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FIGURE 5.4 A basic planetary train. in Software
FIGURE 5.4 A basic planetary train. EAN13 Supplement 5 Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Draw EAN / UCC  13 In None Using Barcode generation for Software Control to generate, create GS1  13 image in Software applications. Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright 2004 The McGrawHill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. EAN13 Supplement 5 Scanner In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Encode GS1  13 In Visual C# Using Barcode creator for .NET framework Control to generate, create EAN13 Supplement 5 image in .NET framework applications. GEAR TRAINS 5.6
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Draw EAN13 In Visual Basic .NET Using Barcode creation for .NET framework Control to generate, create European Article Number 13 image in Visual Studio .NET applications. Generating Barcode In None Using Barcode generation for Software Control to generate, create bar code image in Software applications. direct contact, a pairing that is prevalent in camandgear systems. An explanation and an illustration of the joint types are found in Refs. [5.1] and [5.2] as well as others (see Chap. 3). There are several methods for analyzing planetary trains. Among these are instantcenters, formula, and tabular methods. By instant centers, as in Ref. [5.3] and on a face view of the train, draw vectors representing the velocities of the instant centers for which input information is known. Then, by simple graphical construction, the velocity of another center can be found and converted to a rotational speed. Figure 5.5 illustrates this technique. EAN13 Encoder In None Using Barcode maker for Software Control to generate, create EAN13 image in Software applications. Generate Bar Code In None Using Barcode generation for Software Control to generate, create barcode image in Software applications. FIGURE 5.5 Instantcenters method of velocity analysis.
Data Matrix Drawer In None Using Barcode generator for Software Control to generate, create Data Matrix ECC200 image in Software applications. Drawing Universal Product Code Version A In None Using Barcode printer for Software Control to generate, create GTIN  12 image in Software applications. Calculate VIC24 and VIC45 from V = r (5.10) Painting 2 Of 5 Industrial In None Using Barcode drawer for Software Control to generate, create Code 2 of 5 image in Software applications. ECC200 Drawer In VS .NET Using Barcode generation for Reporting Service Control to generate, create Data Matrix ECC200 image in Reporting Service applications. where r = radius dimension and = angular velocity in radians per second (rad/s). Draw these vectors to scale in the face view of the train. Then VIC24 and VIC45 will emanate from their instantcenter positions. Now draw a straight line through the EAN13 Recognizer In Visual Basic .NET Using Barcode recognizer for .NET Control to read, scan read, scan image in .NET framework applications. Encode GS1 DataBar Limited In Java Using Barcode creator for Java Control to generate, create GS1 DataBar Stacked image in Java applications. Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright 2004 The McGrawHill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Print Bar Code In Java Using Barcode maker for BIRT reports Control to generate, create bar code image in BIRT reports applications. Making DataMatrix In Java Using Barcode encoder for Java Control to generate, create Data Matrix image in Java applications. GEAR TRAINS 5.7
1D Barcode Creation In Visual Studio .NET Using Barcode creator for ASP.NET Control to generate, create 1D Barcode image in ASP.NET applications. ANSI/AIM Code 128 Scanner In C# Using Barcode recognizer for .NET framework Control to read, scan read, scan image in .NET framework applications. GEAR TRAINS
termini of the velocity vectors. The velocity of IC34 will be a vector perpendicular to the line of centers and having its terminus on the velocity gradient. Determine of link 3 by using Eq. (5.10). Thus, VIC24 = r2 2 and VIC45 = r5 5 Choose a scale and construct the two vectors. Next, draw the gradient line and construct VIC34. Scale its magnitude and determine n3 according to n3 = VIC34 60 2 r3 (5.11) where r3 = radius of the arm and n3 is in revolutions per minute. If gear 5 is fixed, then VIC45 = 0; using VIC24, connect the terminus of VIC24 and IC45 with a straight line, and find VIC34 as before. See Fig. 5.6. This line can be called a velocity gradient for link 4.
FIGURE 5.6 Gear 5 is fixed.
Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright 2004 The McGrawHill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. GEAR TRAINS 5.8
MACHINE ELEMENTS IN MOTION
By formula, the relativemotion equation will establish the velocity of the gears relative to the arm; that is, n23 = n2 n3 n53 = n5 n3 Then, dividing (5.13) by (5.12), we see that n53 n5 n3 = n23 n2 n3 (5.14) (5.12) (5.13) which represents the ratio of the relative velocity of gear 5 to that of gear 2 with both velocities related to the arm. The righthand side of the equation is called the train value. If the arm should be held fixed, then the ratio of output to input speeds for an ordinary train is obtained. The equation for train value, which is seen in most references, can be written e= where nF = speed of first gear in train nL = speed of last gear in train nA = speed of arm nL nA nF nA (5.15) The following example will illustrate the use of Eq. (5.15). Example 1. Refer to the planetary train of Fig. 5.4. The tooth numbers are N2 = 104, N4 = 32, and N5 = 168. Gear 2 is driven at 250 r/min in a clockwise negative direction, and gear 5 is driven at 80 r/min in a counterclockwise positive direction. Find the speed and direction of rotation of the arm. Solution. nF = n2 = 250 r/min nL = n5 = +80 r/min e= In Eq. (5.15), 80 n3 13 = 21 250 n3 n3 = 46.2 r/min N2 N4 N4 104 = N5 32 13 32 = 21 168 By tabular method, a table is first formed according to the following: 1. Include a column for any gear centered on the planetary axis. 2. Do not include a column for any gear whose axis of rotation is fixed and different from the planetary axis. 3. A column for the arm is not necessary. 4. The planet, or planets, may be included in a column or not, as preferred. Gears which fit rule 2 are treated as ordinary gear train elements. They are used as input motions to the planetary system, or they may function as output motions. The table contains three rows arranged so that each entry in a column will constitute one term of the relativemotion equation Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright 2004 The McGrawHill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

