� ڶ � � � ƽ � � � � ϵ

ƽ � � � � ϵ � � � � � � � � � � � � � ߶ � � � ͬ һ ƽ � � � ڵ � � � ϵ � �

� ռ � � � ϵ � � � � � � � � � � � � � ߲ � � � ͬ һ ƽ � � � ڵ � � � ϵ � �

� 㽻 � � ϵ � � � � � � � � � ߽ � � � һ � � � � � ϵ � �

ƽ � � � � ϵ � � � � � � � � � � � ໥ ƽ � е � � � ϵ � �

һ � � � � ϵ � � � � � � � � � ߼ Ȳ � � � ȫ � � � � һ � � � ֲ � � � ȫ ƽ � е � � � ϵ � �

2.1 ƽ � � 㽻 � � ϵ

ƽ � � 㽻 � � ϵ � Ĺ � � � ʵ � � � �

2.1.1 � � � ķ ֽ �

� � � � ƽ � � � ı � � eta � � � � � � � � � � � � o � � � � � � � � � Ժ ϳ � Ϊ һ � � � � � � � � � � � � Ψ һ � ģ �

� � � � � � � � � � Ҫ � � һ � � � � ֪ � � � ֽ � Ϊ � � � � � � � � � � � � � 㹻 � � � � � � � � � ƣ � � � ⽫ � Dz � � � � ġ �

2.1.2 � � � � � � � � � � � ϵ � Ͷ Ӱ

ע � �. � � � � Ͷ Ӱ � Ǵ � � � � � � � � � � � � � � � � higher � � � £� � � � � a � � b � � � � � � � � � x ᣨ � � � y ᣩ � � � � � � һ � � ʱ � � � � � � F � � Ͷ Ӱ Fx � � � � Fy � � ȡ � � ֵ � � � � ֮ � � ȡ � � ֵ � �

2.1.3 � � � � Ͷ Ӱ � � � �

� � � � Ͷ Ӱ � � � � � �� � � � � � the awesome һ � � � ϵ � Ͷ Ӱ � � � ڸ � � � � � � � ͬ һ � � � � Ͷ Ӱ � Ĵ � � � � ͡ �

2.1.4 ƽ � � 㽻 � � ϵ � � ƽ � � � � � �

ƽ � � 㽻 � � ϵ � � � Ժ ϳ � Ϊ һ � � � � � � � � � � ƽ � � 㽻 � � ϵ � � � � � � � � � � � � � � gear � � Ȼ � � � � � � � � � � � � � � 㣬 � � � � � � � � ƽ � � 㽻 � � ϵ � � � � � � � ´ � � � ƽ � � ״ ̬ � � ƽ � � 㽻 � � ϵ ƽ � � ı � Ҫ � ͳ � � � � � � � Ǹ � � � ϵ � ĺ � � � F � � � � � 㡣 � �

� �

� � ϵ � � � � � и � � � � � � � � � � � � � � � � � y һ � � � � Ͷ Ӱ � Ĵ � � � � Ͷ � � � � � � 㡣 � � � � � � � � � � � � � ķ � � ̣ � � � � � � � � � � � � the delta ֪ � � � �

2-1 � � � � ͼ � � ʾ Ϊ һ � � � � � ܵ � � � � � � � ˿ � � � � � � � � � � � a � � � ֪ F1 = 2000 n � � ˮ ƽ � � � � F2= 5000 n � � � � ˮ ƽ � � � 30 Ƚ ǣ � F3 = 3000 n � � Ǧ ֱ � � � £� � � � � � � � � � С � � � � � � � � � � � � � � � С � �

� � 2-2 ͼ ʾ Ϊ һ � � � � � � � ػ � װ � a � � � � � G = 2 kn � � � � � � � � ڸ � ˿ � � � � һ � ˣ � � � ˿ � � � � � � һ � ˿ � � � � � � � � a � � � � � ڽ ʳ � � D Ĺ � � � � ϣ � � � � � � � � � ֱ � � AB � � AC ֧ � У � � � � � � ְ 뾶 � � С � � � � С � ɺ � � Բ � � ƣ � � � � � � ֡ � ֱ � � � Լ � � � ˿ � � � � � � � � � � � ƣ � � � � � � Ӵ � � � Ϊ � ⻬ � � � � � � � � � ﱻ � � � � � � � � ʱ � � � � AB � � AC � � � ܵ � � � � �

� � � � Ϊ � � AB � � AC � � � 뻬 � ֽ Ӵ � � � � � � Ը � AB � � AC � � � � � ܵ � � � � Ϳ � � � ͨ � � � � Ի � � ֵ � � � � � � � � � � � � � � � � ˣ � ȡ � � � � Ϊ � о � � � � � � � � � � � � � � � � � ͼ � � � � � � � � � � Ϊ ԭ � 㽨 � � ֱ � � � � � � ϵ � � � � ƽ � � 㽻 � � ϵ ƽ � � � � � � � � ƽ � ⷽ � � � �

� ⾲ � � ѧ ƽ � � � � � � � һ � 㷽 � � � Ͳ � � 裺

1. ѡ � � � о � � � � � � � ѡ � о � � � � � Ӧ � � � � ֪ � � � � � � � � � � � � � � � � � � � the delta ֪ � � � � ֱ � ӹ � ϵ � � � � � � � � � � Ӧ � � ƽ � � � � � � � � � � ֪ � � � � � � the delta ֪ � � � �

2. � � � � � � ͼ � � � � � о � � � � � � � � � � ⲿ � غ ɡ � Լ � � � � � � � � � ʣ � � � � о � � � � � � � � � � � � � � � � � � � o � � � � � � � � � ͼ � �

3. � � � � � � � � ϵ � � � � � � ƽ � � � � � � � � ƽ � ⷽ � � � ڽ � � � � � � � ϵ ʱ � � � � � � � һ � � � � һ � � the delta ֪ � � � � ֱ � �

� ڸ � � � ƽ � � � � � � � � ƽ � ⷽ � � ʱ � � Ҫ ע � � � � � Ͷ Ӱ � � � � � � � š � � � � � � � � � � � f � � ָ � � � ʱ � � ˵ � � ԭ � � � Ji � � � � ʵ � � � � � � � � � � � ෴ � �

2.2 � � � � � � ƽ � � � � ż ϵ

2.2.1 � � � Ե � ֮ � �?(� � � Ϊ � � � �)

1. � � � Ե � ֮ � ص ĸ � � �

Ϊ���������Ը����˶���ת��ЧӦ���������Ե�֮�صĸ��

� � � Ե � ֮ � � � � Mo � � F � � � � � � ʾ � � � � Mo (F) = � � Fd

һ � � أ � � � ƽ � � � � � � � � һ � � F � � � � ƽ � � � � � � ȡ һ � � O � � � �� � � �� � � O 㵽 � � � � � � � ߵ Ĵ � ֱ � � � � d � � Ϊ� � � �� �

Mo (F) = � � 2 � � OAB

� � � Ե � ֮ � � � � һ � � � � � � � � ʽ � е � � � � � � � � � � � � � � � � � � ص � ת � � � � � �

� � � IJ � ͬ � � � � � ز � ͬ � �

� higher � � � � ʹ � � � � � ƾ � � � � � � � ʱ � 뷽 � � ת � � ʱ � � � � � � ȡ � � � ţ � � � ֮ � � ȡ � � � š �

� � � ص ĵ � lambda � � Nmm � �

� � � � � ص Ķ � � � � ֪ � �

1 � � � � � � � � � � F � � � � � � � � � � � ƶ � � � � � � � Ϊ � � � Ĵ � С � � � � � � � � � � ۶ � � u и ı 䣬 � � � Բ � � � ı � � � � � � the awesome һ � � � ĵ � � � � ء �

� � 2 � � � � F = 0 � � � � Mo (F) = 0 � � � � Mo (F) = 0 � � F � � 0 � � � � d = 0 � � � � � � F ͨ � � O � 㡣

� � � ص � � � � � � � � � � � ǣ � � � � � � � � � � � � � � � � � � � � ͨ � � � � � ġ �

2. � � � � � ض � � �

� � � � � � � � � � A � � � � � � � � ƽ � � 㽻 � � ϵ F1� � F2� � - Fn � � � � � � � ĺ � � � F � � � ɻ 㽻 � � ϵ � ĺ ϳ � � � � a

� � � � � � ϵ � и � � � � � ƽ � � � � � � һ � � O � ľ أ � � � OA = l � � � �

Mo (F1) = F1d1= - F1lsina.1= F1 yl

Mo (F2) = F2 yl

Mo (Fn) = Fnyl

� � � � ͼ � � � Կ � � � � � � � � � F � � O � � ľ � Ϊ

Mo = Fd = F (F)lsina.= Fyl

� ݺ � � � Ͷ Ӱ � � � � � �

Fy= F1 y+ F2 y+ - + Fny

FyL = F1 yL + F2 yL + - + Fnyl

� �

= Mo Mo (F) (F1(F) + Mo2) + - + Mo (Fn)

� � � � � ض � � �ƽ � � 㽻 � � ϵ � ĺ � � � � � ƽ � � � � � � � � һ � � ֮ � أ � � � � � � � � � � з � � � � � ͬ һ � � � � � � ص Ĵ � � � � ͡ �

3. � � � Ե � ֮ � ص � � �(� � � ص � � �)

1 � � � � � � � � � ص Ķ � � � ʽ � � � � � � � � � � � � � ۵ awesome ˻ � � � � � � ء �

ע � ⣺ � � � � � d Ǿ � � ĵ � � � � � � � � ߵ ľ � � 룬 � � � � � ۱ � � 봹 ֱ � � � � � � � � � � � ߡ �?

� � 2 � � � � � u � � � � ض � � � � � � � � ء � � � � ֽ �

2-3 � � � � ͼ � � ʾ � � � � � � OBC � � O � � Ϊ � � � � ֧ � � Լ � � � � � � F � � � � � � � C 㣬 � ䷽ � � � Ϊ � � � � � � ֪ OB = l � � BC =H.� � � � � � F � � O � � � � � � ء �

1 � � � � � � � � � � � � � ص Ķ � � � � � � � � �

� � ͼ � � � � � � O � � � � � � F � � � � � ߵ Ĵ � � ߣ � � � � this � � a � �. � � � � � � d � � Ϊ � ߶ oa � � � � ٹ B � � � � � � � � � � � � ߵ � ƽ � � � ߣ � � � � � � ۵ � � ӳ � � ߽ � � � � B 㣬 � � � �

� � 2 � � � � � u � � � � ض � � � � � �

� � � � � F ֽ � � һ � � � � � � � ķ � � �

� � F � � � � � ؾ � � � � � � � � � � � � � � Ե � O � � � � � ص Ĵ � � � � � � �

Mo (F) = Mo (Fcx) + Mo (Fcy) = FhcosA -Flsina.= - F (lsina.- hcosa.)

2.2.2 � � ż � � � � � � � �

1. � � ż � Ķ � � �

� ڹ � � � ʵ � � � f � � � � � � � � � � � � � � � С � � ȡ � � � � � � ෴ � � � � � � � � � ໥ ƽ � е � � � � � � � � a � ʹ � � � � � � � ת � � � � � � � qing � � � � š ˮ � � ͷ � � ת � � � � � � � ̵ ȡ �

� � ż � � � � � � С � � ȡ � � � � � � ෴ � � � � � � � � � ໥ ƽ � е � � � � � � � � � ͼ � е � � � F � � F '� � � � һ � � ż � � � � � � (F� �F ')

� � ż � � � � � 桪 � � � � � � � � � � � ڵ � ƽ � �

� � ż � ۡ � � � � � � � � � � � � � � � ֮ � � Ĵ � ֱ � � � � d

� � ż � � ת � � � � ż ʹ � � � � ת � � � ķ � � �

� � ż ֻ � � ʹ � � � � ת � � � � ı � ת � � ״ ̬ � � � � � � � � � � � �

� � ʹ � � � � ת � � � � Ч Ӧ � � � � � � � Ե � ľ ض � � � � �

� � � � � � � � � � � � һ � � ż � � Ϊ d � � � � ż (F � � F ') � � � � � � ż � � � � һ � � O � ľ � Ϊ

+ Mo Mo (F) (F ') = F (x) + d - F 'x = Fd

� � � ڵ � O � � � � � � ѡ ȡ � ģ � � � � � ż � � � � � � � � � � � � һ � � ľ � = � � ż � � � � � Ĵ � С � � � � ż � ۵ awesome ˻ � � � � � � � � lambda � � � ޹ أ �

� � ż � ء � � � � � ż � � � � � Ĵ � С � � � � ż � ۵ awesome ˻ � � � � � � � M (F, F ') � � M

M (F, F ') = � � Fd � higher � � � � ż � � ʱ � � ת � � ʱ � � � � ż � � Ϊ � � � � � � ֮ Ϊ � � � �

� � ż � ص ĵ � lambda � � Nmm � � � � ż ͬ � � � � һ � � � � � � һ � � � � � � � �

Mo (F) = � � Fd

� � ż � � � � Ҫ � ء � � � � � С � � ת � � � � � � � ƽ � �

2. � � ż � � � � � �

1 � � � � � � ż � ޺ � � � � �

� � ż � � � � � � һ � � � � � � � � Ч � � Ҳ � � � � � � һ � � � � � � ƽ � ⡣

� � � Խ � � � � � � � ż � � � � � � � � � ϵ � � � � � � � � � � � � � � � � � �

� � 2 � � � � ż � � � � � � � � ƽ � � � � � � һ � � � � � � أ � � � � � � � � � � ż � ء �

3 � � � � � � ż � ĵ � Ч � � � � ż � ĵ � Ч � ԡ � � � � � � � � � ͬ һ ƽ � � � � � � � � � ż � � � � � � � ǵ � � � ż � ش � С � � ȡ � ת � � � � ͬ � � � � � � � � � � � � ż � ǵ � Ч � ġ �

� � ż � ĵ � Ч � � � � � �

1 � � � � ż � � � � � � � � � � � � � � � � � � � � � � ת � � � � � ı � � � � � � � � � � � � � a � � � � � ż � � � � � � � � � � � � � � � � � � � � � � � � ڵ � lambda � � � ޹ ء �

2 � � ֻ Ҫ � � � � � � ż � ز � � 䣬 � � � � ͬ ʱ � ı � � � ż � � � � � Ĵ � С � � � � ż � ۵ awesome � � ̣ � � � � � � � ı � � � ż � � � � � � � � � � � a

2.2.3 ƽ � � � � ż ϵ � ĺ ϳ � � � ƽ � �

ƽ � � � � ż ϵ � � � � � � � � � ڸ � � � � � ͬ һ ƽ � � � ڵ Ķ � � � � ż � �

1. ƽ � � � � ż ϵ � ĺ ϳ �

� � � � � � � � ż � ĺ ϳ �

M = M.1+ M2+ - + Mn

� � � � � � � � � � ż � ص � � ڸ � � � � � ż � ص Ĵ � � � � �

2. ƽ � � � � ż ϵ � � ƽ � �

ƽ � � � � ż ϵ � ϳ ɵ Ľ � � Ϊ һ � � � � � � ż � � � � � Ҫ ʹ � � ż ϵ ƽ � ⣬ � ͱ � � � ʹ � � � � ż � ص � � � � 㣬

2-4 � � � � AB � � һ � � � � � � ż � � � a � � � � � ż � � M = 100 nm � � � � � � l = 5 M � � � � � � � � � ز � � ƣ � � � � � ֧ � � � � Լ � � � � � � � �

1 � � � � � � � � � � Ϊ � о � � � � � � � � � � � � � � � � � � � � � � � � � ͼ

Fa.� � � � � � FB� � С � � ȡ � � � � � � ෴ � � � � � � � � ƽ � С �

� � 2 � � � � ƽ � ⷽ � �

2.3 ƽ � � һ � � � � ϵ

ƽ � � һ � � � � ϵ � � � � � � � � � � � � � � � ϵ ĸ � � � � � � � � ߶ � � � ͬ һ ƽ � � � ڣ � � Ȳ � � ཻ � � һ � � � ֲ � � � ȫ ƽ � С �

� � ͼ � � � ػ � � � � � AB � � ƽ � � һ � � � � ϵ � � � � � �

2.3.1 ƽ � � һ � � � � ϵ � ļ �

1. � � � � ƽ � ƶ � � � � � � Ŀ ɴ � � ԡ � � � � � � � � ڸ � � � � ϵ � � � � � � � � � � � � � � � � ڸ � � � � � � ƶ � � � � � � � � ı � � � Ը � � � � � � � � Ч Ӧ � �

� � � ⣺ � � � � � � � ƽ � Ƶ � � � � � � � � � һ lambda � � a

� � � � � � � ڸ � � � � � A � � � � � ƽ F � ƶ � � � � � � � � � � � � � һ � � O � �

� � � � � � ż � � � � � � ż � � Ϊ

M (F, F ') = � � Fd = Mo (F)

� � ʽ � � ʾ � � � � � � � � ż � ص � � � ԭ � � F � � ƽ � Ƶ � � � � � ء �

� � � ǣ � � � � � � � � ڸ � � � � � ƽ � Ƶ � � � � F � � ͸ � � � � � � ż M Ĺ � ͬ � � � � � £� � � � � � � Ч Ӧ � � � � � � F � � � � � � A � � ʱ � � Ч � �

� � � � ƽ � ƶ � � � � � � � � � � ڸ � � � � ϵ � � � � � � � ƽ � Ƶ � � � � � � ϵ � � � � � һ � 㣬 � � � � � 븽 � � һ � � ż � � � li � � � � ż � ص � � � ԭ � � � � ƽ � Ƶ � � � � � ء �

� � � � � � � � ƽ � ƶ � � � � � � Խ � � � � ֽ � Ϊ һ � � � � � � һ � � � � ż � � Ҳ � � � Խ � һ � � � � � � һ � � � � ż � ϳ � Ϊ һ � � � � � �

2. ƽ � � һ � � � � ϵ � � ƽ � � � � � � � � һ � � ļ �

� � � � � � � � ʸ � � x � � ļ н �

Mo � � � � ƽ � � һ � � � � ϵ � � � � � �

= � � � � � � � � � � � � ż � ص Ĵ � � � � ͡ �

Y һ � � � � � � � � � � � � � � ż � ص � � � ԭ � � � � ƽ � Ƶ � � � � � أ � � � � � � � � ص � � ڸ � � � � � � Լ � � � � ĵ � � � � ص Ĵ � � � � ͣ � � � � � � � � � ϵ � � � ڵ � ƽ � � � ϡ � � �

Mo= M.1+ M2+ - + Mn= M.o(F1) + Mo(F2+ - + M)o(Fn)

ƽ � � һ � � � � ϵ � � ƽ � � � � һ � � � � o � һ � � � � ʸF 'R� � һ � � � � � � Mo� �

� � ʸ � Ĵ � С � � � � ԭ � � ϵ � и � � � � � Ͷ Ӱ � � ƽ � � � � � ٿ � � � � � � � � � � ڼ � � � � � � ϡ � � � � С � ͷ � � � � � � � � � ĵ � ѡ � � � ޹ ء �

� � � ص � � � ԭ � � ϵ � � � � � � � Լ � � � � � � � � ص Ĵ � � � � ͣ � � � ֵ һ � � � � � � � � ĵ � ѡ � � � й ء �

3. � � � � � � �

ƽ � � һ � � � � ϵ � � ƽ � � � � � � һ � � � � o � һ � � � � ʸF 'R� � һ � � � � � �MO � � � � � ⲻ � � � � ϵ � � � � � ս � � � � � � � � � һ � � � � � � � � � � � � � � � � � � � � � � � �

F 'R= 0,MO � � 0

F 'R� � 0,MO = 0

F 'R� � 0,MO � � 0

F 'R= 0,MO = 0 (� � ϵ ƽ � �)

2.3.2 ƽ � � һ � � � � ϵ � � ƽ � �

1. ƽ � � һ � � � � ϵ � � ƽ � � � � � �

ƽ � � һ � � � � ϵ ƽ � � ı � Ҫ � � � � � � � � Ϊ � �

2. ƽ � � ƽ � � � � ϵ � � ƽ � � � � � �

ƽ � � ƽ � � � � ϵ � � ƽ � ⷽ � � Ϊ

ƽ � � ƽ � � � � ϵ ֻ � � � � � � � � � � � � ƽ � ⷽ � ̣ � � � � ֻ � � � � � � � � � the delta ֪ � � � �

2-6 � � � � ʽ � � � ػ � � Ľ ṹ � � ͼ � � ͼ � � ʾ � � � � � � � � � � �G= 500 kn � � � � � � � � � C 㣬 � � � ҹ � � � �a.= 1.5m� � � � � � � � � � � �P= 250 kn � � � � � ҹ �B� � Զ � � � �l= 10m� � ƽ � � � � � � � � Ϊ1 G� � � � � � �a.� � �x= 6m� � � � � � � � �b= 3m� � � � � � � � � ػ � � � � � � � � � � � � ʱ � � � � � � � � � � � � ƽ � � � � � �1 G� ķ � Χ � �

� ⣺ ȡ � � � ػ � Ϊ � о � � � � �

� � һ ƽ � � ƽ � � � � ϵ

3. � � � � ϵ ͳ � � ƽ � � � � � �

� � ϵ � � � � � ɶ � � � � � � ͨ � � һ � � � � Լ � � � � ɵ � ϵ ͳ � �

� � � � � � � � ϵ � � � � ƽ � � ʱ � � � � o � � � � � һ � � ϵ � � � � � й � � � Ҳ � � � � ƽ � ⡣ � � � � � � � � � й � � � ϵ � � ƽ � � � � � � ʱ � � � ȿ � � � � � � � � � ϵ ͳ Ϊ � о � � � � � Ҳ � � � � ȡ � � � � � � � � Ϊ � о � � � � � � � y һ � � ѡ ȡ � � � о � � � � � һ � � � � � � ¶ � � � � � � f � � � � � � � � � � � ƽ � ⷽ � ̡ � 3 n

� � ϵ � � � � � � � � ϵ ͳ � ⲿ � � � � � ϵ ͳ � � � � � � � �

� � ϵ � � � � � � � � ϵ ͳ � ڲ � � � � � � � ֮ � � � � ໥ � � � � � �

��ϵ������������ֻ��һ����Եĸ������֮��û���ϸ�������о�����ϵͳƽ��ʱ���������������dzɶԳ��֡��໥��������˿��Բ��迼�ǡ����о�ϵͳ��ijһ�����ֹ�����ƽ������ʱ��ϵͳ���������������ǵ����������ֳ�Ϊ��һ�о�������������������Կ��ǡ�


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