Do you want to create a mechanism that satisfy the required motion?
There are mainly three types of mechanism creation:
Function Generation
When the rotary motion of the input and output links are correlated.
Path Generation
When a point on the coupler of a mechanism is to be along a prescribed path
Motion Generation
When the mechanism is design to guide a rigid body in a prescribed path
In this post we will see how the 3DEXPERINECE CATIA Apps can be used for Path generation.
A four-link mechanism ABCD with a coupler point E is shown in the above figure. Three positions of the input link (θ1, θ2, θ3) and the three positions of the coupler point E given by three values of r and α. It is required to find the dimensions of a, c, e and f along with the location of the pivots A and D given by g, γ and ψ respectively, so that the coupler point E generates the specified path with the motion of the input link AB.
For more information please refer Rattan, S. S. (2014). Theory of Machines, Tata McGraw-Hill Education.
Problem statement: Design a four-link mechanism to coordinate three position of the input link with three positions of the coupler point, the data for which is given below:
tb1, θ1 = 110° r1 = 80mm al1, α1 = 65°
tb2, θ2 = 77° r2 = 90mm al2, α2 = 56°
tb3, θ3 = 50° r3 = 96mm al3, α2 = 48°
gamm, γ = 20 si, ψ = 10 dll, δ = 150
Solution steps are similar to the one shared in the Mechanism Monday: Mechanism Creation🤖 - Part 1.
The main difference is the following code to generate the solution.
/* Code to generate the solution */
let rad, t11, t22, t33, a11, a22, a33, gg, ss, d11, r11, r22, r33 (real)
let p1, p2, p3, t1, t2, t3, c1, c2, c3 (real)
let del, del1, del2, del3, ak1, ak2, ak3 (real)
let ala, alg, alk (real)
let ama, amg, amk, aa, bb, cc, squ (real)
let all, all1, all2, a1, a2, g1, g2, e1, e2 (real)
let g12, a12, e12, g21, a21, e21, gs, p11, p22, p33 (real)
let bet1, bet2, bet3, d22, d33, a3, g3, e3 (real)
let k, tempk, j, tempj (integer)
t11 = tb1*(PI/180)
t22 = tb2*(PI/180)
t33 = tb3*(PI/180)
a11 = al1*(PI/180)
a22 = al2*(PI/180)
a33 = al3*(PI/180)
gg = gamm*(PI/180)
ss = si*(PI/180)
d11 = dell*(PI/180)
r11 = r1*1000
r22 = r2*1000
r33 = r3*1000
for j = 0 while j < 3
{
p1 = 2*r11*cos(t11 - a11)
p2 = 2*r22*cos(t22 - a22)
p3 = 2*r33*cos(t33 - a33)
t1 = 2*r11*cos(a11 - gg)
t2 = 2*r22*cos(a22 - gg)
t3 = 2*r33*cos(a33 - gg)
c1 = r11*r11
c2 = r22*r22
c3 = r33*r33
for k = 0 while k<2
{
del = p1*(t2-t3)+t1*(p3-p2)+(p2*t3 - p3*t2)
del1 = c1*(t2-t3)+t1*(c3-c2)+(c2*t3 - c3*t2)
del2 = p1*(c2-c3)+c1*(p3-p2)+(p2*c3 - p3*c2)
del3 = p1*(t2*c3-t3*c2)+t1*(c2*p3-c3*p2)+c1*(p2*t3-p3*t2)
ak1 = del1/del
ak2 = del2/del
ak3 = del3/del
if k == 0
{
ala = ak1
alg = ak2
alk = ak3
c1 = 2*cos(t11 - gg)
c2 = 2*cos(t22 - gg)
c3 = 2*cos(t33 - gg)
}
tempk = k + 1
k = tempk
}
ama = ak1
amg = ak2
amk = ak3
aa = ama*amg
bb = ala*amg + alg*ama - 1
cc = ala*alg
squ = bb*bb-4*aa*cc
if squ>0
{
all = sqrt(squ)
all1 = (-bb-all)/(2*aa)
all2 = (-bb+all)/(2*aa)
a1 = ala+all1*ama
g1 = alg+all1*amg
a2 = ala+all2*ama
g2 = alg+all2*amg
e1 = sqrt(alk+all1*amk+a1*a1+g1*g1)
e2 = sqrt(alk+all2*amk+a2*a2+g2*g2)
if j == 1
{
g.1 = g12*1mm
a.1 = a12*1mm
e.1 = e12*1mm
h.1 = g1*1mm
c.1 = e1*1mm
f.1 = a1*1mm
g.2 = g12*1mm
a.2= a12*1mm
e.2 = e12*1mm
h.2 = g2*1mm
c.2 = e2*1mm
f.2 = a2*1mm
}
if j == 2
{
g.3 = g21*1mm
a.3 = a21*1mm
e.3 = e21*1mm
h.3 = g1*1mm
c.3 = e1*1mm
f.3 = a1*1mm
g.4 = g21*1mm
a.4 = a21*1mm
e.4 = e21*1mm
h.4 = g2*1mm
c.4 = e2*1mm
f.4 = a2*1mm
}
if j ==0
{
g12=g1
a12=a1
e12=e1
g21=g2
a21=a2
e21=e2
gs=gg
p11=t11
p22=t22
p33=t33
}
if j ==1
{
g1=g21
a1=a21
e1=e21
t11=d11
t22=d22
t33=d33
gg=gs
t11=p11
t22=p22
t33=p33
}
bet1 = acos((r11*cos(a11)-g1*cos(gg)-a1*cos(t11))/e1)
bet2 = acos((r22*cos(a22)-g1*cos(gg)-a1*cos(t22))/e1)
bet3 = acos((r33*cos(a33)-g1*cos(gg)-a1*cos(t33))/e1)
d22 = d11 + bet2-bet1
d33 = d11+ bet3-bet1
a3 = a2
g3 = g2
e3 = e2
p11 = t11
p22 = t22
p33 = t33
t11 = d11
t22 = d22
t33 = d33
gs = gg
gg = ss
}
tempj = j + 1
j = tempj
}
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