ME3200- HW # 6 SOLUTIONS – FALL 2003
Page 1 of 5
University of Utah
Mechanical Engineering Department
Salt Lake City, Utah 84112
ME3200- HW # 6 SOLUTIONS – FALL 2003
Page 2 of 5
University of Utah
Mechanical Engineering Department
Salt Lake City, Utah 84112
ME3200- HW # 6 SOLUTIONS – FALL 2003
Problem 6.57 b)
We are using two methods to find the mechanical adv. as a function
of theta2. Both methods show the same results.
Method 1: Velocity Analysis
clear all
% "Pro6_57b.m" is a Matlab program to calculate & plot the Ma, Mechanical
% advantage as a function of theta2 as it rotate from 60 to 45 degree
Page 3 of 5
University of Utah
Mechanical Engineering Department
Salt Lake City, Utah 84112
ME3200- HW # 6 SOLUTIONS – FALL 2003
% Step 4: find r3
R3(j)=R1(j)+R4(j)-R2(j);
theta3(j)=angle(R3(j));
% ME 3200 Fall 2003
% NOTE: delete the ";" at the end of a line to view a calculation
% Defining the link lengths and operating parameters....
L1=2.4;
L2=0.8;
L3=1.23;
L4=1.55;
theta1=-49*pi/180;
theta2=0;
w2=-1; % assumed
rin=4.26; rout=1;
% Finding the angular velocities using the matrix inversion solution:
A=[-L3*sin(theta3(j)) L4*sin(theta4(j));
L3*cos(theta3(j)) -L4*cos(theta4(j))];
B=[-L2*w2*sin(theta2(j));
L2*w2*cos(theta2(j))];
% Now solving for x=[w3 w4]
x = inv(A)*B;
w3(j)=x(1);
w4(j)=x(2);
% Forloop parameters...
theta2min=60*pi/180;
theta2max=45*pi/180;
steps=15;
dtheta2=(theta2max-theta2min)/steps;
% Now calculating the Mech. adv.
MA(j)=abs((w2/w4(j))*(rin/rout));
end
% The following defines a vector theta2vec where each element
%corresponds to a different theta that the equations will be evaluated at.
%The vector is defined from theta2min to theta2max in increments of dtheta
theta2=theta2min:dtheta2:theta2max;
% Starting a for loop to examine all configurations...
for j = 1 : length(theta2)
% Now to plot the Mechanical advantage
figure(1)
plot(theta2*180/pi,MA)
xlabel('theta2(dgree)')
ylabel('Mechanical Advantage')
title('Mech. adv. vs theta2')
grid on
R1(j)=L1*(cos(theta1)+i*sin(theta1));
R2(j)=L2*(cos(theta2(j))+i*sin(theta2(j)));
% Step 1: find r7 & l7
R5(j)=R2(j)-R1(j);
L5=abs(R5(j));
theta5=angle(R5(j));
% Step 2: find psi
psi=acos((L4^2+L5^2-L3^2)/(2*L5*L4));
% Step 3: find theta4 & r4; This example uses
theta4(j)=theta5-psi;
R4(j)=L4*(cos(theta4(j))+i*sin(theta4(j)));
Method 2: Using the nu, ν and mu, µ
clear all
% "Pro6_57b.m" is a Matlab program to calculate & plot the Ma, Mechanical
% advantage as a function of theta2 as it rotate from 60 to 45 degree
% ME 3200 Fall 2003
% NOTE: delete the ";" at the end of a line to view a calculation
% Defining the link lengths and operating parameters....
L1=2.4;
L2=0.8;
L3=1.23;
L4=1.55;
Page 4 of 5
University of Utah
Mechanical Engineering Department
Salt Lake City, Utah 84112
ME3200- HW # 6 SOLUTIONS – FALL 2003
% Now calculating the Mech. adv.
MA(j)=(L4*sin(mu(j))/L2*sin(nu(j)))*(rin/rout);
theta1=-49*pi/180;
theta2=0;
w2=-10;
rin=4.26;
rout=1;
end
% Now to plot the Mechanical advantage
figure(1)
plot(theta2*180/pi,MA)
xlabel('theta2(dgree)')
ylabel('Mechanical Advantage')
title('Mech. adv. vs theta2')
grid on
% Forloop parameters...
theta2min=60*pi/180;
theta2max=0*pi/180;
steps=15;
dtheta2=(theta2max-theta2min)/steps;
% The following defines a vector theta2vec where each element
%corresponds to a different theta that the equations will be evaluated at.
%The vector is defined from theta2min to theta2max in increments of dtheta
theta2=theta2min:dtheta2:theta2max;
% Starting a for loop to examine all configurations...
for j = 1 : length(theta2)
R1(j)=L1*(cos(theta1)+i*sin(theta1));
R2(j)=L2*(cos(theta2(j))+i*sin(theta2(j)));
% Step 1: find r7 & l7
R5(j)=R2(j)-R1(j);
L5=abs(R5(j));
theta5=angle(R5(j));
% Step 2: find psi
psi=acos((L4^2+L5^2-L3^2)/(2*L5*L4));
% Step 3: find theta4 & r4; This example uses
theta4(j)=theta5-psi;
R4(j)=L4*(cos(theta4(j))+i*sin(theta4(j)));
% Step 4: find r3
R3(j)=R1(j)+R4(j)-R2(j);
theta3(j)=angle(R3(j));
nu(j)=theta2(j)-theta3(j);
mu(j)=theta4(j)-theta3(j);
Page 5 of 5
University of Utah
Mechanical Engineering Department
Salt Lake City, Utah 84112