Velocity Kinematics

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 j ≤ i

$$ {}_0^0 \omega _i = \sum\limits_{j = 1}^i {{}_{j - 1}^0 \omega _j } $$

(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.