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Mechanics of Materials Cutting 13 Calculation of the Normal Side Rake Angle, n an = tan 1 (tan a cos i ) = tan 1 [tan ( 5 ) cos ( 5 )] = 49811 14 Calculations of the Friction Force, FF FF = =

If you try a bunch of stu all at once, you won t know what each change did..

{ (1160 cos ( 5 ) + 244 sin ( 5 ) ) sin ( 49811 )



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If you have two light sensors, you can make your program faster and smarter. These sensors would act like two bumpers. As the left sensor crosses the black line, you can turn the robot left. For the right sensor, you would turn right.

Fp cos i + Fr sin i sin n + Fq cos n + ( Fp sin i Fr cos i )2

+ 535 cos ( 49811 ) 2 + (1160 sin ( 5 ) 244 cos ( 5 ) )

These sensors don t have to be pointed down to the oor. You can point them forward or upward and use them to follow the light from a ashlight.





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= {[(113432) ( 008683) + (53298)] 2 + ( 344172)2}1/2 = 554286 N 15 Calculation of Normal Force, FN FN = (FP cos i + Fr sin i ) cos an Fq sin an = [1160 cos ( 5 ) + 244 sin ( 5 )] cos ( 49811 ) 535 sin ( 49811 ) = 1130036 ( 46453 ) = 117649 N 16 Calculation of Coefficient of Friction, F m = N = 17 Calculation of tan t = t = = =

2 12

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Though the RCX software handles light sensor calibration for you, there are times when you want to do this yourself Most sensors do not return information in useful forms like bright and dark Instead, they return values in a numerical range, such as 0 through 255, or 00 to 10 The values depend not only on what is in front of, or touching, the sensor but also on the ambient environment If a value of 40 is a bright re ection in a normal room, what would it be if the robot is in a brightly lit room If we are thinking about the re ective light sensor, what is a bright re ection on paper The oor of your kitchen To turn the arbitrary, and locally varied, values returned from a sensor into valuable data you need to calibrate the sensor.

= 0471

554286 117649

For a re ective light sensor, you need to know what values it returns for the bright surface as well as a dark line A simple way to do this is to look, reading the light sensor as the robot spins in a circle Remember the largest and the smallest values from the sensor for your de nition of bright and dark (Fig 13-10) You don t want to test against these mininimum (min) and maximum (max) values directly You want to see how close the current light value is to one of them, or the current value s relative position from the midpoint Once you have captured your light values, you can stop the motors for a moment to let the robot come to a stop, and then turn back to the starting position.

m tan 1 m tan 1 (0471) 2523

If you want to make your program really clever, though more complicated, you can keep track of the light values as the program performs its normal duties You can then use these values to keep the min and max ranges up to date as conditions change over time..

= 069444

r cos n Fn = tan 1 c 1 rc sin n 069444 cos ( 49811 ) = tan 1 1 069444 sin ( 49811 ) = 33124

Summary

110 Calculation of Shear Strain, e = cot Fn + tan (Fn an) = cot (32122) + tan [32122 ( 49811)] = 23168 111 Machinability Coefficient, C C = 2Fn + t g = 2(33124) + 2523 ( 5) = 9647 20 Sample Calculation 2 (Work Done Calculation) Symbols V Cutting Velocity Vs Shear Velocity Ps Shear Work Po Output Work hs Shear flow angle Vc Pi Pf hc Friction Velocity Input Work Friction Work Chip flow angle

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