Velocity Kinematics

  • Reza N. Jazar


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


Angular Velocity Jacobian Matrix Coordinate Frame Transformation Matrice Revolute Joint 
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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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