Question

1 of 2 MAE 371 Spring 2019 Project For the slider crank configuration, shown below, derive the expression for the velocity and acceleration of the piston, A (taken positive to the right), as a function of θ (0-7). Plot acceleration of A as a function of θ and find the value of θ for which the acceleration is zero. For the analysis assign a constant value for Additionally, plot the magnitude of the reaction forces RA and RB. Find the conditions where the magnitude of Ra is maximum. Produce Shear and Moment diagrams pertaining to this loading environment (Max IRAl). Treat the linkages as uniform rods. The mass moment of inertia pertaining to a thin rod can be used for the linkages OB 10 AB = 30"

Answer 1

In this solution some basic concepts and formulas of Mechanisms Kinematics are used. For more information, refer to any standard textbook or drop a comment below. Please give a Thumbs Up, if solution is helpful.

Solution :

30 usoud he Hen ceue acc oPis to 2. and a cof oint be, Scanned with CamScanner

(9 + β) r Ft Fc -17D Scaneed with Cam anner

un der waus, Cos e Thrust-o beori mouれab.ltfor ud ch C cle wndplot e'res/wnč Csboterued,with CamScanner

The matlab code to create the plots is follows,

r = 5/12; % Crank radius (= r in ft)
l = 30/12; % Length of Connecting Rod in ft
n = l/r;

w = 20; % Angular Velocity

t = 0:0.1:(pi); % Theta angle
b = asin(r*sin(t)/l); % Beta angle

m = 5+10; % Total mass
g = 32.3; % Acc. due to gravity

Fg = m*g; % Gravity force

Fi = m*r*(w^2)*(cos(t) + (cos(t)/n));

F = Fi+Fg; % Total force of piston

Fc = F./cos(b); % Thurst along connecting rod

Fn = Fc.*sin(b); % Thrust on cylinder sides

Ft = Fc./sin(t+b); % Crank effort

Fr = Fc.*cos(t+b); % Thrust on bearings

aD = r*(w^2)*(cos(t) + (cos(t)/n)); % Acceleration of D
aC = -(w^2).*sin(t).*((n^2 -1 )./((n^2 - (sin(t)).^2)).^(3/2)); % Angulr acceleration of C

subplot(1,2,1)
plot(t,F)
title('Various Forces')
ylabel('Force (in Lbs)')
xlabel('Theta angle, t (in radians)')
grid on

hold on
plot(t,Fc,'cyan')
plot(t,Fn,'black')
plot(t,Ft,'red')
plot(t,Fr,'green')

legend('F','Fc','Fn','Ft','Fr')

hold off

subplot(1,2,2)
plot(t,aD)
title('Various Accelertions')
ylabel('Acceleration in ft/s^2 or rad/s^2')
xlabel('Theta angle, t (in radians)')
grid on

hold on
plot(t,aC,'red')
legend('aD','aC')

Various Accelertions Various Forces 150 100 .50 150 3.5 2.5 1.5 Theta angle, t (n radians) 0.5 Theta angle, t (in radians)

NOTE : Feel free to ask further queries. Your positive rating would be appreciated and motivate me !