global solutions innovation collaboration Pro/Engineer 2001 ú) !9 ?T [?  B ú) !9 ?T [?  B ? 2000 PTC [? = ?# HW? ? [? = ?# HW? ? ?B? 1aú)¤??+? 2aù ???? 3a7yú)+?+? ?=? 1aBV? L è 2aú) ,qy ??  3aF?¨?1?l+? 4aú) ￥y  ? ?? 1a !9D?? !9 2am^? ? aú)¤??+? aù ???? a7yú)+?+? ?=? aú) ,qy ??  aú) ￥y  ? ?? ? 2000 PTC ?B? [? = ?? ? ?B? [? = ?? ? ?B?aú)¤??+? ?B?aú)¤??+? ?=?aù ???? ?=?aù ???? ? ??a7yú)+?+? ? ??a7yú)+?+? ? 2000 PTC ?B?aú)¤??+? ?B?aú)¤??+? Baú)+?+? Baú)+?+? =a P¨9D? ? =a P¨9D? ? ?a? ????¤?ó' ?a? ????¤?ó' [  [  l2 l2 ? 2000 PTC Baú)+?+? Baú)+?+? 1a7y¤?? 2a7y=Q wL a7y=Q wL 3a7y???? a7y???? 4a7y"H wL a7y"H wL ? 2000 PTC 1a7y¤?? ¤?? V[￡ùjS?b ¤?? V[￡ùjS?b ? 2000 PTC 2a7y=Q wL a7y=Q wL 17y conic￥ZE 7y ￥ZE 2·?? ?′ ·?? ?′ 3? ? conic? ? ? ? ? ? 4 ?¨¤??  ?¨¤?? ? 2000 PTC 17y conic￥ZE 7y ￥ZE 7y conic￥ZE ? ??7y 3???5ê4B ? ?ê4 6B? ?Kaê4B??W?b 7y ￥ZE ? ??7y ? ?ê4 6B? ?Kaê4B??W?b ? 2000 PTC 2·?? ?′ ·?? ?′ ·? rho′ ??l conic￥?b Rho=BE/DE 0.05< rho<0.5 ??? Rho=0.5 ?tL 0.5<rho<0.95 ? wL ·? ′ ??l ??? ?tL ? wL ? 2000 PTC 3? ? conic? ? ? ? ? ? 1 ?ê?? ? 2·? rho′ 3 ?M MZ_? ?  ?ê?? ? ·? ′  ?M MZ_? ? ? 2000 PTC 4 ?¨¤??  ?¨¤?? ?? ??j ?¨ ???]??l￥?"dV¨??l￥?? ??Z??|YV??b ?T?B? ^ ?? ?? ?ü?A9F  ?j - V[|???? ??  b ?7 ?T ? ^B? “¤?  ”???5A? ?? ??j[ 3¤?b ?? ??j ?¨ ???]??l￥?"dV¨??l￥?? ??Z??|YV??b ?T?B? ^ ?? ?? ?ü?A9F  ?j V[|???? ??  b ?7 ?T ? ^B? ¤?  ???5A? ?? ??j[ 3¤?b ? 2000 PTC 3a7y???? a7y???? ? 2000 PTC 4a7y"H wL a7y"H wL "H wL ^BHYV ??;á ?¤￥ wL b1  e?"H wL F V[S? =? ?B?￥ j V[S? ?￥M M ?b "H wL ^BHYV ??;á ?¤￥ wL V[S? =? ?B?￥ j V[S? ?￥M M ? ??"H wL ? 2000 PTC =a P¨9D? ? =a P¨9D? ? 1a9D¤m L8 2a9Dj a9D¤m L8 ? 2000 PTC ?a? ????¤?ó' ?a? ????¤?ó' ? 2000 PTC [  [  1aVóq? ?? ? ?7y"H wLb 2a?T"H wLb 3a7y?I ????b 4a7y?S?=Q wLb aVóq? ?? ? ?7y"H wLb a7y?I ????b a7y?S?=Q wLb         ? 2000 PTC l2 l2 ???1D  1?￥¤?+? 2V?? ? óq? ? ? ?7y" H wLi?l"H wLb 37yi i? ?[!a¨b 47y???? 57yò? conic wL ???1D  ?￥¤?+? V?? ? óq? ? ? ?7y" H wLi?l"H wLb 7yi i? ?[!a¨b 7y???? 7yò? wL ? 2000 PTC ?=?aù ???? ?=?aù ???? 1ao ù ? ao ù ? 2a7yù ? a7yù ? 3ao ?? 4a7y?? [  [  l2 l2 ? 2000 PTC 1ao ù ? ?l “ù  ”+? V1?? w ?B"  ?ê￥ ü ?9FB?ù ?b ?l ù  +? V1?? w ?B"  ?ê￥ ? 2000 PTC o ù ? o ù ? ?? ?l ù  w ? 1ù  ?ê￥ ? w ?b ?? ü ? à? ü ? ù  w ? V ?"?? ü ?Dù  w ?￥?Lè b ?? wL ù  w ? ¨Tù  w ?￥èà￥ wL – ù  w ? ?"?? wLèb ù Z_ ¨?? ù ?￥Z_b ?$?l1<°?? v ü ?b ù ? ù Z_D 3?￥ù  w ?-W￥?b ?T ù  w ?$sé5 V1ù ￥ ???s?l ?? ?￥?b èZ_ ?vZ_ ¨ ??lù  w ? ?? ??? ü ??? w ? è￥Z_b sé u× V ?¨?]ù ?￥ù  w ? u×b 7yù  H1 I n/ y í &· ?? w ? ^? V?? ? ü ??? H? Vù b &· ?Tù  w ? ^?? ? Hù Z_A?<°??? ü ?b &· w ?H￥H???μ?? H? ?ù b?V V[ n5ù   ?aHé???V b ù  w ? 1ù  ?ê￥ ? w ?b ?? ü ? à? ü ? ù  w ? V ?"?? ü ?Dù  w ?￥?Lè ?? wL ù  w ? ¨Tù  w ?￥èà￥ wL ù  w ? ?"?? wLèb ù Z_ ¨?? ù ?￥Z_b ?$?l1<°?? v ü ?b ù ? ù Z_D 3?￥ù  w ?-W￥?b ?T ù  w ?$sé5 V1ù ￥ ???s?l ?? ?￥?b èZ_ ?vZ_ ¨ ??lù  w ? ?? ??? ü ??? w ? sé u× V ?¨?]ù ?￥ù  w ? u×b 7yù  H1 I n/ y í ?? w ? ^? V?? ? ü ??? H? Vù b &· ?Tù  w ? ^?? ? Hù Z_A?<°??? ü ?b &· w ?H￥H???μ?? H? ?ù b?V V[ n5ù   ?aHé???V ? 2000 PTC ù ?￥ ?? ù ?￥ ?? ? 2000 PTC 2a7yù ? 17y?? ü ?ù ? 7y?? ü ?ù ? 27y?? wLù ? 7y?? wLù ? ? 2000 PTC 17y?? ü ?ù ? 7y?? ü ?ù ? ? 2000 PTC 27y?? wLù ? 7y?? wLù ? ? 2000 PTC 3ao ?? P¨ “??? ”ê[ V7y w ?W￥??? ?W w ?ê?￥???b w ? V[ ^.dil  1SP&/(*/&&3￥ ,¨￥ ?F# w ?9 V[ ^ L8 ? w ?b 7y???? I n[/yp ·a !9?D V ??t9F??? ??F y+?- -b ·a V[| ?μ???b??B?a  ?a? c?a[LF yyTé?b ·a1E ?7yV ?????+?￥0[ h ? 1S?????7y￥HM MHb ??? ê[ V7y w ?W￥??? ?W w ?ê?￥???b w ? V[ ^.dil  y+?- -b ? ? 2000 PTC 4a7y?? 17ye???? 7ye???? 27yú)??? V[7y ??] ??￥??? - e??ú)b7y?? ?? ￥??? | %??v+?￥ˉ?[#1?l"d ?4￥ ? 8???+?￥31b e???? P¨è?????? ?b?7yú)??? H V[?l? “???F ” ???+?￥ b"d?? ?F-W7y ? 8Vi ?[a é???b 7yú)??? V[7y ??] ??￥??? e??ú)b7y?? ?? ￥??? | %??v+?￥ˉ?[#1?l"d ?4￥ e???? P¨è?????? ?b?7yú)??? H V[?l?  ???+?￥ b"d?? ?F-W7y ? 8Vi ?[a é???b ? 2000 PTC 17ye???? 7ye????  1ê4?v ??  ê4?v ??  2 !???S?   !???S?  3?l????′  ?l????′ ? 2000 PTC  1ê4?v ??  ê4?v ?? ? 2000 PTC  2 !???S?   !???S? ?X ?Z???+? P ?ê?￥?vX N? ?μ ê??v- -T???? h·? Vêí í “???S? ”b &· ?? w ? - YV ? w ? ê | ?·??? w ?b V[ ?iê4 ?? w ?￥ ? b ?1 w ?-W7y???5? ?ê4D? w ? M M￥ w ?b &· 1?? - ????M MH H7y?¤b L= ???| “ OV ” ???￥ ?μdM MHí ?  ^H y? ^???9 ?V ?? ???￥ w ??b ?X ?Z???+? P ?ê?￥?vX N? ?μ ê??v- -T???? h·? Vêí í ???S? ?? w ? YV ? w ? ê | ?·??? w ?b V[ ?iê4 ?? w ?￥ ? b ?1 w ?-W7y???5? ?ê4D? w ? M M￥ w ?b 1?? ????M MH H7y?¤b L= ???| OV ???￥ ?μdM MHí ?  ^H y? ^???9 ?V ?? ???￥ w ??b ? 2000 PTC  3?l????′  ?l????′ ? 2000 PTC 27yú)??? 7yú)???  1ú)???  ú)???  2???F  ???F  3?l¤? T  ?l¤? T ? 2000 PTC  1ú)???  ú)??? e?????]ú)??? V?l ·????F ·???￥? “O? o ” “<°? O ” ·???￥?? ? “?? ” “?? ” ·???F-W￥¤ ?? ·?7y￥+?m?][ -7y￥+?m?-W￥. ?¤ ??b e?????]ú)??? V?l O? o  <°? O ???￥?? ?  ?7y￥+?m?][ -7y￥+?m?-W￥. ? 2000 PTC  2???F  ???F B?tH??? C???F D???F E???F F ? 8￥.?¤ ? 8￥.?¤ ? 2000 PTC  3?l¤? T  ?l¤? T ? 2000 PTC  3?l¤? T  ?l¤? T ? 2000 PTC  3?l¤? T  ?l¤? T ? 2000 PTC [  [   1 2? ??? ü ???? wLù ?b  3ú)ù ?/ ?b  4e???  5ú)??/ ?b  6ò?i_ y??b   ? ??? ü ???? wLù ?b  ú)ù ?/ ?b  e???  ú)??/ ?b  ò?i_ y??b ? 2000 PTC l2 l2 ?1? ? 19Fù ?+?1   !9S! 29Fú)￥ù ? 37ye??ú)??b ?1? ? 9Fù ?+?1   !9S! 9Fú)￥ù ? 7ye??ú)??b ? 2000 PTC ? ??a7yú)+?+? ? ??a7yú)+?+? Ba á í? Ba á í? =aM? ? á í =aM? ? á í ?a ?è á í ?a ?è á í [  [  l2 l2 ? 2000 PTC Ba á í? ?i/ K?Hq ·? ?? ?ê? “e SE ”￥U?)b ·?>?E } ?  S??à B?  ?ê?μ¤?? ?b Pro/ENGINEER P¨ ?)￥?B?? ?b ·? 7bE } ?A?  S?????7y? ?b?t? àμ VKV? ?b?￥ê[b ·? ?? ?S?j? ?y1??E H? P?tjírb ·? ?ê4ˉ? wL ??l á í?￥? ? “ê |? ? ”b7 ^A ?ê |BH ??ˉ? wL￥?a wLHb · ?Tê4 “à?Z_ ”? “ê |? ? ” * 1 ?μê |￥? ?A?ê?D “ à?Z_ ” ü?￥ ü ? b ?i/ K?Hq ? ?? ?ê? ￥U?)b ?>?E } ?  S??à B?  ?ê?μ¤?? ?b P¨ ?)￥?B?? ?b ? 7bE } ?A?  S?????7y? ?b?t? àμ VKV? ?b?￥ê[b ? ?? ?S?j? ?y1??E H? P?tjírb ? ?ê4ˉ? wL ??l á í?￥? ? ê |? ? b7 ^A ?ê |BH ??ˉ? wL￥?a wLHb ?Tê4 à?Z_ ? ê |? ?  * 1 ?μê |￥? ?A?ê?D à?Z_ ü?￥ ü ? b ? 2000 PTC Ba á í? ê[ ?l <°?e SE ? ? ü ???é  ?<°? “e SE ”b ?Y ?￥ “ á í ”VC1? ?Z Tb <°?E A ?ê | ?E ? %??? ?￥ê ??Z_b “e SE ” %??+?é ￥? ?e?b?+?é ? ? ? ü ? ?D “E_E ”<°b à?Z_  “à?Z_ ” A ?? ? ü ? ?D “ e SE ”<°b? ?￥_ Z_ ? D “à?Z_ ” ü?b ? ? ü ???é  ?<°? b ?Y ?￥ á í VC1? ?Z Tb <°?E A ?ê | ?E ? %??? ?￥ê %??+?é ￥? ?e?b?+?é ? ? ? ü ? ?D à?Z_ à?Z_ A ?? ? ü ? ?D <°b? ?￥_ Z_ ? à?Z_ ? 2000 PTC =aM? ? á í =aM? ? á í 1a<°?e SEL a<°?e SEL 2a¨?F￥EL?l? a¨?F￥EL?l? 3a P¨E? ? a P¨E? ? 4a P¨M? ? á í￥?i Y[ a P¨M? ? á í￥?i Y[ 5a? ?￥Z_ ?? a? ?￥Z_ ?? ? 2000 PTC 1a<°?e SEL a<°?e SEL  FA??lBH?S x-vector horizontal vector￥ELb "d P¨?HEL ??_? ?b ? ? ü ? ^<°?e SELb  FA??lBH?S ￥ELb "d P¨?HEL ??_? ?b ? ? ü ? ^<°?e SELb 7y<°?e SEL??i[/+? 1  2 3 7y<°?e SEL??i[/+?  ? 2000 PTC 2a¨?F￥EL?l? a¨?F￥EL?l? ??le SE? XZ_Ea F V[??ê4¤ ??F￥EL ? e?? ?b ??le SE? Z_Ea F V[??ê4¤ ??F￥EL ? e?? ?b ? 2000 PTC 3a P¨E? ? a P¨E? ? ? 2000 PTC 4a P¨M? ? á í￥?i Y[ a P¨M? ? á í￥?i Y[ P¨M? ? á í￥?i Y[ 1M? ? á í? ? ^?B?+?yNA?5 P¨  a￥ +?b 2e SELA??M M￥ L8F? P¨à?Z_"? b 3 X_ EL? ?De SELM?b 4 ?μ?F￥EL?A??? ?¤? ü ?M???1 péM?b 5¤? ü ? V[D ??ELM?b 6 ?T¤? ü ?D ?μ￥EL? ^M??  S?5 V [ P¨? ??l 7 S?b P¨M? ? á í￥?i Y[ M? ? á í? ? ^?B?+?yNA?5 P¨  a￥ +?b e SELA??M M￥ L8F? P¨à?Z_"?  _ EL? ?De SELM?b  ?μ?F￥EL?A??? ?¤? ü ?M???1 péM?b ¤? ü ? V[D ??ELM?b  ?T¤? ü ?D ?μ￥EL? ^M??  S?5 V [ P¨? ??l 7 S?b ? 2000 PTC 5a? ?￥Z_ ?? a? ?￥Z_ ?? Normal to the original trajectory Normal to trajectory  <°?e SE  <°?E Pivot direction  à?Z_  <°?e SE  <°?E  à?Z_ ? 2000 PTC ?a ?è á í 1a7y ?è á í￥?? a7y ?è á í￥?? 2a ?è á í￥ê[ a ?è á í￥ê[ ? 2000 PTC 1a7y ?è á í￥?? a7y ?è á í￥?? 1A?¤?BH á í } ?Lb 2 } ?L V[ ^M?￥b 3?? } ?LaA?·? ? ′b 4¤"¤?? ?b 5"d? } ?L? ?  á í? ?b A?¤?BH á í } ?Lb  } ?L V[ ^M?￥b ?? } ?LaA?·? ? ′b ¤"¤?? ?b "d? } ?L? ?  á í? ?b ? 2000 PTC 2a ?è á í￥ê[ a ?è á í￥ê[ 1Pè·è 2YVà<°?EL 3 ?  ^è ?M? 4¨¤???m? ? e? ?  Pè·è YVà<°?EL  ?  ^è ?M? ¨¤???m? ? e? ?  ? 2000 PTC [  [   1a7y á í?  2a P¨m?7yM? ??  a7y á í?  a P¨m?7yM? ?? ? 2000 PTC l2 l2 ? ú?1D 17y á í? 27yM? ? á í 3M? ? á í￥ ?? 4 P¨ ?è á íb 7y á í? 7yM? ? á í M? ? á í￥ ?? ? 2000 PTC