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giving a kinetic energy of less than 5 joules. Where did the other 14 joules go The problem is that this velocity is the average velocity across the entire fall, most of which is spent going really slow. The kinetic energy would need to be calculated for the nal velocity of the ball when it hit. This is trickier, and is not explored here. Sorry.



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Precision Engineering not restrict the bearing length Ultimately, the completed design of the whole spindle is shown in Figure 743 Here the work spindle consists of both aerostatic journal and thrust bearings From Table 710, it is seen that for externally pressurized gas bearings, a thrust face must be provided to carry the axial load This is even more critical when designing the grinding spindle, as the forces will be concentrated in the axial direction Most bearings have linear operating characteristics up to an eccentricity ratio of 05 as can be seen from Figure 75 Thus, this permits an accurate estimation of the radial stiffness for values below an eccentricity of 05 In addition, higher

3

Fig 742: An aerostatic grinding spindle [29]

Fig 743: A typical ultra-precision aerostatic spindle and drive system [2]

rAp, p) = l( - Ie)





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1. Statics is the study of the forces on objects as they just sit there. Dynamics is more concerned with forces of objects in motion. Note that kinematics is also the study of motion. They go hand in hand: kinematics of motion, dynamics of the forces behind the motion. 2. Cutting paper uses shearing forces, and scissors are often called shears. Crushing a grape uses compression force and breaking a string involves tension. Examinations also include tension, but of a di erent sort. 3. The vertical part of the motion is the part that ghts gravity. This is calculated as the sine of the angle: v sin 10 v 0:17 So as we push the robot up the ramp, it is ghting 17% of gravity s force, or an acceleration of 1.67 m/s2. Now that you know the acceleration ghting the climb of the robot, what else can you calculate, assuming you also know the weight of the robot 4. Your knee, like your elbow, is the fulcrum for a second-class lever. Your ankle, however, is the fulcrum in the center of the rst-class lever that is your foot. 5. 25 teeth, each taking 0.125 inch, uses up 3.125 inches total. This would be the circumference of the gear, so the gear s radius is just about a half inch: c 2 r 3:125 6:283 r r 3:125 6:283

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eccentricity ratios are used to provide a capacity to withstand an overload It is important to consider the geometrical error for the manufacturing process at this stage since the bearing clearance comes into picture Figure 744 indicates the actual load capacity that can be achieved by aerostatic bearings at a supply pressure of 100 lbf/in2 (689 kPa), which is common for industrial applications The figure is useful for obtaining a rough idea of the load capacity for a given dimension For other values of the supply pressure, the load capacity can be corrected by multiplying with

( Po Pa )

r 0:497

where (Po Pa) is expressed in lbf/in For example, the information in Figure 744 is valid for e = 05 and a supply pressure gauge of 100 lbf/in2 A diameter of 2 in is given with a load capacity of 100 lbf From the figure, a length of 3 in which will give a load value (145 lbf, on interpolation of curve 100 lbf and 150 lbf) that is higher than the load capacity at the intersection of the length and accordingly the diameter is chosen For a supply pressure gauge of less than 100 lbf/in2, a correction factor is required (as indicated before) Therefore, for the available supply pressure gauge that is 75 lbf/in2, the corrected load capacity is

The big gear has a diameter of 4.97 inches giving a radius of 2.485 inches. The circumference is then: c 2 2:485 c 15:61 Leaving room for 125 teeth. Okay, 124.9 teeth. The math, as shown, rounds the numbers, losing a bit of accuracy. The mechanical advantage is then 5:1 or 1:5, depending on how you look at it. Note that this is essentially the same as 15.61:3.125, the relative circumferences of the gears. For that matter, it s also the same as the ratio of the diameters, 0.994:4.97.

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