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124 Robot Dynamics

(3.2.37)

It is a fundamental property that the kinetic energy is a quadratic function of
the joint velocity vector and the potential energy is independent of .
The terms required in Lagrange’s Equation (3.2.14) are now given by

(3.2.38)

(3.2.39)

(3.2.40)

Therefore, the arm dynamical equation is

(3.2.41)

Defining the Coriolis/centripetal vector

(3.2.42)

and the gravity vector

(3.2.43)

we may write

(3.2.44)
which is the final form of the robot dynamical equation we have been seeking.
The units of elements of M(q) corresponding to revolute joint variables
2
q i =θ i are kg-m . The units of the elements of M(q) corresponding to prismatic
joint variables q i =d i are kilograms. The units of elements of V(q, )and G(q)
corresponding to revolute joint variables are kg-m /s . The units of elements
2
2
2
of V(q, ) and G(q) corresponding to prismatic joint variables are kg-m/s .

Copyright © 2004 by Marcel Dekker, Inc.