According to Fig。 2, the deviation equations can be further simplified for the convenience in formulation and calculation。Height deviation:

Fig。 2。   Tooltip deviations due to the change of the tool inclination angle (assuming A is the fulcrum)。

2。3。 Mechanism and design of three curved   slopes

The mechanism of three curved slots that work simultaneously can be illustrated in Fig。 3。 To compensate the  tooltip deviations when the toolholder is  rotating, point  A has to  move     simul-

Fig。 3。 Principle diagram showing three curved slots that work simultaneously to automatically compensate tooltip deviations。

taneously。 This can be achieved by setting point A to move along a fixed and curved slot (Curve 3)。 A hole is made at point A, and a shaft is inserted through the hole and the curved slot (Curve 3)。 Thus, if the shaft moves along Curve 3, point A on the toolholder will move at the same distance along Curve 3 accordingly。 Curved Slot 2 (Curve 2) is  added between  the  toolholder and Curve 3 in order to move the shaft, and hence, point A along Curve 3。 When Curve 2 travels linearly to the right relative to Curve 3, the shaft will be pushed up along Curve 3。 To be able to change the tool inclination angle, point B on the toolholder must move along a curved slot (i。e。 Curve 1) relative to point A。 Both Curves 1 and 2 are set on a moving input link。 It should be noted that Curves 1 and 2 have an inherent relationship because the location of point B on Curve 1 depends on the location of point A on Curve 2 for any required tool inclination angle。 Curve 3 should be designed in such a way that it will make point A move to the opposite direction but at the same distance with respect to the tooltip deviations。 As a result when the tool inclination angle is rotated by an angle q, the distance that point A should move in X direction must be equal to the tooltip radial deviation at the same angle q。 Similarly, the distance that point A should move in Y direction must be equal to the tooltip height deviation at the same angle q。

Therefore, according to the coordinate system shown in Fig。 3, the equation of Curve 3 can be expressed as,

w

x(q)=r= 2sinq+L1(1—cosq) (5)

w y(q)=h=L1sinq+2(cosq—1)

The function of Curve 2 is to move point A along Curved Slot 3, as shown in Fig。 3。 The vertical height of Curve 2 must be larger than the total height deviation of the tooltip。 The minimum length of Curve 2 can be found   as

h+ h

minL2=tanq +tanq

q2 the slope angle of Curve  2;

h the positive maximum tooltip height  deviation;

h— the negative maximum tooltip height  deviation;

L2 is also the distance between Curve 1 and Curve 3 when both are at the center line of the toolholder corresponding to the tool inclination   angle0。

The angle of Curve 2 (q2) and the stroke (Ls) are inversely proportional。 Either of them should be chosen, considering the availability of working space。 The stroke Ls is the distance the input link travels。源-于,优Y尔O论U文.网wwW.youeRw.com 原文+QQ75201,8766

The function of Curve 1 is to move point B relative to point A until the desired tool inclination angle is reached。 Curve 1 is obtained by determining the position of point B relative to the position

of point A on Curve 2。 According to the coordinate system shown in Fig。 3, the equation  for Curve 1 can be derived  as,

h x(q)=L2—(La+Lb)=L2—tanq   —L2cosq=L2(1—cosq)—