Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_88

6/87 The four-bar mechanism lies in a vertical plane and is controlled by crank \(OA\), which rotates counterclockwise at a steady rate of \(60 \text{ rev/min}\). Determine the torque \(M\) which must be applied to the crank at \(O\) when the crank angle \(\theta = 45^\circ\). The uniform coupler \(AB\) has a mass of \(7 \text{ kg}\), and the masses of crank \(OA\) and the output arm \(BC\) may be neglected. 6/88 Repeat the analysis of Prob. 6/87 with the added information that the mass of crank \(OA\) is \(1.2 \text{ kg}\) and the mass of the output arm \(BC\) is \(1.8 \text{ kg}\). Each of these bars may be considered uniform for this analysis. Given values: Crank \(OA\): \(L_{OA} = 80 \text{ mm} = 0.08 \text{ m}\), \(m_{OA} = 1.2 \text{ kg}\) Coupler \(AB\): \(L_{AB} = 240 \text{ mm} = 0.24 \text{ m}\), \(m_{AB} = 7 \text{ kg}\) Output arm \(BC\): \(L_{BC} = 200 \text{ mm} = 0.2 \text{ m}\), \(m_{BC} = 1.8 \text{ kg}\) Rotation: \(\omega_{OA} = 60 \text{ rev/min} = 2\pi \text{ rad/s} \text{ (CCW)}\), \(\alpha_{OA} = 0\) Configuration: \(\theta = 45^\circ\) Pivot locations: \(O\) at \((0,0)\), \(C\) at \((190, -70) \text{ mm}\)