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0593_C06_fm Page 194 Monday, May 6, 2002 2:28 PM

194 Dynamics of Mechanical Systems

gravitational forces acting on these bodies are represented by equivalent gravity (weight)
force systems consisting of single vertical forces W , W , and W as in Figure P6.7.1B.
3
2
1
Finally, suppose we want to find an equivalent gravity force system for the entire arm
consisting of a single force W passing through the shoulder joint O together with a couple
with torque M. Find W and M. Express the results in terms of the angles θ , θ , and θ ;
2
3
1
the distances r , r , r , , , and ; the force magnitudes W , W , and W ; and the unit
2
3
3
1
2
2
3
1
1
vectors n , n , and n shown in Figures P6.7.1A and B.
y
z
x
P6.7.2: See Problem P6.7.1. Table P6.7.2 provides numerical values for the geometric
quantities and weights of the arm model of Figures P6.7.1A and B. Using these values,
determine the magnitudes of W and M.
TABLE P6.7.2
Numerical Values for the Geometric Parameters and Weights
of Figures P6.7.1A and B
i θθ θ θ (°) r i (in.) i (in.) W i (lb)
i
1 45 4.45 11.7 5.0
2 15 6.5 14.5 3.0
3 30 2.5 6.0 1.15
P6.7.3: See Problems P6.7.1 and P6.7.2. Suppose the equivalent force system is to be a
wrench, where the couple torque M is a minimum. Locate a point G on the line of action
of the equivalent force. Find the magnitudes of the equivalent wrench force and minimum
moment.
P6.7.4: Three springs are connected in series as in Figure P6.7.4. Find the elongation for
the applied forces. The spring moduli and force magnitudes are listed in Table P6.7.4.
k k k
1 2 3
FIGURE P6.7.4
Three springs in series. F F

TABLE P6.7.4
Physical Data for the System of Figure P6.7.4
Force F Spring Moduli 12 lb (lb/in.) 50 N (N/mm)
6 10
k 1
5 12
k 2
8 7
k 3
P6.7.5: See Problem P6.7.4. Let the springs of Problem P6.7.4 be arranged in parallel as in
Figure P6.7.5. Find the elongation δ for the applied forces. Assume that the springs are
sufficiently close (or even coaxial) so that the rotation of the attachment plates can be
ignored.
P6.7.6: A block is resting on an incline plane as shown in Figure P6.7.6. Let µ be the
coefficient of friction between the block and the plane. Find the inclination angle θ of the
incline where the block is on the verge of sliding down the plane.
P6.7.7: See Problem P6.7.6. Let the inclination angle θ be small. Let the drag factor (f) be
defined as an effective coefficient of friction that accounts for the small slope. Find f in
terms of µ and θ. What would be the value of f if the block is sliding up the plane?