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166 REFERENCES

PROBLEMS
Section 3.2
3.2–1 Dynamics. Find the dynamics for the spherical wrist in Example
A.2–4.

3.2–2 Dynamics from Derived Equations. In Example 3.2.2 we found the
dynamics of the two-link planar elbow arm from first principles. In
this problem, begin with the expressions for the kinetic and potential
energy in that example and:
(a) Write K in the form (3.2.29) to determine M(q).
(b) Use (3.2.42) and (3.2.43) to determine V(q, ) and G(q).

3.2–3 Dynamics from Derived Equations. Repeat Problem 3.2–2 for the
three-link arm in Example 3.2.3.

Section 3.3
3.3–1 Prove (3.3.22) by finding V (q) and V (q).
p1 v1
3.3–2 Prove (3.3.23) by finding the matrices V (q).
i
3.3–3 Prove (3.3.27).

3.3–4 Coriolis Term. Find V (q) and V (q) in (3.3.40).
cor cen
3.3–5 Coriolis Term. Demonstrate that the Coriolis/centripetal term in the
dynamics equation may be expressed [Paul 1981] as V(q, )= vec{V(q,
)}where

with

and T i defined in Appendix A. Compare this to V m1, V m2, V m as
defined in Section 3.2.

3.3–6 Bounds and Structure. Derive in detail the results in Example 3.3.1.

Copyright © 2004 by Marcel Dekker, Inc.