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732 Solid Regions Although the global geometric properties of cam disks can be described as those of a planar contour, the presence of nonsymmetric hubs, keyways, and the like render the cam plate a 3-D solid of a general shape By the latter we mean a solid that cannot be generated by a simple extrusion or sweeping of the planar contour in a direction perpendicular to its plane In this case, the global properties are those of a 3-D region R bounded by a closed surface S, namely, its volume V, its vector rst-moment q, and its 3 3 inertia matrix about point O These are de ned V dV

24:

Method public virtual bool ContainsKey(object k) public virtual bool ContainsValue(object v) public virtual IDictionaryEnumerator GetEnumerator( ) public static Hashtable Synchronized(Hashtable ht)

Again, from the mean-value theorem of integral calculus, a vector c exists such that q = Vc and vector c, once more, de nes the location of the centroid C of R Correspondingly, the three components of c in a frame F (O, x, y, z) are given by ci, for i = 1, 2, 3, that is, c = [c1, c2, c3]T The moment of inertia of R about C is then de ned as IC which then reduces to I xx I C = I xy I xz where

5 Use the technique of logarithmic differentiation to calculate the derivative of each of the following functions (a) x 3 (b) x2 + 1 x3 x

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Description Returns true if k is a key in the invoking Hashtable Returns false otherwise Returns true if v is a value in the invoking Hashtable Returns false otherwise Returns an IDictionaryEnumerator for the invoking Hashtable Returns a synchronized version of the Hashtable passed in ht

Because Hashtable does not maintain an ordered collection, there is no specific order to the collection of keys or values obtained Hashtable also has two protected properties: EqualityComparer and KeyComparer Two other properties called hcp and comparer are flagged as obsolete Hashtable stores key/value pairs in the form of a DictionaryEntry structure, but most of the time, you won t be aware of it directly because the properties and methods work with keys and values individually For example, when you add an element to a Hashtable, you call Add( ), which takes two arguments: the key and the value It is important to note that Hashtable does not guarantee the order of its elements This is because the process of hashing does not usually lend itself to the creation of sorted tables Here is an example that demonstrates Hashtable:

2 2 I xx [( y - c2 ) + ( z - c3 ) ]dx dy dz R 2 2 I yy [( x - c1 ) + ( z - c3 ) ]dx dy dz R 2 2 Izz [( x - c1 ) + ( y - c2 ) ]dx dy dz R R

// Demonstrate Hashtable using System; using SystemCollections; class HashtableDemo { static void Main() { // Create a hash table Hashtable ht = new Hashtable(); // Add elements to the table htAdd("house", "Dwelling"); htAdd("car", "Means of transport"); htAdd("book", "Collection of printed words"); htAdd("apple", "Edible fruit"); // Can also add by using the indexer ht["tractor"] = "Farm implement"; // Get a collection of the keys ICollection c = htKeys; // Use the keys to obtain the values foreach(string str in c) ConsoleWriteLine(str + ": " + ht[str]); } }

Part II:

sin x (x 3 + x) x 2 (x + 1)

As in the case of planar contours, the foregoing calculations involve multiple integrals, in this instance, three Reduced formulas transforming these calculations into surface and even line integrals are provided later

The output from this program is shown here:

book: Collection of printed words tractor: Farm implement apple: Edible fruit house: Dwelling car: Means of transport

For static and dynamic balancing, and also for dynamic analysis (Koloc and Vaclacik, 1993), the determination of the cam global geometric properties is of the utmost importance For example, very often the cam axis of rotation and the principal axis of inertia perpendicular to the cam disk are skew Therefore, to balance the cam statically and dynamically, their global volumetric properties must be calculated The calculation of these and the local properties requires the introduction of suitable numerical techniques that will be discussed later

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