Let's **break down the solution into 2 steps** as requested, with explanations at each step. --- ## **Step 1: Draw the Free Body Diagram (FBD) of Each Link** ### **Link 2 (L₂)** - Acts as a crank, connected at \(O_2\). - Forces: - Reaction at \(O_2\): \(O_{2x}, O_{2y}\) - Force at point A from Link 3: \(F_{A}\) - Accelerations: - Translational acceleration at midpoint: \(a_{q2}\) (10 m/s² at 200°) - Torques: - External/internal torque at joint A: \(T_{12}\) ### **Link 3 (L₃)** - Acts as a coupler, connected at A and B. - Forces: - Force at A from Link 2: \(F_{A}\) (equal and opposite to force on Link 2) - Force at B from external force \(F_B\) (30 N at θ = 70°) - Accelerations: - Translational acceleration at midpoint: \(a_{q3}\) (12 m/s² at 210°) - Torques: - Internal driving torque: \(T_3\) (to be found) **Explanation:** Drawing the FBD helps visualize all forces, moments, and accelerations acting on each link and sets the stage for writing the equations of motion. --- ## **Step 2: Write the Equations of Motion for Each Link** ### **Link 2:** - **Force equations (in X and Y):** \[ \sum F_x = m_2 a_{q2x} \] \[ \sum F_y = m_2 a_{q2y} \] - **Torque equation:** \[ \sum M_{O_2} = I_2 \alpha_2 \] ### **Link 3:** - **Force equations (in X and Y):** \[ \sum F_x = m_3 a_{q3x} \] \[ \sum F_y = m_3 a_{q3y} \] - **Torque equation about center of mass or a point:** \[ \sum M_A = I_3 \alpha_3 \] Where \(M_A\) is the moment about point A, including \(T_3\), reaction at B, and force at midpoint. **Explanation:** These equations allow us to solve for the unknowns: reaction forces at the joints, the driving torque \(T_{12}\), and the internal torque \(T_3\). --- ## **Final Answer** **Step 1:** Draw the FBDs, clearly showing all applied, reaction forces, and torques for both links as described above. **Step 2:** Write the corresponding force and torque equations for each link, as shown, to solve for the unknowns (joint reactions, \(T_{12}\), and \(T_3\)). > **You would use the provided numerical data (mass, acceleration, moments of inertia, etc.) and the direction of each vector (given in magnitude and angle) to solve these equations numerically for the specific values.** If you want to continue with the **numerical solution for \(T_3\)**, please let me know!