a. For the robot in Figure 3, derive the Jacobian for the position of the end...

 

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a. For the robot in Figure 3, derive the Jacobian for the position of the end effector, °PEE, measured in frame 0, °J. b. Given an external force vector, f = Vx derive the joint torques and forces required to resist this external force. c. Given, f = [1N fy fexerted on the end effector, 0.5N 0.2N]", q = Crad 0.3m -"rad]', derive the numeric joint torques and forces required to resist this external force, where, L = 0.25 m, a1 = 0.05 m, L2 = 0.05 m, L3 = 0.4 m, Z1 Ld2 X1 Z2 zp Z3 L2 Lt m3 Zo. Xo Z.e For the Robot in Figure 3, the forward kinematics are shown below. Derive the solutions of inverse kinematics (61 dz 03) of the end effector, °PEE, in analytical form. Identify how many valid solutions there are in total. -L3s1s3 – aicı - L2c1 + dzs1 °pEE = [y] = [ L3cis3 – aisı – Lzsı - dzcı ] L+ L3C3 a. For the robot in Figure 3, derive the Jacobian for the position of the end effector, °PEE, measured in frame 0, J. b. Given an external force vector, f = fx derive the joint torques and forces required to resist this external force. c. Given, f = [1N fy fFexerted on the end effector, 0.5N 0.2N]", q =Crad 0.3m -"rad]", derive the numeric joint torques and forces required to resist this external force, where, L1 = 0.25 m, az = 0.05 m, L2 = 0.05 m, L3 = 0.4 m, La2 X1 m2 Z2 dz X3 L1 O m3 a. For the robot in Figure 3, derive the Jacobian for the position of the end effector, °PEE, measured in frame 0, °J. b. Given an external force vector, f = Vx derive the joint torques and forces required to resist this external force. c. Given, f = [1N fy fexerted on the end effector, 0.5N 0.2N]", q = Crad 0.3m -"rad]', derive the numeric joint torques and forces required to resist this external force, where, L = 0.25 m, a1 = 0.05 m, L2 = 0.05 m, L3 = 0.4 m, Z1 Ld2 X1 Z2 zp Z3 L2 Lt m3 Zo. Xo Z.e For the Robot in Figure 3, the forward kinematics are shown below. Derive the solutions of inverse kinematics (61 dz 03) of the end effector, °PEE, in analytical form. Identify how many valid solutions there are in total. -L3s1s3 – aicı - L2c1 + dzs1 °pEE = [y] = [ L3cis3 – aisı – Lzsı - dzcı ] L+ L3C3 a. For the robot in Figure 3, derive the Jacobian for the position of the end effector, °PEE, measured in frame 0, J. b. Given an external force vector, f = fx derive the joint torques and forces required to resist this external force. c. Given, f = [1N fy fFexerted on the end effector, 0.5N 0.2N]", q =Crad 0.3m -"rad]", derive the numeric joint torques and forces required to resist this external force, where, L1 = 0.25 m, az = 0.05 m, L2 = 0.05 m, L3 = 0.4 m, La2 X1 m2 Z2 dz X3 L1 O m3