ECE 763Homework #4Due October 31, 2011The purpose of this homework is to:(a) Assign coordinate frames to the MITSUBISHI RM-501 robot,(b) Determine its link parameters, and(c) Derive its kinematic equations.The basic dimensions and movement range of each of the joints of the MITSUBISHIRM-501 are shown on the following page. Also, t he five joint axesˆZ1throughˆZ5are shown. Note thatˆZ2,ˆZ3, andˆZ4are parallel and directed inward. A referencecoordinate system which is fixed to the table on which the MITSUBISHI is mountedwithin the workstation has been defined as [ˆXS,ˆYS,ˆZS]. The position and orientationof the base coordinate system [ˆX0,ˆY0,ˆZ0] with respect to this is specified throughtheST0homogeneous transformation. Note that the base coordinate system is justmoved up along theˆZSaxis by 250mm. A tool coordinate system [ˆXT,ˆYT,ˆZT] isalso shown. It is fixed to the end effector and has its origin at its center. Its positionand orientation with respect to the coordinate system fixed to link 5 , [ˆX5,ˆY5,ˆZ5], isspecified through the5TThomogeneous transformation.Assignment:(a) Show the coordinate frames for the MITSUBISHI, ([ˆXS,ˆYS,ˆZS],[ˆX0,ˆY0,ˆZ0],. . . , [ˆX5,ˆY5,ˆZ5],[ˆXT,ˆYT,ˆZT]), in the “zero” configuration, t hat is, with theangles θ1= θ2= θ3= θ4= θ5= 0. Be sure that your definition of thecoordinate frames is consistent with that given in class and also allows the “zero”configuration to be attainable (within t he joint limits).(b) Give a table specifying the link parameters for the MITSUBISHI:Link α a d θ12345(c) Determine the values fori−1Tifor i = 1, . . . , 5,ST0, and5TT.(d) FindjT5for j = 0, . . . , 4. Be sure to simplify any trigonometric equations as youare a ble. Use simplified notation whenever possible such as c12for
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