Hand L2 02 Elbow Motor Base Motor A Path Of Hand Finish Start B Figure P7 7 Figure P7 Illustrates A Robot Arm That 1 (58.74 KiB) Viewed 22 times
Hand L2 02 Elbow Motor Base Motor (a) Path of Hand Finish Start (b) Figure P7 7. Figure P7 illustrates a robot arm that has two "links" connected by two "joints"-a shoulder or base joint and an elbow joint. There is a motor at each joint. The joint angles are 0 and 02. The (x, y) coordinates of the hand at the end of the arm are given by x = L cos 6, + L2 cos (0, + 8) y = L, sin 0, + L2 sin (0, + 02) where Li and L2 are the lengths of the links. Polynomials are used for controlling the motion of robots. If we start the arm from rest with zero velocity and acceleration, the following polynomials are used to generate commands to be sent to the joint motor controllers 0,(1) = 0,(0) + a + a2/4 + azr 02(1) = 02(0) + bir + b2r4 + b37
= — = = b. Use MATLAB to solve for the polynomial coef cients given the values tp = 2 sec, 01(0) = -19°, 02(0) = 44°, 01(tf) = 43°, and 02(tr) = 151°. (These values correspond to a starting hand location of x = 6.5, y = 0 ft and a destination location of x = 0, y = 2 ft for L1 4 and L2 = 3 ft.) c. Use the results of part b to plot the path of the hand. = =
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