1. Newton-Raphson Example 4:
Solutions of system of nonlinear equations:
Newton-Raphson Example 4:
The kinematic equations for a Four-Bar mechanism can be written as (5th semester, Mechanisms Course)
L2=0.15 m L3=0.45 m L4=0.28 m s1=0.2 m s1 L2 L3 L4 θ2 θ3 θ4 3 4 2 1
Where link 2 is the input member. How do you calculate θ3 and θ4 when θ2=120°.
-0.075
0.13

2. Following changes are made in the computer program.
Solutions of system of nonlinear equations:
Following changes are made in the computer program.
Sub newtonrn_Click()
- - -
40 n=2
41 xb(1)=0.5:xb(2)=1:xh(1)=.001:xh(2)=.001
- -
45 ‘…Error equations…
a(1,1)=-0.45*Sin(xb(1)):a(1,2)=0.28*Sin(xb(2))
a(2,1)=0.45*Cos(xb(1)):a(2,2)=-0.28*Cos(xb(2))
b(1)=-(0.45*Cos(xb(1))-0.28*cos(xb(2))-0.275)
b(2)=-( *Sin(xb(1))-0.28*Sin(xb(2)))
46 ‘...
End sub
(Initial angle values must be given in RADIAN)
ANSWER:
θ3=0.216 rad (12.37°)
θ4=0.942 rad (53.97°)
clc;clear
[x,y]=solve('0.45*cos(x)-0.28*cos(y)=0.275',' *sin(x)-0.28*sin(y)=0');
vpa(x,6)
vpa(y,6)
Solution with MATLAB

3. Newton-Raphson Example 5:
Solutions of system of nonlinear equations:
Newton-Raphson Example 5:
Kinematic equations for a crank mechanism are given below (5th semester Mechanisms Course)
L2=0.15 m L3=0.6 m θ3 L2 L3 θ2 s
Where link 2 (crank) is the input member. How dou you calculate θ3 and s with computer when θ2=60°.
0.075
0.1299

4. Following changes are made in the computer program.
Solutions of system of nonlinear equations:
Following changes are made in the computer program.
Sub newtonrn_Click()
- - -
40 n=2
41 xb(1)=-1:xb(2)=0.8:xh(1)=.001:xh(2)=.001
- -
45 ‘…Error equations…
a(1,1)=-0.6*Sin(xb(1)):a(1,2)=-1
a(2,1)=0.6*Cos(xb(1)):a(2,2)=0
b(1)=-( *Cos(xb(1))-xb(2))
b(2)=-( *Sin(xb(1)))
46 ‘...
End sub
ANSWER:
θ3= rad (-12.5°)
s= m
Solution with MATLAB
clc;clear
[x,y]=solve(' *cos(x)-y=0',' *sin(x)=0');
vpa(x,6)
vpa(y,6)

5. Newton-Raphson Example 6:
Solutions of system of nonlinear equations:
Newton-Raphson Example 6:
The time-dependent locations of two cars denoted by A and B
are given as
clc;clear
t=solve('t^3-t^2-4*t+3=0');
vpa(t,6)
Solution with MATLAB
At which time t, two cars meet?
Sub newtonr1_Click ()
' CHANGE LINES 30, 35 AND 37 FOR DIFFERENT PROBLEMS
30 x = 1: AERROR = .0001
niter1 = 5: niter2 = 20: ir = 0: Call cls1
32 xp = x
35 f = x ^ 3 - x ^ * x + 3
37 f1 = 3 * x ^ * x - 4 …
End Sub
ANSWER
T=0.713 s
t=2.198 s
Using roots command in MATLAB
a=[ ];roots(a)

6. Graph Plotting Example 7:
From a vibration measurement on a machine, the damping ratio and undamped vibration frequency are calculated as 0.36 and 24 Hz, respectively. Vibration magnitude is 1.2 and phase angle is -42o. Write the MATLAB code to plot the graph of the vibration signal.
Given:
z=0.36
ω0=24*2*π (rad/s)
A=1.2
Φ=-42*π/180 (rad)=-0.73 rad
ω0= rad/s ω -σ α

7. yt=1.2*exp(-54.3*t).*cos(140.7*t+0.73); plot(t,yt) xlabel(‘Time (s)');
Graph Plotting:
clc;clear
t=0:0.002:0.1155;
yt=1.2*exp(-54.3*t).*cos(140.7*t+0.73);
plot(t,yt)
xlabel(‘Time (s)');
ylabel(‘Displacement (mm)');