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The inclined plane, a simple ramp, is the simplest of the simple machines. You use it when you walk up a hill. If you have a large hill in your town, think about how much easier it is to walk up a path to the top than to have to climb straight up a wall of the same height. This is the inclined plane in action. There are di erent ways to think about the inclined plane. We shall look at how it helps us raise objects against the acceleration of gravity rst. Starting with an object on the ground, gravity is accelerating it down at the brisk rate of 9.8 m/s2. The force developed by this acceleration is directed straight down into the ground (Fig. 3-5). What happens when you put that same object on a slippery slope (Fig. 3-6) Assuming there is no friction, it will slide down to the bottom of the ramp. While gravity is accelerating the block straight down, the ramp is in the way.



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As shown in Figure 537, each motor is made of only two parts a coil assembly and a magnet assembly The coil assembly encapsulates copper windings within a core material which is either epoxy based or made of steel The copper windings conduct current, I The magnet assembly consists of rare earth magnets, mounted in an alternating polarity on a steel plate, which generates magnetic flux density, B When the current and the flux density interact, force, F are generated in the direction shown in the figure where F = I B The advantages of linear motors are quoted from Anarod, one of the leading market providers of linear motor drives, and are as follows: Unlimited travel Linear motors do not have limitations on travel displacements Since the stationary magnet assemblies can be easily joined to form any length of motor, the travel length can be made as long as necessary Since the same moving coil assembly could be used





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(7-50)

Fig. 3-4.

Flux density (B) Current ( I )

Force ( F )

Fig. 3-5.

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for any travel length, there is no trade-off in the performance as a function of travel Screw driven systems, on the other hand, have critical speed limitations and higher inertia with added length Speed limitations, high inertia, and low stiffness are major performance tradeoffs with larger travels with other drive techniques They are used in LRTs (Light Rail Transit) Velocity Linear servo motors can be used in both very low and very high velocity applications, all with a very high precision They can precisely operate at velocities ranging from less than 1 m/sec (000004"/sec) to more than 10 m/sec (400"/sec) Ball screws and lead screws have critical speed limitations Belt drives exhibit a lower stiffness Rack-andpinion drives typically have a backlash and a poor low velocity performance They thus provide very low feed rates in ultra-precision machines and very high feed rates in large mould and die machine tools Acceleration Linear motors have a high ratio of peak force to motor inertia (about 30:1) Therefore, almost all of the motor force can be used to accelerate the moving load and perform useful work In typical screw-driven systems, a large portion of the motor torque is lost in overcoming the rotary inertia of the motor, coupling and screw Smoothness of motion Brushless linear servo motors can provide an extremely smooth motion, since they have no contacting surfaces to cause a jitter In contrast, ball screws are not as smooth due to the vibrating nature of the balls entering and exiting the ball nut raceways, which is easily observed in sub-micron systems Belt and rack-and-pinion drives also have contacting mechanisms, which are susceptible to friction and backlash caused vibrations Accuracy and repeatability With linear motors, the only limit to total system accuracy and repeatability is the sensing device and the bearings of the positioning system In rotary driven systems, there are additional factors, which affect these performance variables, including backlash, hysteresis, lost motion and jitter Stiffness Linear servo motors have a very high stiffness, typically higher than a stage s bearings and structural members With ball screws and rack-and-pinion drives, the couplings,.

At this point, the force from gravity is split into two parts. Each of these two parts describes a direction. The force of gravity is directed down, which makes it the force direction. This acceleration can be described by its own vector. In our simpli ed, twodimensional world, the X ordinate in the vector is the amount of acceleration

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