Question

3-19. Suppose that the two-link planar robot shown in Fig. P3.18 is located in the first quadrant and is oriented in the elbow up position. If the tip of the robot is located at the point P(x, y)- (9,9), determine the values of θ1 and θ2. Assume 6 in. and /2 8 in

Answer 1

Let angle MOM^1 = theta_1 angle POm = alpha angle POM^1 = alpha + theta_1 = theta bar By construction Joint OP and distance formula we have OP = squareroot 9^2 + 9^2 = 9 squareroot 2 Also, Note that alpha = theta_1 + thetabar Using the law of series Sin alpha/8 = sin (180 - theta_2)/9 squareroot 2 = sin theta_2/9 squareroot 2 and alpha = tan^-1 2(y/x) = tan^-1 2 (9/9) = tan^-1 2 and theta_2 = cos^-1 (9^2 + 9^2 - 6^2 - 8^2/2 times 6 times 8) (using law of cosires) theta_2 = cos^-1 (81 + 81 - 36 - 64/2 times 6 times 8) = cos^-1 (62/2 times 6 times 8) = cos^-1 (31/48) theta_2 = cos^-1 (31/48) = 49.771 and alpha = tan^-1 2 = 63.434 therefore theta_1 = sin^-1 (l_2 sin (theta_2)/squareroot x^2 + y^2) + tan^-1 2 (y/x) theta_2 = sin^-1 (8 times sin (49.771)/9 squareroot 2) + 63.434 = sin^-1 (8