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µÎ °³ÀÇ ±â¾î°¡ ¸Â¹°¸± ¶§ °¢ ±â¾îÀÇ Ä¡(teeth)´Â °°Àº Á¢¼±(common tangent)À¸·Î Á¢ÃËÇÏ°í µÎ ¸Â¹°¸² ±â¾îÀÇ Ç¥¸é¿¡ °°Àº Á¢ÃËÆ÷ÀÎÆ®¿¡¼ ºÎµúÈù´Ù. ¸¸¾à ÀÌ Á¢¼±ÀÌ µÎ ±â¾îÀÇ Á߽ɻçÀÌ¿¡ ±×¾îÁø´Ù¸é Á¢¼±ÀÇ ¹ý¼±(normal)ÀÌ ±â¾îÁ߽ɰ£ ¼±ºÐ°ú ¼·Î ¸¸³ª´Â Á¡(P)¸¦ ¡®pitch point¡¯¶ó°í ÇÑ´Ù.(the normal to the common tangent intersects the center to center line at point P)
ÀÏÁ¤ÇÑ ¼Óµµºñ¸¦ À¯ÁöÇϱâ À§Çؼ Á¢¼±ÀÇ ¹ý¼±ÀÌ ÀÌ·ç´Â ±â¾î°£ Á¢ÃËÁ¡Àº ¹Ýµå½Ã pitch point¸¦ Åë°úÇØ¾ß ÇÑ´Ù.(the normal to the common tangent at the point of gear tooth contact must always pass through the pitch point) ±×¸®°í ÇÇÄ¡Æ÷ÀÎÆ®´Â µÎ ±â¾îÀÇ Á߽ɼ±»óÀ§¿¡ ³õ¿©¾ß ÇÑ´Ù. ÀÌ·¯ÇÑ »óŸ¦ ¡®conjugacy¡¯¶ó°í ÇÑ´Ù. Á¢¼±ÀÇ ¹ý¼±°ú ÇÇÄ¡Æ÷ÀÎÆ®¸¦ Åë°úÇÏ´Â ±â¾î°£ Á߽ɼ±ÀÇ ¼öÁ÷¼±°úÀÇ °¢µµ¸¦ ¡®pressure angel¡¯À̶ó°í ÇÑ´Ù. °¢ ±â¾îÀÌ¿¡¼ ÇÇÄ¡Æ÷ÀÎÆ®´Â ±â¾îÀÇ Á߽ɰú °°Àº °Å¸®¿¡ ÀÖ´Ù. ÇÇÄ¡Æ÷ÀÎÆ®¸¦ ¼·Î ¿¬°áÇÑ ¿øÀ» ¡®pitch circle¡¯À̶ó°í ÇÑ´Ù. ÀÌ °ÍÀº ±â¾î¸¦ Á¤ÀÇÇϴµ¥ »ç¿ëµÇ´Â ¾ÆÁÖ Áß¿äÇÑ ¿ë¾î°¡ µÈ´Ù.
Conjugacy¸¦ À§ÇÑ µÎ »óÅ°¡ ¸¸³ª´Â ÇüÅÂÀÇ ¹«ÇѼö(infinite number)°¡ Àִµ¥ ´ëºÎºÐ Çö´ë ±â¾îÀÇ ¼³°èÁ¶°Ç¿¡´Â ÃæÁ·µÇÁö ¾Ê´Â´Ù. µû¶ó¼ ÀϹÝÀûÀÎ ÇüÅÂÀÇ ¼³°èÀÎ ¡®involute¡¯·Î Á¦À۵Ǵµ¥ ÀÌ Àκ¼·ùÆ® ¼³°è´Â ¿øÀÇ circumference ·ÎºÎÅÍ unwoundµÇ¾úÀ¸¹Ç·Î ´ç°ÜÁø ¼±ÀÇ ³¡¿¡ °î¸é±ËÀûÀ» ³ªÅ¸³»°í ÀÖ´Â Çü»óÀÌ´Ù.(curve traced by the end of a tight string as it is unwound from the circumference of a circle)
±â¾î¹Ú½º¿¡ ³»ÀåµÇ´Â °¡Àå ´ëÇ¥ÀûÀÎ ±â¾îÀÇ ÇüÅ´ spur, Helical, Crossed helical, worm, bevel·Î ±¸ºÐÇÒ ¼ö ÀÖ´Ù.
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