Question

4 In the mechanism shown, the centre of mass of link 3 is at G3, which is located at the centre of link 3. The mass of link 3 is 0.5 kg. Its moment of inertia about G; is 0.0012 N-s2-m. The weights and moments Of inertia of members 2 and 4 may be neglected. Link 2 is driven at a constant angular velocity of 50 rad/s CW by the torque applied to link 2. The mechanism moves in the horizontal plane, and friction may be neglected. (a) Find the magnitudes and directions of the inertia force and inertia torque acting on link 3. (b) Find the magnitudes and directions of the forces exerted on link 3 by link 2 at A and by link 4 at B 5 rad/s 90° OA-20 mm AB-70 mm OB-60 mm O,0,-80 mm T2 G 43.9 mm/s 369 mm/s 100 mm/s 500 mm/s 51.4 mm/s 75.6 mm/s 371 mm/s (Velocity Polygon) (Acceleration Polygon) 81.9 mm/s

Answer 1

Solution: given in the problem are The basic position, velocity & acceleration diagram So using that we calculate the acceleration of link 3 By redrawing the acceleration polygon in to scale of 12.5 m/s 2 below 4.37 m/s2 36.9 m/s2 Acceleration Polygon aG3 12.5 m/s 2 50 m/s2 39.8 m/s2 37.1 m/s2 abA3 83 8.16 m/s2 ac39.8 m/s2-39,800 mm /s2 lab/A337.1 m/s2- 37,100 mm /s2 ay A 37.100 530 rad /s2 CCW 70

Inertia force ( analysis: Inertial force in the link 3 is a0.537.1)-18.55 kg -m/s2 - 1855 N (opposite ac fis Since link 3 has angular acceleration, hence the link 3 has inertia moment, so it's calculated by, M13'a0.0012530) 0.636 N-m (opposite la or CW) Draw the free body diagram of the each link and solve graphically, Draw the offset line to replace the inertia force and moment at h distance Calculate the h M3 0.636 0.0343 m 34.3 mm h A318.55 f13 A 90 G3 M13 OB F32 F2 A A Force Scale 10 N 90 OA V13 G3 T 13 F1 М fi3 3 43 F23 F43 Force polygon for limk 3

From the above diagram, we know the direction of F4 & F because link 4 is a 2 force member Fa -F34 Now we find out the force F because the force Fg must pass through point A and intersect of fiand Fa Now sum of the force in the link 3 F-fi3+F3+ F43 0 From the force polygon, F 22.2 N & F43 7.54 N -