Module_02 Homework#
A flywheel is accelerated using two cords attached to the top and bottom of the outer radii. Its acceleration when the forces are first applied is \(\alpha = -50~rad\hat{k}\). Where \(\hat{k}\) points upwards out of the diagram. The moment of inertia is equal to \(I = mr^2/2 = 100~kg (0.1~m)^2/2 = 0.5~kg-m^2\). Use the Newton-Euler equations. What are the applied forces, \(F\)?
A mechanical sliding mechanism is designed for two arms to move the roller at point C along the ground. A force \(F=100~N\) is applied at the connecting link. The long arm OA has length \(l_1 = 50~mm\) and the short arm has length \(l_2 = 42.43~mm\). A restoring force, \(R\), is applied to prevent the system from accelerating
a. What angle, \(\theta_1\), would the restoring force be \(R=0\)?
b. When the system is in the given configuration above, what is the restoring force \(R\)?
Two four-bar linkage mechanisms are being compared for an engineering system. Look at the geometry and motion videos and answer the questions about kinematic motion for a given time.
a. four-bar linkage shown in the video here
"\(l_1 = 0.25~m,~l_2 = 1~m,~ l_3 = 1~m\)
\(dx = 1~m ~and~ dy = 0~m\)
at time, \(t\), link 1 (OA) is rotating at 10 rad/s. The positions of the pins are as follows
\(r_0 = 0\hat{i} + 0 \hat{j}\) [m]
\(r_A = -0.203\hat{i}+0.1459\hat{j}\) [m]
\(r_B = 0.494\hat{i} + 0.863\hat{j}\) [m]
\(r_C = 1\hat{i} + 0\hat{j}\) [m]
What are the rotation rates for links 2 and 3 (AB and BC, respectively)
b. four-bar linkage shown in the video here
"\(l_1 = 0.25~m,~l_2 = 1~m,~ l_3 = 1~m\)
\(dx = 1~m ~and~ dy = -0.25~m\)
at time, \(t\), link 1 (OA) is rotating at 10 rad/s. The positions of the pins are as follows
\(r_0 = 0\hat{i} + 0 \hat{j}\) [m]
\(r_A = 0\hat{i}+0.25\hat{j}\) [m]
\(r_B = 0.968\hat{i} + 0.499\hat{j}\) [m]
\(r_C = 1\hat{i} - 0.5\hat{j}\) [m]