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Unformatted text preview: MMAE 350 D. Rempfer Problem Set IV Page 1 of 4 Due Date: October 11, 2006 1. We consider a robot-arm problem similar to the one discussed in class (see picture). A robot arm consisting of two segments of length r and l is con- trolled by adjusting the length of the two actuators a 1 and a 2 such that a desired position ( p x ,p y ) of the tip of the arm is obtained. Write the MAT- LAB code that is necessary to find the actuator lengths s 1 , s 2 of actuator a 1 and a 2 , respectively, given the position of the end-point of the robot arm, ( p x ,p y ), and the lengths of the two segments of the arm, r and l . You can do this by following these steps: l r d a 2 a 1 y x r/2 r/2 a. Write a MATLAB m-file rpos that computes the position of the robot arm given the input parameters r , l , and a vector containing s 1 and s 2 . As its output, the function should return a single vector-valued variable containing the x- and y-position of the robot arm as its components. You may want to make sure the input lengths s 1 and s 2 are restricted appropriately (both must be positive, there are obvious restrictions on the allowed lengths for actuator a 2 , and you may assume that the first robot arm (of length r ) only moves within the first quadrant of the coordinate system shown). b. Write a MATLAB m-file drpos that computes the Jacobian matrix of the function rpos , given the same input parameters as for rpos . As its output, this function should return a single matrix-valued variable containing the 4 elements of the Jacobian....
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This note was uploaded on 05/04/2008 for the course MMAE 350 taught by Professor Rempher during the Spring '05 term at Illinois Tech.
- Spring '05