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In Chap 2 we discussed the basic parabolic, sinusoidal, and cycloidal curves for cam-follower DRD action We also showed in Chap 3 how these curves and others can be modi ed and combined to form a variety of cam pro les Ignoring the torsional aspect of the cam drive (assuming the cam runs at a constant speed), the two fundamental dynamic objectives in designing cam pro les are: 1 to have the smallest possible maximum acceleration and thus the minimum dynamic load on the high-speed follower; 2 To avoid resonant vibratory response in the follower caused by high harmonic content in the designed cam pro le These fundamental objectives are not related Let us compare the basic cam pro les as a means of describing the harmonic content that is addressed in the later paragraphs The parabolic curve has the smallest maximum acceleration but has a high harmonic content, since the Fourier expansion for a parabolic curve has an in nite number of terms Because each term is associated with a certain forcing frequency, it may induce resonance vibrations in the follower at some of those frequencies at some speed as the system is brought up to speed The cycloidal cam, on the other hand, having but a fundamental frequency in the acceleration curve, has a minimum harmonic content The cycloidal pro le is the least likely to excite vibration in the follower, but this occurs at the expense of high acceleration Furthermore, it has a more than 50 percent higher maximum acceleration than does the parabolic pro le In design, it is necessary to nd a cam pro le that has the fewest and lowest possible harmonics, though, in the end, nature calls for a compromised balance of all factors, requiring judicial trade-offs There is no perfect solution A number of acceptable harmonic curves have been developed in consideration of these thoughts Note that for a DRD motion event, the Fourier series used must be an odd harmonic curve, which has polar symmetry with respect to the midpoint of the curve Gutman 1-3 Harmonic (Gutman, 1961) 15 2pq 1 6pq q sin sin y = h b 96p b b 32p y = h b 2pq 1 6pq 15 1 - 16 cos b - 16 cos b hp 8b 3 hp 2 4b 3 2pq 6pq 15 sin b + 3 sin b 2pq 6pq 15 cos b + 9 cos b (411).

public int CompareTo(float value)

=Max([Revenue]) In ([Year])

public override bool Equals(object obj) public bool Equals(float obj) public override int GetHashCode( ) public TypeCode GetTypeCode( ) public static bool IsInfinity(float f) public static bool IsNaN(float f)

Part II:

y =

=Max([Revenue]) In ([Year])

Method public static bool IsPositiveInfinity(float f) public static bool IsNegativeInfinity(float f) public static float Parse(string s) public static float Parse(string s, IFormatProvider provider) public static float Parse(string s, NumberStyles style) public static float Parse(string s, NumberStyles style, IFormatProvider provider) public override string ToString( ) public string ToString(string format) public string ToString(IFormatProvider provider) public string ToString(string format, IFormatProvider provider) public static bool TryParse(string s, out float result)

.

y =

22:

Meaning Returns true if f represents positive infinity Otherwise, returns false Returns true if f represents negative infinity Otherwise, returns false Returns the binary equivalent of the numeric string in s If the string does not represent a float value, an exception is thrown Returns the binary equivalent of the numeric string in s using the culture-specific information provided by provider If the string does not represent a float value, an exception is thrown Returns the binary equivalent of the numeric string in s using the style information provided by style If the string does not represent a float value, an exception is thrown Returns the binary equivalent of the numeric string in s using the style information provided by style and the culture-specific format information provided by provider If the string does not represent a float value, an exception is thrown Returns the string representation of the value of the invoking object in the default format Returns the string representation of the value of the invoking object as specified by the format string passed in format Returns the string representation of the value of the invoking object using the culture-specific information specified in provider Returns the string representation of the value of the invoking object using the culture-specific information specified in provider and the format specified by format Attempts to convert the numeric string in s into a float value If successful, the value is stored in result and true is returned If no conversion takes place, false is returned This differs from Parse( ), which throws an exception on failure Attempts to convert the numeric string in s into a float value using the style information provided by style and the culture-specific format information provided by provider If successful, the value is stored in result and true is returned If no conversion takes place, false is returned This differs from Parse( ), which throws an exception on failure.

public static bool TryParse(string s, NumberStyles style, IFormatProvider provider, out float result)