Maple Computer Animation Fourbar Linkage Using Maple
Maple Maple i
Maple Maple ii
Abstract "Four-Bar Linkage" is very general in our life, so we can learn the knowledge of "Four-Bar Linkage" in mobile. And, we will discuss that how to use this software of Maple to analyze "Four-Bar Linkage" in this topic, and to simulate the operation manual of "Four-Bar Linkage". First, we will introduce the basic knowledge of Maple, and its characteristics and the instruction that is used in this formula. Then, we also will deduce and calculate the formula of the angle "Four-Bar Linkage". The last is to introduce the formula. We separate this formula into two parts. One is the calculating of angle. After importing the length of "Four-Bar Linkage" and one of the angle, we will know the other angles, and this will let the other people who learn "Four-Bar Linkage" know the condition this quickly through this formula. The other is the simulating of animation, and we will through this to know the condition of action of "Four-Bar Linkage", and to deepen the impression of learners. iii
1 1 1.1 1 1. Maple 3.1 Maple 3. Maple 4 3 10 3.1 10 3. 14 3.3 15 4 19 4.1 19 4. 19 4.3 0 4.4 1 4.5 iv
5 17 8 cross 9 v
.1 plot... 7. display... 8.3 animate... 9 3.1...10 3....14 3.3...18 4.1...19 4....0 4.3...1 4.4... 4.5...4 4.6...4 4.7...5 4.8...6 4.9...6 1 cross...31 vi
1 1.1 Maple 1
1. A. B. Maple C.
Maple Maple.1 Maple Maple A. 500 Maple Maple B. C.D 3D 3
D. Fortran C. Maple Maple [> : ; Maple A.restart Maple Maple : a=4 > a:=4; a := 4 a +3 A 4 19 > a^+3; 19 restart 4
>restart; a a > a; a B.if fi : if < > then < > else < > : larger a b >larger:=(a,b)->if (a>b) then a else b fi; >larger := proc(a, b) >option operator, arrow; >if b < a then a else b fi >end 5 3 larger 5 5
> larger(5,3); 5 C.evalf Maple 10 : a > a:=5/3; a := 5/3 a > evalf(a); 1.666666667 D.Plot plot([[1,y1],[,y],[]3,y3],.) 6
: plots >with(plots): >data:=([0,0],[3,4],[9,7]); data := [0, 0], [3, 4], [9, 7] > plot([data]);.1 plot 7
: plots >with(plots): f()=sin() F > F:=plot(*sin(),=-Pi..Pi,y=-Pi..Pi): f()= G > G:=plot(,=-3..3): > display({f,g}). display F.animate animate([f(,t),g(,t),t=low..high],=low..high) 8
: >with(plots): >animate([sin(t),sin(u)*cos(t),t=0..*pi],u=0..pi,frames=10); A B C D.4 animate 9
3 3.1 a b. c. d θ. θ 3 θ 4 3.1 A a A (1) A = a cosθ (1) Ay a y Ay () A y = a sin θ () 10
B X B B Y B A B y X Y b b ( B A ) + ( B A = ) y y (3) B O X Y c 4 ( B d ) c = + B y (4) (4) (3) (5) B = a b + c d A B ( A d ) ( A d ) y y (5) (5) S = a b + c ( A d ) d (6) (6) (5) B Ay B = S ( A d ) y (7) 11
(4) (7) (8) A y B y B y + S d c = 0 (8) A d (8) B y P = A y ( A d ) + 1 (9) ( d S ) Ay Q = (10) A d R = ( d S ) c (11) (9) (10) (11) B y Q ± Q 4PR B y = (1) P B B A B X A B y A B Y A B Arctangent y y θ 3 1
B y A 1 y θ = 3 tan (1) B A B O4 X B d B O4 Y B 0 Arctangent θ 4 y B y 0 θ = tan 1 4 (13) B d 13
3. CH=1 CH= OPEN CROSS a,b,c, A = acosθ A y = asinθ P = A y ( A d ) + 1 a S = b + c ( A d ) d Q Ay ( d S ) = R = ( d S ) c A d Q + Q 4PR B y = P Q Q 4PR B y = P A y B y B = S A ( d) θ 3 = tan 1 B B y A A y θ 4 B = tan 1 B d y 0 3. 14
3.3 a,b,c,d, 3 4 > restart; OPEN cross > ch:=1; ch := 1 > a:=; a := > b:=7; b := 7 > c:=9; c := 9 15
> d:=6; d := 6 > p1:=40; p1 := 40 > t1:=(p1*pi/180): > A:=a*cos(t1): > Ay:=a*sin(t1): > p:=((ay*ay)/((a-d)*(a-d)))+1: > s:=(a^-b^+c^-d^)/(*(a-d)): > r:=(d-s)^-c^: > q:=(*ay*(d-s))/(a-d): > if ( ch=1 ) then By:=(-q+(q^-4*p*r)^(1/))/(*p) > else By:=(-q-(q^-4*p*r)^(1/))/(*p) fi: > B:=s-((*Ay*By)/(*(A-d))): > t3:=arctan((by-ay),(b-a)): > f3:=t3/pi*180: > t4:=arctan(by,(b-d)): 16
> f4:=t4/pi*180: 3 > A3:=evalf(f3); A3 := 83.185486 4 > A4:=evalf(f4); A4 := 113.789613 > with(plots): >data1:=[0,0],[a*cos(t1),a*sin(t1)],[a*cos(t1)+b*cos(t3), a*sin(t1)+b*sin(t3)]: > data:=[d,0],[d+c*cos(t4),c*sin(t4)]: > data3:=[d,0],[0,0]: >plot([data1,data,data3],aes=frame,scaling=constrained); 17
3.3 18
4 4.1 360 a µ θ (A,Ay) ( a µ Ay) µ θ animate a >line1:= animate([(u/a)*a,(u/a)*ay,u=0..a], t=pi/..(5/)*pi): >line1; 4.1 19
4. (d,0) θ4 c θ (d,0) (d+c*cos(θ),c*sin(θ)) (d+v*cos(θ),v*sin(θ)) v θ animate >line:=animate([d+v*cos(t4),v*sin(t4),v=0..c], t=pi/..(5/)*pi): >line; 4. 4.3 (A,Ay) θ3 b θ (A,Ay) ( A+b*cos(θ),Ay+b*sin(θ)) 0
(A+w*cos(θ),Ay+w*sin(θ)) w θ animate >line3:=animate([a+w*cos(t3),ay+w*sin(t3),w=0..b], t=pi/..(5/)*pi): >line3; 4.3 4.4 d d (d,0) (*cos(0),*sin(0)) animate > line4:=animate([*cos(0),*sin(0),=0..d],t=pi/..4*pi): 1
>line4; 4.4 4.5 > restart; > ch:=: > speed:=50: > a:=3: > b:=6: > c:=7:
> d:=5: > A:=a*cos(t): > Ay:=a*sin(t): > p:=((ay*ay)/((a-d)*(a-d)))+1: > s:=(a^-b^+c^-d^)/(*(a-d)): > r:=(d-s)^-c^: > q:=(*ay*(d-s))/(a-d): > if ( ch=1 ) then By:=(-q+(q^-4*p*r)^(1/))/(*p) else By:=(-q-(q^-4*p*r)^(1/))/(*p) fi: > B:=s-((*Ay*By)/(*(A-d))): > t3:=arctan((by-ay),(b-a)): > t4:=arctan(by,(b-d)): > with(plots):with(plottools): 1 1 >line1:=animate([(u/a)*a,(u/a)*ay,u=0..a],t=pi/..4*pi, scaling=constrained,frames=speed,thickness=,color=blue): >line1; 3
4.5 1 1 > line:=animate([d+v*cos(t4),v*sin(t4),v=0..c],t=pi/..4*pi, scaling=constrained,frames=speed,thickness=,color=green): >line; 4.6 1 1 4
>line3:=animate([a+w*cos(t3),ay+w*sin(t3),w=0..b],t=pi/..4*pi, scaling=constrained,frames=speed,thickness=,color=red): >line3; 4.7 1 1 >line4:=animate([*cos(0),*sin(0),=0..d],t=pi/..4*pi, scaling=constrained,frames=speed,thickness=,color=yellow): >line4; 5
4.8 > display([line1,line,line3,line4],aes=none); 4.9 5 6
Maple 7
[1] Robert L. Norton Design Of Machinery Mc Graw Hill 1999 [] MALPLRE 6 001 [3] Maple V Release 3 1994 cross 8
cross > restart; > ch:=; ch := > a:=; a := > b:=7; b := 7 > c:=9; c := 9 > d:=6; d := 6 > p1:=40; p1 := 40 > t1:=(p1*pi/180): > A:=a*cos(t1): > Ay:=a*sin(t1): > p:=((ay*ay)/((a-d)*(a-d)))+1: 9
> s:=(a^-b^+c^-d^)/(*(a-d)): > r:=(d-s)^-c^: > q:=(*ay*(d-s))/(a-d): > if ( ch=1 ) then By:=(-q+(q^-4*p*r)^(1/))/(*p) > else By:=(-q-(q^-4*p*r)^(1/))/(*p) fi: > B:=s-((*Ay*By)/(*(A-d))): > t3:=arctan((by-ay),(b-a)): > f3:=t3/pi*180: > t4:=arctan(by,(b-d)): > f4:=t4/pi*180: > A3:=evalf(f3); A3 := -115.33361 > A4:=evalf(f4); A4 := -145.8943987 > with(plots): > data1:=[0,0],[a*cos(t1),a*sin(t1)] >,[a*cos(t1)+b*cos(t3),a*sin(t1)+b*sin(t3)]: > data:=[d,0],[d+c*cos(t4),c*sin(t4)]: 30
> data3:=[d,0],[0,0]: > plot([data1,data,data3],aes=frame,scaling=constrained); 1 Cross 31