system by expanding and contracting the actuators. The definition of kinematic parameters is shown in Table 1. In that case, six parameters of the base parameters are used to express the local coordinate system of itself and six parameters of the stage parameters are also used to express the local coordinate system. Some parameters are freely chosen to define coordinate system. Therefore, these parameters(bx1, by1, bz1, bz4, by6, bz6, sx1, sy1, sz1, sz4, sy6, and sz6) are redundant and are possible to be zero. The Eq. (1) is used in the simulation is expressed for one of six equations of closed links. One closed link is shown in Fig. 3 where P is a vector of the stylus, R is a coordinate transformation matrix expressing the orientation of the stage, S is a vector of the joint of the stage, B is a vector of the joint of the base plate and A'n is offset of an actuator.. = − ' n n n n A P RS B A + (1) Sn=[Xn, Yn, Zz] : Coordinates of stage joints Bn=[Xn, Yn, Zz] : Coordinates of base joints : φ θ φ θ φ φ φ φ θ φ φ φ φ θ φ θ φ φ φ φ θ φ φ φ θ θ φ θ φ ⎡ ⎤ − + ⎢ ⎥ = + − ⎢ ⎥ ⎢ ⎥ − ⎣ ⎦ Rotating matrix C C C S S S C C S C S S R S C S S S C C S S C C S S C S C C φ : Turning angle around z axis [deg], θ: Turning angle around y axis [deg], φ: Turning angle around x axis [deg] A'n: Offset of an actuator, An: Amount of actuator expansion and contraction n=1∼ 6 Base Stage