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Velocity Kinematics

  • Reza N. Jazar

Abstract

The angular velocity of link (i) in the global coordinate frame B0 is a summation of global angular velocities of the links (j), for ji
$$ {}_0^0 \omega _i = \sum\limits_{j = 1}^i {{}_{j - 1}^0 \omega _j } $$
(8.1)
where
$$ {}_{j - 1}^0 \omega _j = \left\{ \begin{gathered} \dot \theta _j {}^0\hat k_{j - 1} if joint i is R \hfill \\ 0 if joint i is P. \hfill \\ \end{gathered} \right. $$
(8.2)
The velocity of the origin of B i attached to link (i) in the base corrdinate frame is
$$ {}_{i - 1}^0 \dot d_i = \left\{ \begin{gathered} {}_0^0 \omega _i \times {}_{i - 1}^0 d_i if joint i is R \hfill \\ \dot d_i {}^0\hat k_{i - 1} + {}_0^0 \omega _i \times {}_{i - 1}^0 d_i if joint i is P \hfill \\ \end{gathered} \right. $$
(8.3)
where θ and d are DH parameters, and d is a frame’s origin position vector.

Keywords

Angular Velocity Jacobian Matrix Coordinate Frame Transformation Matrice Revolute Joint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Reza N. Jazar
    • 1
  1. 1.Department of Mechanical EngineeringManhattan CollegeRiverdale

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