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3.2 Lagrange-Euler Dynamics 121

we may write the kinetic energy of link i as

(3.2.21)

Let us briefly discuss the pseudo-inertia matrix before proceeding to find the
arm total kinetic energy. Let

i r=[x y z 1] T

be the coordinates in frame i of the infinitesimal mass dm. Then, expanding
(3.2.20) yields

(3.2.22)

where the integrals are taken over the volume of link i. This is a constant
matrix that is evaluated once for each link. It depends on the geometry and
mass distribution of link i. In fact, in terms of the link i moments of inertia

(3.2.23)

cross-products of inertia

(3.2.24)

and first moments

Copyright © 2004 by Marcel Dekker, Inc.