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REFERENCES 167

3.3–7 Bounds and Structure. Derive the bounds and structural matrices for
the two-link polar arm in Example 3.2.1. Use:
(a) The 1—norm.
(b) The 2-norm .
(c) The ∞—norm.

3.3–8 Bounds and Structure. Repeat Problem 3.3–7 for the three-link
cylindrical arm in Exercise 3.2.3.

3.3–9 Bounds Using 2-Norm. Derive the bounds for the two-link planar
elbow arm in Example 3.3.1 using the 2—norm.
Section 3.4
3.4–1 Prove (3.4.15).

3.4–2 Hamiltonian State Formulation. Demonstrate that (3.4.15) is
equivalent to

with the skew-symmetric matrix defined in Section 3.3.

3.4–3 Hamiltonian State Formulation. Use (3.4.17) to derive the
Hamiltonian state-variable formulation for the two-link polar arm
in Example 3.2.1.

3.4–4 Hamiltonian State Formulation. Repeat Problem 3.4–3 for the two-
link planar elbow arm in Example 3.2.2.
Section 3.5
3.5–1 Cartesian Dynamics. Complete Example 3.5.1, computing the
nonlinear terms in Cartesian coordinates.

3.5–2 Cartesian Dynamics. Find the Cartesian dynamics of the two-link
polar arm in Example 3.2.1.
3.5–3 Cartesian Dynamics. Find the Cartesian dynamics of the two-link
planar elbow arm in Example 3.2.2.
Section 3.6

3.6–1 Actuator Dynamics. Verify that the arm-plus-actuator dynamics (3.6.6)
has the properties listed in Table 3.3.1.

Copyright © 2004 by Marcel Dekker, Inc.