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徐小湛的博客

高等数学课件、函数图形动画、数学软件应用

 
 
 

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齿轮传动(Maple动画)  

2012-04-28 11:11:57|  分类: 高等数学图形动画 |  标签: |举报 |字号 订阅

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用数学软件Maple的动画模拟齿轮传动过程

 
动画1
 

齿轮传动 - calculus - 徐小湛的博客

说明:小齿轮的转速是大齿轮3倍,中齿轮的转速是大齿轮2倍。
 
动画2

齿轮传动 - calculus - 徐小湛的博客

 

动画1Maple程序:
with(plots):with(plottools):

R1:=6:R2:=3:R3:=2:k:=R1/R2:h:=R1/R3:

x1:=t->R1*cos(t): y1:=t->R1*sin(t):

x2:=t->R1+R2+R2*cos(t): y2:=t->R2*sin(t):

x3:=t->R1+2*R2+R3+R3*cos(t): y3:=t->R3*sin(t):

yuan1:=plot([x1(t),y1(t),t=0..2*Pi],color=green,thickness=3):

yuan2:=plot([x2(t),y2(t),t=0..2*Pi],color=blue,thickness=3):

yuan3:=plot([x3(t),y3(t),t=0..2*Pi],color=brown,thickness=3):

K:=120:for i from 0 to K do ti:=i*2*Pi/K:

xian11[i]:=plot([t*cos(ti)-0*sin(ti),t*sin(ti)+0*cos(ti),t=-R1..R1],thickness=10,color=green):

xian12[i]:=plot([0*cos(ti)-t*sin(ti),0*sin(ti)+t*cos(ti),t=-R1..R1],thickness=10,color=green):

xian21[i]:=plot([R1+R2+t*cos(-k*ti)-0*sin(-k*ti),t*sin(-k*ti)+0*cos(-k*ti),t=-R2..R2],thickness=8,color=blue):

xian22[i]:=plot([R1+R2+0*cos(-k*ti)-t*sin(-k*ti),0*sin(-k*ti)+t*cos(-k*ti),t=-R2..R2],thickness=8,color=blue):

xian31[i]:=plot([R1+2*R2+R3+t*cos(h*ti)-0*sin(h*ti),t*sin(h*ti)+0*cos(h*ti),t=-R3..R3],thickness=6,color=brown):

xian32[i]:=plot([R1+2*R2+R3+0*cos(h*ti)-t*sin(h*ti),0*sin(h*ti)+t*cos(h*ti),t=-R3..R3],thickness=6,color=brown):

od:

xian11:=display(seq(xian11[i],i=0..K),insequence=true):

xian12:=display(seq(xian12[i],i=0..K),insequence=true):

xian21:=display(seq(xian21[i],i=0..K),insequence=true):

xian22:=display(seq(xian22[i],i=0..K),insequence=true):

xian31:=display(seq(xian31[i],i=0..K),insequence=true):

xian32:=display(seq(xian32[i],i=0..K),insequence=true):

display(xian11,xian12,xian21,xian22,xian31,xian32,yuan1,yuan2,yuan3,scaling=constrained);

 
 
动画2Maple程序:
with(plots):with(plottools):
R1:=6:R2:=3:R3:=2:k:=R1/R2:h:=R1/R3:
x1:=t->R1*cos(t): y1:=t->R1*sin(t):
x2:=t->R1+R2+R2*cos(t): y2:=t->R2*sin(t):
x3:=t->R1+R2+R3*cos(t): y3:=t->R2+R3+R3*sin(t):
yuan1:=plot([x1(t),y1(t),t=0..2*Pi],color=green,thickness=3):
yuan2:=plot([x2(t),y2(t),t=0..2*Pi],color=blue,thickness=3):
yuan3:=plot([x3(t),y3(t),t=0..2*Pi],color=brown,thickness=3):
K:=120:for i from 0 to K do ti:=i*2*Pi/K:
xian11[i]:=plot([t*cos(ti)-0*sin(ti),t*sin(ti)+0*cos(ti),t=-R1..R1],thickness=10,color=green):
xian12[i]:=plot([0*cos(ti)-t*sin(ti),0*sin(ti)+t*cos(ti),t=-R1..R1],thickness=10,color=green):
xian21[i]:=plot([R1+R2+t*cos(-k*ti)-0*sin(-k*ti),t*sin(-k*ti)+0*cos(-k*ti),t=-R2..R2],thickness=8,color=blue):
xian22[i]:=plot([R1+R2+0*cos(-k*ti)-t*sin(-k*ti),0*sin(-k*ti)+t*cos(-k*ti),t=-R2..R2],thickness=8,color=blue):
xian31[i]:=plot([R1+R2+t*cos(h*ti)-0*sin(h*ti),R2+R3+t*sin(h*ti)+0*cos(h*ti),t=-R3..R3],thickness=6,color=brown):
xian32[i]:=plot([R1+R2+0*cos(h*ti)-t*sin(h*ti),R2+R3+0*sin(h*ti)+t*cos(h*ti),t=-R3..R3],thickness=6,color=brown):
od:
xian11:=display(seq(xian11[i],i=0..K),insequence=true):
xian12:=display(seq(xian12[i],i=0..K),insequence=true):
xian21:=display(seq(xian21[i],i=0..K),insequence=true):
xian22:=display(seq(xian22[i],i=0..K),insequence=true):
xian31:=display(seq(xian31[i],i=0..K),insequence=true):
xian32:=display(seq(xian32[i],i=0..K),insequence=true):
display(xian11,xian12,xian21,xian22,xian31,xian32,yuan1,yuan2,yuan3,scaling=constrained);
 

齿轮传动 - calculus - 徐小湛的博客

 
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