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These equations facilitate converting from one family of dimensional units to another By having the cam pro les in the mathematical form of Eq (21) or Eq (22) we also can easily nd the other characteristics, by differentiation From the foregoing equations, we see that each successive derivative can be determined from the slopes of any point on the previous curve Thus, at any point the slope of the displacement curve yields the velocity of the follower The slope of the velocity curve is the acceleration of the follower, and the slope of the acceleration curve is the jerk of the follower This procedure is called the graphical-slope differentiating method It is presented for a quick appraisal of the displacement, velocity, acceleration, and jerk curves Utilizing the graphical-slope method, the velocity curve is reasonably accurate and the acceleration curve is at best only an approximation With the graphical-slope method, the determination of the signs (positive or negative) is essential for a fundamental understanding of the follower motion and dynamics Let us establish as positive (+) the displacement of the follower above the lowest point in the displacement diagram (Fig 21a) Therefore, the velocity is positive if the follower moves in the direction of positive displacement and negative if it moves in the opposite direction That is, velocity is positive on the rise and negative on the fall The acceleration follows a similar convention Therefore the acceleration is positive when its direction is that of the positive displacement Throughout this book, the word deceleration is not used because it does not indicate the direction of acceleration and would therefore cause confusion regarding the direction of inertia load The slope of the curves at any point gives us another method for determining signs Sloping upward to the top right the slope is positive, and sloping upward to the top left the slope is negative Also, a vertical slope at a point in any of the curves has an in nite value and is called a discontinuity because it has two values at the point being studied Some concepts discussed in this chapter are:.

// Execute the query and display the results foreach(Account acc in accInfo) { if(str != accFirstName) { ConsoleWriteLine(); str = accFirstName; } ConsoleWriteLine("{0}, {1}\tAcc#: {2}, {3,10:C}", accLastName, accFirstName, accAccountNumber, accBalance); } ConsoleWriteLine(); } }

The Asc function will return the ASCII value of a character value in the string input_ parameter provided

The output is shown here:

(a) Displacement curve (slope equals velocity)

Accounts in sorted order: Jones, Jenny Jones, Ralph Jones, Ralph Jones, Ralph Krammer, Betty Krammer, Ted Smith, Albert Smith, Carl Smith, Sara Smith, Sara Smith, Sara Smith, Tom Smith, Tom Acc#: 108CK, Acc#: 434CK, Acc#: 454MM, Acc#: 436CD, Acc#: 968MM, Acc#: 897CD, Acc#: 445CK, $1098 ($12332) $98713 $1,92385 $5,14667 $3,22319 ($21367)

integer Asc(string input_parameter)

Acc#: 078CD, $15,34599 Acc#: 843CK, $34500 Acc#: 543MM, $5,01740 Acc#: 547CD, $34,95579 Acc#: 132CK, $10023 Acc#: 132CD, $10,00000

In the query, look closely at how the orderby clause is written:

(b) Velocity curve (slope equals acceleration)

The Char function will return the character associated with the ASCII value indicated in number input_parameter

var accInfo = from acc in accounts orderby accLastName, accFirstName, accBalance select acc;

Here is how it works First, the results are sorted by last name, and then entries with the same last name are sorted by the first name Finally, groups of entries with the same first

string Char(number input_parameter)

The follower displacement motion y refers to the knife-edge follower or the pitch curve center of the roller follower if employed The follower velocity y or y is an indication of both the cam pressure angle and the cam torque The follower acceleration y or y is critically signi cant for design considerations Acceleration values are related to the system inertia forces in which the maximum acceleration establishes the maximum inertia forces The shape of the follower acceleration curve is of critical concern for the design of moderate- to high-speed machines From it, analysis can be made for cam-follower system shock, noise, wear, and vibration The acceleration curve shall have no discontinuities where it blends with the dwell action of the motion Acceleration values at each point are related to the radius of curvature of the cam pro le, which in turn relates to the surface stresses and wear Over the complete rise-fall motion, the following is true: y dq = 0 and ydt = 0 (211)

Part I:

and last name are sorted by the account balance This is why the list of accounts under the name Jones is shown in this order:

string, most commonly a carriage return For example, if you wanted to create a report header cell with your report title followed by a carriage return and the date the report was executed, the following formula would accomplish this: