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Robot Dynamics Lecture Notes - ETH Z

Robot Dynamics Lecture NotesYouJanuary 6, 2017 Contents1 ..32 .. of Positions ..6 Cartesian coordinates ..6 Cylindrical coordinates ..7 Spherical coordinates .. Velocity .. of Linear Velocities ..7 Cartesian Coordinates ..8 Cylindrical Coordinates ..8 Spherical Coordinates .. Matrices .. vs. Passive Rotation ..11 Passive Rotation ..11 Active Rotation .. Rotations .. of Rotations .. of Rotations ..13 Euler Angles ..13 Angle Axis ..18 Unit Quaternions .. Velocity .. Derivatives of Rotation Parameterizations ..22 Time Derivatives of Euler Angles ZYX Angular Velocity .23 Time Derivatives of Euler Angles XYZ Angular Velocity .24 Time Derivatives of Euler Angles ZYZ Angular Velocity.

m number of end-effector configuration parameters m0 number of operational space coordinates = minimal number of end-effector configuration parameters machine precision x the star stands for a desired value q generalized coordinates J Jacobian matrix JA analytical Jacobian matrix J0 basic Jacobian matrix N = N(J) null-space projector matrix 2

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