Problem Description Figure 1 shows a CAD model of a 2-DOF translational pick-and-place parallel robot, which consists of a base, a platform and two kinematic chains, each is composed of two sets of parallelograms connected by an elbow in between. The rotations of the actuated links are individually manipulated by two motors, providing the platform with a 2-DOF translational movement capability. Since the motions of two bars in a parallelogram are identical, a five-bar planar linkage shown in Figure 2 can be used for kinematic and dynamic analyses of the robot. Assume that the gripper picks an object from point 1 and place it to point 6, following the path shown in Figure 2. Motion of the gripper along the x or y axis complies with the piecewise displacement rule: = 2 2 ( 1 2 sin (2 ))， 0 ≤ ≤ 1 where denotes magnitude of the maximum acceleration of the gripper along a specified axis and T denotes the corresponding time interval. l1= 0.375 m the length of the actuated proximal link (driving link) l2 = 0.900 m the length of the distal link e=0.085m the offset from the point O to point A (i =1,2) Inertial parameters: m= 2.0 kg the equivalent mass of the moving platform (including 0.8kg assumed payload) mArA=0.50kg·m the equivalent mass radius product of the actuated proximal link. l= 0.240 kg.m2 the equivalent moment of inertia of the active link about its rotary axis Ratio of the gear reducer: n = 20 :1 The coordinates of the nodes on the path in the O xy coordinate system are: P1(-b/2 -H-h) P2(-b/2 -H-h/2) P3 P4 P5(-b/2 -H-h/2) P6(-b/2 -H-h) H=0.7m, b=0.7m, h=0.025m The maximum acceleration of the gripper in the segment along the x and y axes are given by , = 140.0/ 2 , = 35.0/ 2 Problems Use Matlab to Determine the total time needed to bring an object from P1 to P6 Compute and plot the angular velocity and angular acceleration of the actuated proximal links vs. time Compute and plot the torque and power of the actuated proximal links vs. time Determine the rated torque and power of two servomotors necessary to generate the specified motion
