A need is therefore identified to improve the previous work [15] by introducing a new mechanism with better tooltip compensating accuracy, a wider range of angle adjustment and a mechanical structure suitable for CNC machines。 A three linkages and three curved slots combined mechanism has been developed in this work to overcome the two limitations as above-mentioned。 The three curved slots, which are nonlinear in nature, have proven to be accurate in automatically compen- sating tooltip deviations for a wide adjusting range of tool inclination angles。

2。 Description of the new CNC tooling   mechanism

It has long been known that tool inclination angle plays an important role in determining the machining performance, thus it would be desirable if the inclination angle can be on-line con- trolled in CNC machine-based automatic machining   systems。

2。1。 Basic structure of the new CNC tooling   mechanism

For the new CNC tooling mechanism, the tooltip always keeps at a desired point in space,

i。e。 its working point, without any deviation while the tool inclination angle is being changed simultaneously during the machining  process。

The new tooling mechanism is structured   by

1。 three linkages which adjust the tool inclination angle automatically and    continuously;

2。 three curved slots that work simultaneously to compensate tooltip    deviations;

3。 a standard toolholder for standard indexable tool   inserts;

4。 a stepping motor with linear output;   and

5。 a standard tool shank or adapter that can be attached to the tool turret on CNC lathes。

The entire tooling system including the stepping motor fits into the standard tool shank on the turret inside CNC lathes。 The mechanism of the three linkages/three curved slots is schematically shown in Fig。  1。

2。2。 Formulation of the tooltip deviations resulted from a change in inclination angle

For a tool holder to be able to change the inclination angle in 3-D (oblique) machining pro- cesses, it is necessary to rotate the toolholder about one point, which functions as a fulcrum, on the toolholder。 The tooltip cannot be chosen as that point because it is the contact point between tool and workpiece。 Assuming that the toolholder rotates about point A, the tooltip will have two types of deviations from the contact point with the workpiece, the height deviation h and the

Fig。 1。    Schematic diagram of the new CNC tooling   mechanism。

radial deviation r as shown in Fig。 2。 The equations of the deviations can be referred to the previous work [15], that  is,

Height Deviation: h={(w) +L2∗sin(a+q)—

Radial Deviation: r=L1—{(2) +L

where w is the height of the toolholder, L1 is the distance between the tooltip and the fulcrum on the toolholder, a is  a function  of w  and  L1, and q is  the  angle  being rotated which  is equal in magnitude to the required inclination   angle。

It should be noted that the tooltip deviations are not symmetric about the workpiece axis。 It means, for example, that the radial deviation when the angle is q will be different from when it is —q。 Therefore, hand rare used to refer to the tooltip deviations when the angle q is positive, and h—  and r—  for a negative  angle。