??????? ???????? ?????? ????? ?? ????? ????? ????? ??? ??????? ?? ??????? ??????? ??????. ????? ??? ??????? ??? ????? ??????? ?????? ???? ??? ???? ????? ?????? ?? ???? ???? ?? ????? ?????? ????? ?? ????? ?????. ??? ??? ?????? ??????? ????? ?? ??????? ??? ??? ?????? ?????? ???? ???? ???? ??? ????? ??????? ?????? ??? ????? ???????? ?????? ????? ?? ????? ??? ?????? ???? ?????? ????????? ??? ??? ??????? ??????? ????????? ??????? ??? ???? ????? ?????.
????? ?? ??????? ???????? ?????? ????? ??????
??????? ???????? ?????? ????? ?? ????? ????? ??? ??? ???? ??? ???? ??? ????? ?????? ????? ??? ????? ??? ?????? ???? ?????? ?????? ???????. ???? ???????? CNC ??? ?????? ?????? ??????????? ??? ???? ????????? ??????? ???? ???? ????? ???????? ????????? [1].
?? ????? ??????? ???????? ?????? ????? ??????? ???? ???? ????? ????? ?????? ???? ???? ??? ????? ??? ????? ??????. ???? ???? ?????? ?? ???????? ???????? ?????? - ?????? ?? ???? ??????? ???? G - ????? ????? ???????? ?????? ????? ????? ?????? ??????. ?? ???? ?????? ??? ??? ???? ????? ????? ?????? ???????? ?????? ????? ???????.
??? ??????? ???????? ?????? ????? ???????? ?????? ????? ????? ?????? ????? ????? ??????? ???? ??? ?? ?????? ??????. ???? ??????? ?????? ??????? ?? ???????? ?????? ????? ??? ??????? ??????? ??????? ????????? ??????? ?????? ?????? ???????.
??? ??? ??????? ???????? ?????? ????? ???? ?????? ???????. ???? ?????? ??????? ????? ??????? ?? ?????? ??????? ??????? ??? ??? ????????? ???????? ???? ????????? ?? ???????? ???????? ??????? ??? ???? ????? ?? ?????.
?? ????? ???????? ??????? ?????? ???? ?? ??????? ???????? ?????? ????? ????? ?????? ?? ??????? ????????? ???????.
????? ??????? ???????? ?????? ????? ??????
???? ????? ????? ??????? ???????? ?????? ????? ??? ??????? ??????? ????????? ???? ??? ??? ?????? ???? ??????. ??? ???????????? ??????? ?? ???? ??????? ?? ???? ??????? ??????? ??????? ??? ???????? ???????????. ??? ????? ?? ?? ???????? ????????? ??? ???????? ????? ??? ??????? ????????? ??? ???? ???? ????? ????? ?? ????? ???????? ???????.
??? ???? ?????? ?????? ?? ??????????? ??????????? ?? ????? ??????? ??????? ?????? ?? ????????? ??????? ?????. ??????? ????????? ????? ?????? ?????? ??????? ??????? ???????? ???????? ?? ??????? ??????? ??????? ?????? ???? ????????. ????? ??? ??????? ???????? ??? ??? ??? ????? ?????? ??????? ????? ???????? ???? ????? ??? ????? ???????.
????? ????????? ?????????? ???? ?? ???????? ?? ?????????? ????????????? ????? ?????? ?????? ??????????. ??? ????? ?????? ?????? ???????? ?????? ????? ??? ????? ????????? ??????????? ????? ????????? ?????? ??????? ??????? ???? ?? ??????? ?? ???????.
??? ??? ???????? ?????? ??? ????? ??? ??????? ??????? ???? ????. ???? ????? ?????? ????? ????? ???????? ??????? ??????? ??????? ??????? ???????? ??????? ??????? (CAD) ???????? CAM? ??? ???? ????????? ?????? ??? ????? ??????? ??????? ???? ?????? ???? ?????.
????? ??????? ??????? ????? ?????? ?????? ????? ??? ???????? ?????? ?????? ????? ?????? ??????? ????? ???? ?????? ???? ?????. ?? ?????? ?? ??? ??? ??? ????????? ?? ????? ??????? ?????? ???? ??? ???? ??? ????????? ??????? ?????? ??? ??????? ????????.
?? ?? ????? ?????? ??????? ???????? ?????? ??????
????? ?????? ??????? ????? ?????? ?????? ??? ?????? ????????? ?????????? ????? ???? ???? ?????? ?????? ????? ??? ????? ?????.
???? ???? ???????? ?????? ??????? ????? ???????. ??? ????? ?? ???? ????? ??? ?????? ????? ?? ???????? ????? ???? ?????????? ???????? ????? ????? ????? ?? ???? ????????.
?????? ????? ?? ??? ???? ????? ????????. ????? ???? ???? ??????? ????? ??? ?????? ???? ??? ??????? ????? ????? ???? ???? ????? [2]. ???? ??????? ????? ?????? ?? ???? ???? ???? ????? ??????? ?????????.
????? ????? ?? ?????? ???? ??? ??? ????? ???? ????? ????? ??????? ?????. ??? ????? ?????? ?? ??????? ?? ??????? ?? ??????? ?? ????? ?? ?????? ?? ????? ??????? ?? ????? ????? ?????? ???? ???? ????? ?? ?????? ?? ???? ?????. ????? ???????? ??? ???? ?????? ??????? ????? ???? ???? ???? ?????? ????? ?????? ?????? ???????? ?????? ?????. ???? ????? ??????? ?????? ????? ????? ???????? ????? ????????? ??? ???????? ???? ???? ????? ????????.
???? ?? ????? ????????? ???????? ????? ??? ??????? ???? ??????? ???? ???????? ?????? ??? ??????? ??? ????? ????? ???????? ????? ????? ???????? ????? ???????. ????? ??? ??????? ?????? ?????? ??????? ??? ????? ????.
?? ?? ????? ??????? ??????? ????? ?????? ???????
??????? ??????? ???????? ????? ?????? ?????? ???????? ?????? ?????
???? ??????? ??????? ????? ?????? ?????? ???????? ???? ?????? ?????? ????? ??? ????? ?????. ??? ??????? ?????? ????? ????? ??? ????? ?????????? ???? ?????? ?????? ?????? ?????? ??????? ???????? ?????????.
??????? ??? ????????? ??? ???? ???? ?? ??? ????????? ????? ????? ??????????? ?????? ???? ???? ????? ????? ??????. ??????? ????? ????????? ???????? ?? ??????? ??????? ?????? ??????? ??????? ???????? ????? ?????.
??????? ????? ????? ????? ?????? ?????? ???????? ?????? ?????
????? ??????? ??????? ??????? ??? ???? ???? ????? ?????? ?????. ???? ??????? ???????? ???????? ?? ????? ???????? ??????? ?????? ?? ????? ?????? ??? ???? ?? ????? ????? ????? ?? ????? ???????.
??????? ????????? ??????? ?? ??????? ??????? ??????? ??? ???? ???? ????? ???????? ??????? ??? ??????? ?? ??? ????? ???????.
??????? ??????? ????? ?????? ?????? ?????? ???????
???? ??????? ??????? ?????? ??????? ??? ??????? X ?Y ?Z. ??? ????????? ????? ??? ????? ?????? ????? ?? ????????? ??? ????? ?????? ?????? ?? ????? ??????? ????? ?????? ?????? ???????? ?????? ????? ????????? ?? ????? ???????.
??? ????? ?? ???? ?????? ???????????? ??? ?? ??????? ??? ??????? ???????? ??????? ?? ????? ???? ?? ????? ???? ??? ??????? ????? ????????? ?????? ???????.
??????? ????? ?????? ??????? ????? ?????? ?????? (CNC)
????? ??????? ??????? ????? ?????? ?????? ??? ????? ????? ????? ????? ??? ????? ????? ?????? ???? ????? ????? ?? ???? ????? ???????? ???????? ????? ??????? ?????. ???? ??? ??? ?????? ???? ??????? ?? ??? ??? ?? ?????? ???????.
??? ????? ??????? ????? ????? ??????? ?? ?????? ??????? ???????? ?????? ????? ????? ????? ??? ????? ????? ???????? ??????? ????.
?????? 1: ?????? ??? ????? ??????? ??????? ????? ?????? ?????? ???????
| ??? ???????? | ????? ???? ??????? | ??????? ????????? | ????????? ??????? |
|---|---|---|---|
| ?????? ????? ?????? | ????? | 3-5 ????? | ??????? ????? ?????? ???????? ??????? |
| ?????? ??????? ?????? | ???? | 3-4 ????? | ????? ?????? ???????? ??????? |
| ?????? CNC ??? 3 ????? | ??????? ?? ?????? | ?? ?? ? | ?????? ??????? ????? ???????? |
| ?????? ????? ?????? ?????? ??? 5 ????? | ????? ????????? | X? Y? Z + ????? | ??????? ????????? ??????? ???????? ??????? |
??? ??? ????? ??????? ???????? ?????? ????? ????? ?????? ??????
?? ????? ??????? ???????? ?????? ????? ?? ????? ?????? ??????? ??? ?? ?????? ????? ???? ??????? ??? ???? ???? ???? ?????. ????? ?? ????? ?? ????? ??????? ?? ??? ?????? ?????? ???????.
????? ????? CAD
???? ??? ??? ??????? ???????? ?????? ????? ?????? ????? ???? ????? ??????? ???????? ?????? ????? ??????? ?????????. ?? ??? ???????? ???? ????????? ????? ???? ??????? ???????? ??? ??????. ???? ??? ??????? ??????? ????? ??????? ????? ??????? ????? ??????? ???? ??? ??????? ??????? ?????.
????? ???? ??????? ???????? ?????? CAM
????? ?????? ????? ??????? ??????? ???????? ??? ???? ??? ?????? ??????? ??????? ???????. ???? ???? CAM ?????? ??????? ???? ???? ???? ???? ????? ??? ???? ????? [3].
??? ?????? ??????? ????? ???? ?????? ????????? ?? ???? ???? ??????? ????? ??????? ???? ?????. ??? ????? ??? ???????? ???? ???? ???? ????? ???? ?????? ???? ???? ??????.
????? ??? G
??? ????? ?????? ???????? ???? ?????? CAM ?????? ?????? ??????? ??? ??? ???? ??????? ????? (??? G). ???? ????? ?????? ??????? ?????? ???? ??????? ??????? ???????? ?????? ???? ?????? ??? ??????.
??? ??? ??? ??? ?????? ????? G ??? ???? ?????? ?? ?????? ??????? ????? ?????? ??????.
????? ????????
???? ???????? ?????? ???????? ?? ???? ????? ????? ????? ?????? ???? ????? ??? ????? ????? ??? ??? ????? ????????. ?? ???? ??? ??? ??????? ???????? ??? ?????????? ??????? ?????? ??????? ?????. ???? ??????? ?????? ???????? ????? ?????? ??????? ????? ???? ???.
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?????? 2: ??????? ????????? ?? ??? ??? ??????? ???????? ?????? ?????
| ????? ??? ????? | ????? | ??????? ???????? ????????? |
|---|---|---|
| ????? CAD | ????? ????? ??????? ??????? | ?????? CAD |
| ????? CAM | ????? ???? ??????? ??????????? ??????? ????? | ?????? CAM |
| ????? ??? G-Code | ????? ?????? ??????? ??? ??????? ???????? | ??????? ?????? |
| ????? ???????? | ????? ???? ????? ?????? ?????? | ????????? ???????? |
| ??????? ????? | ????? ?????? ????? | ?????? ????? ????? ?????? ?????? ???????? ??????? |
?? ?? ?????? ??????? ???????? ?????? ????? ????????
???? ???????? ?????? ?????? ???????? ?????? ????? ????? ?????? ?? ??????? ???? ???? ???????? ?????? ?????? ?? ?????? ???????? ??? ???? ?????. ????? ?? ????? ??? ??? ??????????? ??????? ????? ???? ???? ??????? ??? ???? ????? ???????.
????? ?????
???? ????? ?????? (????? ?????? ???????? ??? ????? ?????? ????? ?????) ????? ???????. ????? ??? ???????? ???? ?????? ??????? ?????? ????? ????? ???? ????? ?????? ??? ???? ??? ????? ????? ????? ?? ?????? ????????.
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????? ???????
????? ?? ????? ??????? ?? ??? ????? ???? ??? ???? ?????. ???? ??????? ??? ??????? ????? ???? ??? ??????? ???????? ?? ????? ??????? ?? ???????? ??? ????????? ???????????.
???? ?????? ????? ??? ?????? ????? ???????? ??????? ????????? ????????? ??? ????? ????? ??????? ???????? ?????? ?????? ???? ????? ????? ?????? ?????. ????? ??????? ????? ?????? ???? ??????? ?? ????????? ????????.
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???? ????? ????? ????? ??? ?? ???? ????? ???? ??????? ?????? ?????? ?? ?????? ???????. ????? ???? ??????? ??????? ??? ??????? ????? ?? ??????? ?????? ????????? ????? ???? ????? ?? ??????? ??? ?????????? ??? ????? ??? ????? ??? ?????? ?????? ?????? ???????.
?? ?????? ????????? ?? ????? ????? ????? ??? ???? ???????. ??? ???? ??????? ????? ????? ??????? ????? ????? ?? ???? ??????? ??? ?? ????? ??????? ??????? ??? ????? ????? ??? ????????? ?? ??????? ????? ??????. ????? ??? ??? ?? ????? ?????? ???????? ??? ?????? ?????????? ?????? ?????????? ??????????? ???? ????? ?? ???? ????? ???? ??????.
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?? ?? ????? ??????? ???????? ?????? ??????
????? ????? ??????? ???????? ?????? ?????? ???? ?????? ????? ?? ???? ?????? ??????? ??????? ?? ??????? ???????. ???? ???? ???? ????? ?? ?????. ???? ??? ?? ???? ??????? ????????? ???????? ????????? ???? ???????? ?????? ?????? ????? ?????? ?????? ????? ????? ?????? ???????? ??????? ???? ?????? ????? ????? ?????.
??? ???? ????? ?????? ?????? ???? ???????????. ???? ???????? ??????? ???????? ?????? ????? ????? ???? ????? ??????? ???????? ?? ????? ?????? ??? ????? ??????. ????? ??? ??? ??????? ???? ???? ???????? ?????? ????? ??????? ?????? ??????? ??????? ??????? ???????? ??? ??????? [5].
???? ??????? ????? ?? ?????????. ????? ????? ?????? ???????? ?????? ?????? ??????? ?????? ???? ????? ???????? ??? ?????? ??? ?????? ?? ????????. ???? ???? ???? ????? ???? ?? ????? ???????? ??? ???? ????? ??? ??????? ????? ????? ??????.
??? ?? ??????? ???????? ?????? ????? ?????? ???? ???? ?? ????? ??????? ??????? ???????. ????? ??? ??????? ??????? ??????? ??????? ???????? ??????? ??????? ????????? ??? ????? ??? ??????? ???????? ??? ?? ?????? ??? ???? ????? ?????? ?? ????? ?? ????? ????????.
?? ?? ???? ??????? ???????? ?????? ??????
??? ????? ?? ??? ???????? ??? ????? ???????? ?????? ????? ?? ????? ?????. ????? ?? ???? ??????? ??????? ?? ???????? ???????. ??????? ??? ?? ??????? ??? ??????? ???? ?????? ?? ???? ????? ??? ????? ?????? ?? ?????? ??????? ???? ????? ?? ????.
????? ????? ?? ??????? ??????? ?????? ?????? ????????. ????? ??????? ??????? ???????? ?????? ????? ????????? ???????? ?????. ??? ???? ??????? ?????? ?????? ???????? ??????? ?????? ??????? ????? ??????? ????? ???????.
???? ?? ????? ???????? ?????? ??????? ????? ??????? ?????? ?? ??????? ???? ?????????? ?? ??????? ???????? ??????? ?????. ??? ????? ?? ?? ????????? ?????? ??????? ???? ?? ????? ??? ??? ???????? ??? ???? ????? ??? ????? ?????? ??????? ????? ?????. ??? ???? ??? ??????? ??????? ????? ?????? ?????? ????? ?? ???? ?????? ??????? ????? ?????? ??????? ????????? ?? ??????? ????????? ????? ????? ?????????? ?????? ????????.
???????
[1] ?? ????? ?. (2022? 23 ??????/????? ?????). ?? ?? ????? ??? ?????? ?? ??????? ???????? ?????? ?????.
[2] ?? ????????. (2025? 22 ??????/????? ?????). ??? ????? ?????? ????? ?????? ??????: ?? ????? ?? ?????? ???? ??????.
[3] ????? ??????. (2026). ????? ??????? ???????? ?????? ?????: ??? ????? ?????? ?????????? ????????? ???????.
[4] ?????? (2026). ?? ?? ??????? ???????? ?????? ?????? ???? ???? ?? ???????? ?????????? ???????? ???????.
[5] ??? ??? (2021). ????? ???????? ?????? ?????: ??? ??????? ??????? ???? ????.
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