(Solved): Q1) Q2) Figure R1 illustrates the kinematic model of a SCARA robot manipulator. Please answer th ...

Q1)

Q2)

Figure R1 illustrates the kinematic model of a SCARA robot manipulator. Please answer the following questions for the robot manipulator illustrated in Figure R1. Z?, Z3 1? 13 EPSON a) Robot manipulator. Figure R1. Scara robot manipulator. %0 b) Kinematic model of the robot manipulator. $? Yo 0? Xo OD E 0?,03 4? +P Assume that i) V = [V?, V?, V?]¹ represents the linear veloicity vector of the end effector E in which v, vy and v? are linear velocities along x, y, and z axes, respectively and ii) w = [W?, Wy, W?]T represents the angular veloicity vector of the end effector E in which w, Wy and w, are angular velocities about x, y, and z axes, respectively. Find the linear and angular velocity vectors (i.e., V and w) of the end effector E when 1? = 950mm, 4? = 250mm, /3 = 250mm and 44 = 750mm; ? = 47° and ? = 12 degrees per second 02 = -63? and 2 = -17 degrees per second 03 = 72° and 3 = 23 degrees per second p = 225mm and p = 27 mm per second radian/s. O V = [-0.0443, 0.0147, 0.0270]¹ m/s and w = [0, 0, 0.3142] O V = [-0.0225, 0.0332, 0.0618]¹ m/s and w = [0, 0, 0.3142]¹ radian/s. O V = [0.8320, -2.6331, 0.0270]¹ m/s and w = [0, 0, 18]¹ degree/s. O V = [-0.0563, 0.0372, 0.0135]¹ m/s and w = [0, 0, 0.3142] radian/s. O V = [-0.0443, 0.0147, 0.0270]¹ m/s and w = [0, 0, 0.3142]¹ radian/s. O V = [0.0221, -0.0138, 0.0117]¹ m/s and w = [0, 0, 0.3142] radian/s. O V = [0.0331, -0.0176, 0.0368]¹ m/s and w = [0, 0, 0.3142]¹ radian/s. O V = [0.0372, 0.0241, 0.0167]¹ m/s and w = [0, 0, 0.3142]¹ radian/s. O V = [-0.1274, 0.3950, 0.4528]¹ m/s and w = [0, 0, 0.3142] radian/s. O V = [-0.5798, 0.5578, 0.1958]¹ m/s and w = [0, 0, 0.3142]¹ radian/s. Assume that i) V = [v?, vy, v?]¹ represents the linear veloicity vector of the end effector E in which ?, ? and ? are linear velocities along x, y, and z axes, respectively and ii) w = [W?, Wy, W?]] represents the angular veloicity vector of the end effector E in which w, wy and we are angular velocities about x, y, and z axes, respectively. Find the join velocity vector q = [?, 02, 03, p¹¹ when 1? = 950mm, 1? = 250mm, 3 = 250mm and 44 = 750mm; 1 = 47°, ? = -63°, 3 = 72° and p = 225mm; V = [58 mm/s, 47 mm/s, 26 mm/s]T and w = [0, 0, 35 degree/s]T. O q = [-0.1921, 0.5240, 0.2790, 0.260]T O q = [-0.2545, 0.4572, 0.3455, 0.5623]T q = [0.4345, -0.2542, 0.4565, 0.2593]T ? = [0.2348,-0.6274, 0.3673, 0.2342]¹ q = [0.4457, 0.2562,-0.1856, 0.4254] Oq [0.6239, 0.1385, -0.3256, 0.3321]¹ O q = [0.9456,-0.6243, -0.4693, 0.1734] O q = [0.8593,-0.7049, -0.3847, 0.2342]