# Z x y q 2 0 q 3 q 1 z x y q 2 q 3 0 q 1 4 exercise

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zxyq2=0q3q1zxyq2q3=0q14Exercise Robot 1iθdaα10q1002q200-9030q3004.1SketchIn a right-handed XYZ coordinate frame, draw a sketch of this robot showing the spatial relation-ships between the coordinate frames associated with each link.x0z2z0zxy2x1,2x3z3z1d1d32d1d312MECEE 4602: Intro to Robotics, Fall 2018
4.2Forward KinematicsCompute the transform matrixbTeefrom the base of the robot to its end-effector.
4.3Inverse KinematicsAssume we require the end-effector to be at position [a, b, c]T, and we do not care about end-effectororientation.Show how to compute the values for all the robot joints such that the end-effectorachieves the desired position.Be sure to list all possible solutions.If the number of solutionsdepends on certain characteristics ofa, bandc, explain how and why.
13MECEE 4602: Intro to Robotics, Fall 2018
4.4Differential KinematicsCompute the manipulator Jacobian with respect to end-effector position (and ignoring end-effectororientation).Find all the joint configurations where the Jacobian becomes singular; for each ofthem, briefly explain why the robot is in a singular configuration (for example, which direction ofend-effector motion is impossible or which robot joint has no effect on end-effector position).
5.1SketchIn a right-handed XYZ coordinate frame, draw a sketch of this robot showing the spatial relation-ships between the coordinate frames associated with each link.x0z1z0x3z3zxy12d3x1,2z2l114MECEE 4602: Intro to Robotics, Fall 2018
5.2Forward KinematicsCompute thetranslation partof the transform matrixbTeefrom the base of the robot to itsend-effector.

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Term
Fall
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Tags
Rotation matrix, Jacobian