HW3 (2)

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Dec 6, 2023

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MEM455 HW03 Part 1 - Matlab Reverse Displacement Analysis for the 3RRR Parallel Robot This assignment is for the 3RRR parallel robot discussed in class. The following Matlab conventions are consistent with the notes where for double subscripts the second index counts the robot leg (i.e. virtual serial robot). 1. Examine and run the program demo_robot_parallel.m . This draws a sample parallel robot showing the three virtual serial robots using data_3RRR_default.m . 2. Use the RobotSketch package to draw the configuration shown in the figure as a test. a) Make copies of the files and label them demo_robot_parallel_HW03.m and data_3RRR_HW03.m b) For data_3RRR_HW03.m use the figure to change dh.a, dh.elbowplus , dh.p1 and dh.t (note δ ei is part of dh.t ). c) To run, in demo_robot_parallel_HW03.m set dh_robot_data = ’data _3RRR_ HW03’ .
3. Update data_3RRR_HW03.m so instead of picking the joint angles off the figure they are calculated from end-effector location dh.Xe . (You can overwrite the previous figure values.) a) data_3RRR_HW03.m should call the function dh = RRR3_reverse(dh) that calculates the joint angles dh.t from end-effector location dh.Xe . b) RRR3_reverse should call the function dh.t(i,:) = RRR_RDA(dh_serial) that was written for the serial robot in HW02 and, i. i=1:3 counts the virtual serial robots. ii. The input dh_serial has the same structure as dh but is for virtual serial robot i only, similar to HW02. iii. The output dh.t(i,:) requires changing the HW02 function line, from: function dh = RRR_RDA(dh) %HW02 version to: function dht = RRR_RDA(dh) %HW03 version - note dht and not dh.t where dht is a copy of the dh.t calculated in the HW02 version. This is needed because dh.t cannot be used as an output variable in Matlab. 4. Hand-in the following: a) Program listings.( data_3RRR_HW03.m, RRR_RDA.m, RRR3_reverse.m ) (To maximize your points, make sure that the programs are well commented.) b) The inputs dh.a, dh.Xe, dh.elbowplus, and dh.p1 c) The calculated dh.t (including the δ ei ). d) Printout of the robot configuration.
Part2 1. For parallel robots, why are the grounded joints usually actuated ones? 2. The figure below shows a 3PRR parallel robot where the P joints are actuated. a. Based on your understanding of the 3RRR robots, convincingly reason that the 3PRR robot should have the same number of solutions to the forward displacement problem. (You may use a figure.) b. What are the total number of solutions to the reverse displacement problem? c. Sketch one alternative solution to the reverse displacement problem.
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