Method of milling an interior region
A method is disclosed for generating a tool path for milling a region of a workpiece having first, second and third sides. The method includes: generating a first arc having a corresponding in-process material boundary intersecting the first side and which is tangent to the second side and to the third side; generating a succession of one or more second arcs, having a corresponding in-process material boundary which intersects the first side, is parallel to the first arc, and progresses by a corresponding first predetermined value from the first arc toward the first side until the in-process material boundary corresponding to one of the second arcs has a maximum distance from the first side less than the first predetermined value; and thereafter generating a succession of transition passes connecting each one of the second arcs end to end with the first arc to form the tool path.
1. An automated method for generating a tool path for milling a region of a workpiece with a milling cutter, the region comprising a first side, a second side and a third side, the method comprising the steps of:
generating with a processor a first arc having a corresponding in-process material boundary which intersects the first side and which is tangent to the second side and to the third side;
generating with the processor a succession of one or more second arcs, each one of which being characterized by: (1) having a corresponding in-process material boundary which intersects the first side, (2) being parallel to the first arc, and (3) progressing by a corresponding first predetermined value from the first arc toward the first side until the in-process material boundary corresponding to one of the second arcs has a maximum distance from the first side that is less than the first predetermined value; and thereafter
generating with the processor a succession of transition passes connecting each one of the second arcs, end to end, with the first arc to form the tool path.
2. The method of claim 1 , wherein the first arc has a shape such that the set of all points contained within the region between the first arc and the first side form a convex set.
3. The method of claim 2 , wherein the first arc is a segment of a conic.
4. The method of claim 3 , wherein the first arc is a segment of a circle.
5. The method of claim 1 , wherein the first predetermined value is a constant.
6. The method of claim 1 , wherein the first predetermined value is selected according to a shape of each second arc.
7. The method of claim 1 , wherein each corresponding first predetermined value is selected to maintain engagement of the milling cutter to be within a predetermined range for at least a portion of the succession of arcs.
8. A non-transitory computer readable storage medium having an executable program stored thereon, wherein the program instructs a computer to generate a tool path for milling a region of a workpiece with a milling cutter, the region comprising a first side, a second side and a third side, the method comprising the steps of:
generating with a processor a first arc having a corresponding in-process material boundary which intersects the first side and which is tangent to the second side and to the third side;
generating with the processor a succession of one or more second arcs, each one of which being characterized by: (1) having a corresponding in-process material boundary which intersects the first side, (2) being parallel to the first arc, and (3) progressing by a corresponding first predetermined value from the first arc toward the first side until the in-process material boundary corresponding to one of the second arcs has a maximum distance from the first side that is less than the first predetermined value; and thereafter
generating with the processor a succession of transition passes connecting each one of the second arcs, end to end, with the first arc to form the tool path.
9. The non-transitory computer readable storage medium of claim 8 , wherein the first arc has a shape such that the set of all points contained within the region between the first arc and the first side form a convex set.
10. The non-transitory computer readable storage medium of claim 9 , wherein the first arc is a segment of a conic.
11. The non-transitory computer readable storage medium of claim 10 , wherein the first arc is a segment of a circle.
12. The non-transitory computer readable storage medium of claim 8 , wherein the first predetermined value is a constant.
13. The non-transitory computer readable storage medium of claim 8 , wherein the first predetermined value is selected according to a shape of each second arc.
14. The non-transitory computer readable storage medium of claim 8 , wherein each corresponding first predetermined value is selected to maintain engagement of the milling cutter to be within a predetermined range for at least a portion of the succession of arcs.
15. A machine for generating a tool path for milling a region of a workpiece with a milling cutter, the region comprising a first side, a second side and a third side, comprising:
a processor coupled to a memory, wherein the processor is programmed to generate the tool path by the steps of:
generating a first arc having a corresponding in-process material boundary which intersects the first side and which is tangent to the second side and to the third side;
generating a succession of one or more second arcs, each one of which being characterized by: (1) having a corresponding in-process material boundary which intersects the first side, (2) being parallel to the first arc, and (3) progressing by a corresponding first predetermined value from the first arc toward the first side until the in-process material boundary corresponding to one of the second arcs has a maximum distance from the first side that is less than the first predetermined value; and thereafter
generating a succession of transition passes connecting each one of the second arcs, end to end, with the first arc to form the tool path.
16. The machine of claim 15 , wherein the first arc has a shape such that the set of all points contained within the region between the first arc and the first side form a convex set.
17. The machine of claim 16 , wherein the first arc is a segment of a conic.
18. The machine of claim 17 , wherein the first arc is a segment of a circle.
19. The machine of claim 15 , wherein the first predetermined value is a constant.
20. The machine of claim 15 , wherein the first predetermined value is selected according to a shape of each second arc.
21. The machine of claim 15 , wherein each corresponding first predetermined value is selected to maintain engagement of the milling cutter to be within a predetermined range for at least a portion of the succession of arcs.