barcode printing c# .net Copyright 2004 by The McGraw-Hill Companies, Inc Click Here for Terms of Use in Software

Printer DataMatrix in Software Copyright 2004 by The McGraw-Hill Companies, Inc Click Here for Terms of Use

Copyright 2004 by The McGraw-Hill Companies, Inc Click Here for Terms of Use
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where C is a constant In addition it may be noted that with V, the vertex, the distance GV = FV Construction: Given, in Fig A3, the vertex V, the axis VA, and a point P on the curve, a) Enclose parabola in rectangle VAPB b) Divide VB and BP into the same number of equal parts, and draw lines parallel to VA c) Join division points on BP with vertex V d) The intersection of these lines gives points on the parabola VP
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FIGURE A2 Parabola FIGURE A3 Construction of the parabola
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A hyperbola is a curve generated by a point moving so that the difference of its distances from two xed points, called the foci, is a constant 1 General Case The equation is: X2 Y2 - 2 =1 a2 b where a and b are distances shown in Fig A4 Also F1 and F2 are the foci Therefore, from the de nition the distance d - e = c, a constant Construction: Given foci F1 and F2 and distance 2a in Fig A4,
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a) With F1 and F2 as centers, draw arcs, such as F1P b) With the same centers and radius F1P minus distance 2a, strike arcs intersecting the other arcs giving points on the curve c) Repeat using new radius F1P
P e F2
F1 a a
FIGURE A4 Hyperbola
b Y 4 A 3 2 1 OB P
FIGURE A5 Rectangular hyperbola
2 Rectanglar One of the most frequently employed curves in engineering is the rectangular or equilateral hyperbola (Fig A5)
CAM DESIGN HANDBOOK
The equation becomes XY = C Construction: Given OX and OY as asymptotes of the curve and any point P on the curve, a) Draw PA and PB b) Mark any points 1, 2, and 3, etc, on PB, and through these points draw lines parallel to OX, and also lines through O c) From the intersection with line AP extended draw lines parallel to OA d) The intersections give the hyperbola
A4 LOGARITHMIC SPIRAL
This is a radial curve having a constant pressure angle When used on a cam, it provides the smallest radial cam for a given pressure angle limitation (Fig A6) The polar equation is r = ae bq where r = radius to any point on curve, in a = spiral base-circle radius, in 1 b= tan g
r Spiral base circle
FIGURE A6 Logarithmic spiral
g = 90 - a = constant angle at any point between radial line and tangent to the curve, deg a = pressure angle, deg q = angle between radius r and beginning point on the curve e = 2718 = base of natural logarithms Construction: Given angle g and the base-circle radius in Fig A7, a) Draw lines MP, PN, and OD b) Make equal division intercepts of line PM
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549 P g Base circle radius, a
R F F D
FIGURE A7 Construction of the logarithmic spiral
c) From point O, swing arc of radius BF intersecting arc of radius DF from point D d) This gives one point F on the curve; other points are found in a similar manner utilizing the same centers O and D It may be noted that portion DQ of the curve is subject to greater error than portion DR Caution and accuracy are suggested for this critical range
A5 INVOLUTE OF A CIRCLE
This is a curve generated by the end of a string unwinding from an involute base circle of radius a (Fig A8) The equation of the involute is r q = - 1 a
2 12
r - tan -1 - 1 a
g Radius of curvature
FIGURE A8 Involute of a circle
Construction: Given the base circle having radius a in Fig A8,
CAM DESIGN HANDBOOK
a) Divide the circle into a convenient number of parts b) Draw tangents at these points c) Lay off on these tangents the recti ed lengths of arcs from the tangency points to the starting point d) These points give the curve
APPENDIX B
BASIC CAM CURVE FACTORS
Table B1 SIMPLE HARMONIC MOTION FACTORS 552 Table B2 CYCLOIDAL MOTION FACTORS
Table B3 MODIFIED TRAPEZOIDAL CURVE FACTORS 554 Table B4 MODIFIED SINCE CURVE FACTORS
Curve factors have been developed to establish the cam pro le, the velocity, and acceleration of the follower easily These factors are tabulated data calculated from the curve equations in Chaps 2 and 3 In the tabulated values the cam angle factor goes from 0 to 120 and the displacement factor K goes from 0 to 1 To determine increments on a cam, the given values of q must be multiplied by the ratio b/120 For example, if b is 60 , the increment is 60/120 = 1/2 degree The following equations can be employed to establish the follower characteristics: Displacement Velocity Acceleration y = Kh, in w y = Cv h , in/sec b w y = Ca h , in/sec2 b
where K, CV, and Ca are the displacement factor, the velocity factor, and the acceleration factor, respectively; w is the camshaft speed, deg/sec; and h is total rise in inches for cam angle b, degrees
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