> restart: libname := libname, "C:/libs/MBSymba.mla": with(MBSymba_r6):
Vector Loop
definition of he vectors
> AB := make_VECTOR(rotate('Z',q),a1,0,0): show(AB); crank
> BC := make_VECTOR(rotate('Z',theta2),a2,0,0): show(BC); coupler
> DC := make_VECTOR(rotate('Z',theta3),a3,0,0): show(DC); rocker
> AD := make_VECTOR(ground,a4,0,0): show(AD); frame
closing the vector loop: definition of a closure vector
> closure := AD + DC - BC - AB: show(closure);
this expression must be null
> phi := {comp_X(closure) , comp_Y(closure) };
find the solution with respect to the variables theta[2] andtheta[3] which depend on the generalized coordinate q(rotation of the crank)
> solve(phi, {theta2,theta3} ):
select one solution
> solution := allvalues(%):
extract the solutions
> theta2 := subs(solution,theta2);
> theta3 := subs(solution,theta3);
Numerical Solution
numerical results for specified length [m]
a1 = crank length
a2 = coupler length
a3 = rocker length
> dataset := [a1=0.1, a2=0.4, a3=0.25, a4=0.30 ]; crank, coupler and rocker
num_sol := subs(dataset, solution):
> interface(displayprecision=3):
coupler angle against crank angle
> theta2 := subs(dataset, theta2);
> plot(theta2, q=0..2*Pi, labels=[q, "[rad]"], title="theta2 vs. q");
rocker angle against crank angle
> theta3 := subs(dataset, theta3);
> plot(theta3, q=0..2*Pi, labels=[q, "[rad]"], title="theta3 vs. q");
Animation of the Mechanism
Plot of the mechanism
> A := origin(ground):
> B := A + AB: #show(B);
> C := B + BC:# show(C);
> D2 := A + AD:# show(D2); Note: Maple reserves D for differential operator
> with(plots):with(plottools):
##Generate frames for the animation
> N:=10; ##number of steps
for n from 0 to N-1 do
> q := evalf(Pi*n/N);
crank AB
> crank ||n := plot( {subs(dataset,[ [comp_X(A)+0.01*cos(q),comp_Y(A)+0.01*sin(q)], [comp_X(B),comp_Y(B)] ])}, color=black, thickness=3);
coupler BC
> coupler ||n := plot( {subs(dataset,[ [comp_X(B),comp_Y(B)], [comp_X(C),comp_Y(C)] ])}, color=black, thickness=3);
rocker DC
> rocker ||n := plot( {subs(dataset,[ [comp_X(C),comp_Y(C)], [comp_X(D2),comp_Y(D2)] ])}, color=black, thickness=3):
revolute joints
> revj_A ||n := disk( subs(dataset,[comp_X(A), comp_Y(A)]), 0.01, color=yellow);
> revj_B ||n := disk( subs(dataset,[comp_X(B), comp_Y(B)]), 0.01, color=yellow);
> revj_C ||n := disk( subs(dataset,[comp_X(C), comp_Y(C)]), 0.01, color=yellow);
> revj_D ||n := disk( subs(dataset,[comp_X(D2),comp_Y(D2)]),0.01, color=yellow);
mechanism
> four_bar||n := display ( {crank||n, coupler||n, rocker||n
,revj_A||n, revj_B||n, revj_C||n, revj_D ||n
});
> end:
Display the animation
> display([ four_bar||(0..N-1)], insequence=true, scaling=constrained);
