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122 Robot Dynamics

(3.2.25)

with m the total mass of link i, and

(3.2.26)

the coordinates in frame i of the center of gravity of link i, we may write

(3.2.27)

These quantities are either tabulated in the arm manufacturer’s specifications
or may be computed from quantities tabulated there.
Returning now to our development, the total arm kinetic energy may be
written as

(3.2.28)

Since the trace of a sum of matrices is the sum of the individual traces, we
may interchange summations and the trace operator to obtain

or
(3.2.29)

where the n×n arm inertia matrix M(q) has elements defined as

(3.2.30)

Copyright © 2004 by Marcel Dekker, Inc.