1. In Figure Q1, a rigid arm OABC has three links, which is rotating vertically about...

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1. In Figure Q1, a rigid arm OABC has three links, which is rotating vertically about the Z- axis with angular velocity , = 5k (rad/s) and angular acceleration a₁. The vertical link OA with a fixed bearing to the ground has a length of L₁ = 0.5 m . The link AB with a length of L₂ = 0.4 m is inclined at an angle of ß. The link BC is L₂ = 0.3 m long and parallel with the Y-axis at that time instant. A circular disk with a radius of R is spinning about link BC, and rolling on the ground without slippery. The rolling disk is in contact with the flat ground surface at point Q. The spinning velocity relative to link BC is denoted as w₂. There is a collar P moving along a shaft integrated in the radial axis of the disk. At that time instant, the shaft is aligned at angle from the positive Z-axis. The collar P is located at distance Lp from the disk center, point C. The relative motion equations in Table 1 may be found useful. (a) Let ß = 60°. Find the absolute velocity vector of point C. (5 marks) (b) Determine the spinning velocity of the disk @22 and the absolute angular velocity of the disk. (5 marks) (c) Given the absolute angular acceleration of the disk adisk = 60 rad/s², determine angular acceleration vectors, a, and a disk (5 marks) (d) When = 7/6 (rad), Lp = 0.15 m, and the collar is moved at speed of ip = 4 m/s, and acceleration of Ï₂ = 2 m/s² relative to the shaft. Find the absolute velocity vector, and acceleration vector of point P. (10 marks) X B 201 0 y Figure Q1 B (0₂ 0 R 1. In Figure Q1, a rigid arm OABC has three links, which is rotating vertically about the Z- axis with angular velocity , = 5k (rad/s) and angular acceleration a₁. The vertical link OA with a fixed bearing to the ground has a length of L₁ = 0.5 m . The link AB with a length of L₂ = 0.4 m is inclined at an angle of ß. The link BC is L₂ = 0.3 m long and parallel with the Y-axis at that time instant. A circular disk with a radius of R is spinning about link BC, and rolling on the ground without slippery. The rolling disk is in contact with the flat ground surface at point Q. The spinning velocity relative to link BC is denoted as w₂. There is a collar P moving along a shaft integrated in the radial axis of the disk. At that time instant, the shaft is aligned at angle from the positive Z-axis. The collar P is located at distance Lp from the disk center, point C. The relative motion equations in Table 1 may be found useful. (a) Let ß = 60°. Find the absolute velocity vector of point C. (5 marks) (b) Determine the spinning velocity of the disk @22 and the absolute angular velocity of the disk. (5 marks) (c) Given the absolute angular acceleration of the disk adisk = 60 rad/s², determine angular acceleration vectors, a, and a disk (5 marks) (d) When = 7/6 (rad), Lp = 0.15 m, and the collar is moved at speed of ip = 4 m/s, and acceleration of Ï₂ = 2 m/s² relative to the shaft. Find the absolute velocity vector, and acceleration vector of point P. (10 marks) X B 201 0 y Figure Q1 B (0₂ 0 R