4.2. Conversion to the tool path
In this step, the workpiece surface data such as the chamfering point P; the normal vector N; the feed vector F and the tool axis vector D are converted to the tool attitude data such as the tool axis vector D; the geometrical tool vector Tg and the functional tool vector Tf . The vector D in the workpiece surface data is the same one in the tool attitude data. The vector Tf ; standing for the tool pushing direction is obtained as an inverse vector of N: The problem is how to relate Tf to Tg.
As a simple method, let us use Tf as Tg: The tool path generated by the method is shown in Fig.10. With the method, however, the change in N directly influences Tg: When the robot is driven by Tg; as shown in Fig. 11, the change in the robot attitude becomes large, and makes the robot joints easily reach to the rotational angle limit. It is due to the direct generation of Tg(=Tf) from an inverse vector of N.
As is mentioned above, Tf can be defined as an arbitrary vector within a plane having the vector Tf as its normal vector. When Tf is fixed, the tool can rotate around D. Therefore, Tg can arbitrarily be selected from Tf ; which exists infinitely around D: This is because five degrees-of-freedom is enough for the tool though a robot has six degrees-of-freedom. In other words, a degree of freedom is redundant.
Based on the above characteristics, Tf can be converted to the Tg; considering an attitude of the robot. The concept is realized by making selection of Tg so that Tf may make the changes in the robot attitude as small as possible.
Fig. 12 illustrates the developed method to generate Tg from Tf with smaller changes in the robot attitude using “reference point”, where
O is the reference point, R the reference vector, l the A plane having D as normal vector and including Tf .
O is placed near the basement of the robot. R is generated on the basis of the direction from P to O; therefore, R represents the direction from the robot location to the chamfering point. If Tg could be kept near to R; the change in the tool attitude will be kept small because R is changed smoothly according to changes of the chamfering point.
On the other hand, Tf can be selected from all the vectors included within l because Tg is included within l, as is mentioned above. In other words, Tg can be selected from all the vectors included within l. In order to satisfy both requirements, Tg is selected as projected R on l. Then, the tool can keep the attitude near to the direction from robot to the chamfering point and change its attitude smoothly. Besides, it makes no influence to a chamfering condition.
As a result, the robot can be driven by the path with smaller changes in the attitude, as shown in Fig. 13, and the tool attitude prevents the robot joints from reaching their limit of rotational angle. The tool path generated by the method is shown in Fig.14.