ABSTRACT
From the 5, in this description, an interference free toolpath can be derived, but an interference free tool path with which material is removed slice by slice can be extracted from a tool path surface P , derived di rectly from R as follows. We restrict ourselves to cut ting tools that consist of a cylindric part with height hc and a rotation symmetric remaining part with height hr . In the case of a ball end tool the remaining part is a hemisphere with radius hr and in the case of a flat end tool the remaining part is empty and hr = 0. Without loss of generality, let the tool direction be in the — z di rection and the tooltip be positioned at the origin of T as indicated in figure 5. Further, we assume that T ro tates around the z-axis of T. Let R x y = {(®j y) I : (x, y , z) G R} and let for all (x, y) G R x y R ( y) =
sup{z | (as, y,z) £ i2}. Let 8max be the height of So, Train = inf{R(x, y) | (*, y) e Rx y the minimal height of R as measured along the z-axis. R can be obtained in I = Round JIp((smax - (rmin + hr))/he) stages. At each stage a slice is removed by following a plane par allel to the xy-plane or by following the boundary of (F ® (—T)) U ( i* 0 (—H))- The slices are removed in a top down fashion such that in the first milling stage the tooltip is positioned at each point (*, y) 6 R x y at height m a x (i£ (z ,y ),« m<iar - hc — /i,.). Hence, interfer ence between H and S is avoided. Next, for j = 2 . . .1 the tooltip is positioned in the jth milling stage at each point (*, y) e R x y with R(x, y) < 8 m ax ( j - l ) h e-h r in the zy-plane at height m ax(i2(x, y), smax — j he-hr). If the jth. slice is being milled, the stock-in-progress S is always identical to R above the height smax — (j — 1 )hc and upon completion o f milling this slice, 5 is identical to R above smax - jh c• Since H can hit 5 only above that slice, interference between S and H is avoided.
