System Dynamics
System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 3, Problem 3.40P

A single link of a robot arm is shown in Figure P3.40. The arm mass is m and its center of mass is located a distance L from the joint, which is driven by a motor torque T m through two pairs of spur gears. We model the arm as a pendulum with a concentrated mass m. Thus we take the arm’s moment of inertia I G to be zero. The gear ratios are N 1 = 2 (the motor shaft has the greater speed) and N 2 = 1.5 (the shaft connected to the link has the slower speed). Obtain the equation of motion in terms of the angle O θ , With T m as the input. Neglect the shaft inertias relative to the other inertias. The given values for the motor and gear inertias are

I m = 0.05 kg m 2 I G 1 = 0.025 kg m 2 I G 2 = 0.1 kg m 2 I G 3 = 0.025 kg .m 2 I G 4 = 0.08 kg m 2

The values for the link are

m = 10 kg L = 0.3 m

Chapter 3, Problem 3.40P, A single link of a robot arm is shown in Figure P3.40. The arm mass is m and its center of mass is

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Chapter 3 Solutions

System Dynamics

Ch. 3 - The motor in Figure P3.11 lifts the mass mL by...Ch. 3 - Instead of using the system shown in Figure 3.2.6a...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Derive the expression for the equivalent inertia...Ch. 3 - Prob. 3.18PCh. 3 - The geared system shown in Figure P3.19 represents...Ch. 3 - Prob. 3.20PCh. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - For the geared system shown in Figure P3.23,...Ch. 3 - For the geared system discussed in Problem 3.23,...Ch. 3 - The geared system shown in Figure P3.25 is similar...Ch. 3 - Consider the rack-and-pinion gear shown in Figure...Ch. 3 - The lead screw (also called a power screw or a...Ch. 3 - Prob. 3.29PCh. 3 - Derive the equation of motion of the block of mass...Ch. 3 - Assume the cylinder in Figure P3.31 rolls without...Ch. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - A slender rod 1.4 m long and of mass 20 kg is...Ch. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - The pendulum shown in Figure P3.38 consists of a...Ch. 3 - Prob. 3.39PCh. 3 - A single link of a robot arm is shown in Figure...Ch. 3 - 3.41 It is required to determine the maximum...Ch. 3 - Figure P3.42 illustrates a pendulum with a base...Ch. 3 - Figure P3.43 illustrates a pendulum with a base...Ch. 3 - 3.44 The overhead trolley shown in Figure P3.44 is...Ch. 3 - Prob. 3.45PCh. 3 - The “sky crane” shown on the text cover was a...
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