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### 3.3.  TRANSFER-FUNCTION AND STATE-VARIABLE REPRESENTATION OF TYPICAL MECHANICAL CONTROL-SYSTEM DEVICES

Mechanical control-system devices can generally be classified as being either translational or rotational. The major difference between the two is that we talk of forces and translational units in the former, and torque and angular units in the latter. Newton’s three laws of motion [3] govern the action of both types of mechanical systems. Basically, these laws state that the sum of the applied forces, or torques, must equal the sum of the reactive forces, or torques, for a body whose acceleration is zero. Another way of stating this is that the sum of the forces must equal zero for a body at rest or moving at a constant velocity. We shall consider some representative translational systems and then some rotational systems. The basic concepts illustrated and developed here should be sufficient to enable the reader to handle more complex systems.

#### A.  Mechanical Translation Systems

The three basic characteristics of a mechanical translational system are mass, stiffness, and damping. Mass represents an element having inertia. Stiffness represents the restoring force action such as that of a spring. Damping, or viscous friction, represents a characteristic of an element that absorbs energy. The symbols for the various quantities used in our analyses are shown in Table 3.1.

1. Force Applied to a Mechanical System Containing a Mass, Spring, and Damper. The case of a force f(t) applied ...

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