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Try This: For levers, let s build a LEGO lever machine. In the ne tradition of these types of projects, the construction steps are depicted in pictures, shown in Fig. 3-9. The last step, and an informative example showing range of motion, is in Fig. 3-10. Pushing down on the long arm of the lever creates an upward force on the short arm. While the long arm moves four times as far, the short arm creates four times the force. You can hang weights at di erent points on this machine to get a feel for how it works. How does it feel when you hang the weight on the long end



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40 0 500 3125 016

Fig. 3-9.

125 500 0 025

85 500 0 1471 034

Fig. 3-10.

0 0 0 08

Force Analysis In the preceding example, assume a machining force of 130 N in Phase 2, a coefficient of friction of 008, and a moving mass of 23 kg (20 kg slide and a customer load and a 3 kg assumed mass for the motor coil) Finally, assume a magnetic attraction of 2,000 N Using the force equations, the resulting forces in this example are shown in the following table: Table 53 Force analysis for a linear motor drive

Fig. 3-11.

1 2 3 4

178 719 0 250





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instead of the short end Try the weight at di erent positions and see how it a ects the force and range of motion. A formal description of the lever is given in Fig. 3-11. This lever is known as a rst-class lever. All levers have the same three pieces. The pivot in the middle is the fulcrum. The distance from the fulcrum to where the input force, or e ort (E), is applied is the e ort arm (dE). The distance from the fulcrum to where the force is used is the resistance arm (dR). The lever is applied against resistance

178 0 130 308

Fig. 3-12.

178 338 0 1442

0 0 0 0

(R). If dE is larger than dR, then your force is increased. The mechanical advantage is calculated as: MA dE dR 3-7

Note: The sign indicates the direction of the force opposite the direction of the motion The motor has to provide a force equal in magnitude and opposite in direction to Ft

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To sum up the progress in drive systems, Table 54 discusses the future trend in high-speed machining It is clear that as the linear motor drive has many advantages, it is much costlier and is therefore used only for certain high end applications On the other hand, although the lead ball screw is inferior, it is used for most other applications and is sufficient for certain normal applications Table 55 compares the different feed drives It can be seen that the progress is from the conventional machining centre to a high lead ball screw and to a linear motor, which is used, in high-speed machining centres Along with this advancement, the progress in terms of feed rate and acceleration rate is also quite clear Table 54

(7-51a)

Equation (3-7) is essentially the same as equation (3-4) for the wedge. Though we look at several di erent simple machines, each with their own approach to increasing force, the principles behind each one are the same. Force is force, and the rules governing force are not going to change. If we seem to be getting more force at the output of a mechanism, somewhere inside it we are spending velocity or distance to get it. A second-class lever is shown in Fig. 3-12, and a third-class lever in Fig. 3-13. These have the same pieces as a rst-class lever, just in di erent positions. Note that the third-class lever has you pushing harder to get greater distance, backward from the rst and second-class levers. Your arm is a third-class lever with your elbow at one end, your wrist at the other, and the muscle attached in between.

Machining centre Cost of machine Use Feed rate m/min Acceleration rate Static servo stiffness Position loop gain/s Temperature control

A pulley is essentially a wheel. Where a wheel wears a skirt of rubber so it has a lot of friction, the pulley has a groove for a rope around its edge. Pulleys are designed so they don t add much friction to the machine they are a part of. Methods for removing friction are explored in a later chapter.

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