Trigonometry Tables and Handy References for Engineers

Transcription

1 $1 Trigonometry Tables and Handy References for Engineers No matter what angle you figure... Carr Lane is your best answer for jig-and-fixture components! AUTHORIZED DISTRIBUTOR A-L Tool Supply P.O. Box Milwaukee, WI PRINTED IN U.S.A. Rev. 2/2014 COPYRIGHT 2014 CARR LANE MFG. CO.

2 Toggle Clamps With Safety Locks Avoid accidents by using Carr Lane s toggle clamps, available in the following varieties, many with optional safety locks: made in usa Horizontal Handle Vertical Handle Push/Pull Latch Action Air-Powered Toggle Edge Clamps Visit our web site: carrlane.com

3 TABLE OF CONTENTS Thread Sizes and Tap Drills...2 Standard Drill Sizes...4 Counterbored Holes for Cap Screws...6 Geometric Dimensioning and Tolerancing...7 Surface Finishes...12 Clamping Force of Standard Clamp Straps...13 Basic Numbering System for Steels...14 Machinability Comparison of Various Metals...15 Hardness Conversions and Tensile Strength...16 Metric Prefixes...23 Conversion Factors for Units of Measure...24 Trigonometry Calculations...45 Trigonometry Tables...50

4 USA THREADS Basic Tap Thread Major Drill 2

5 METRIC THREADS Basic Tap Thread Major Drill 3

6 USA DRILL SIZES /

7 METRIC DRILL SIZES.35mm mm mm

8 6 SCREW DIA #0 #2 #4 #5 #6 #8 #10 1/4 5/16 3/8 7/16 1/2 5/8 3/4 7/ /4 1-1/2 1-3/4 2 A COUNTERBORE DIA 1/8 3/16 7/32 1/4 9/32 5/16 3/8 7/16 17/32 5/8 23/32 13/ /16 1-3/8 1-5/ /8 2-3/4 3-1/8 B COUNTERBORE DEPTH C COUNTERSINK DIA NORMAL FIT #49 #36 #29 #23 #18 #10 #2 9/32 11/32 13/32 15/32 17/32 21/32 25/32 29/32 1-1/32 1-5/16 1-9/ /16 2-1/16 CLOSE FIT #51 3/32 1/8 9/64 #23 #15 #5 17/64 21/64 25/64 29/64 33/64 41/64 49/64 57/64 1-1/64 1-9/ / /32 2-1/32 METRIC SOCKET-HEAD CAP SCREWS M1.6 M2 M2.5 M3 M4 M5 M6 M8 M10 M12 M14 M16 M20 M24 M30 M36 M42 M mm 4.40mm 5.40mm 6.50mm 8.25mm 9.75mm 11.20mm 14.50mm 17.50mm 19.50mm 22.50mm 25.50mm 31.50mm 37.50mm 47.50mm 56.50mm 66.00mm 75.00mm 1.6mm 2mm 2.5mm 3mm 4mm 5mm 6mm 8mm 10mm 12mm 14mm 16mm 20mm 24mm 30mm 36mm 42mm 48mm 2.0mm 2.6mm 3.1mm 3.6mm 4.7mm 5.7mm 6.8mm 9.2mm 11.2mm 14.2mm 16.2mm 18.2mm 22.4mm 26.4mm 33.4mm 39.4mm 45.6mm 52.6mm 1.95mm 2.40mm 3.00mm 3.70mm 4.80mm 5.80mm 6.80mm 8.80mm 10.80mm 13.00mm 15.00mm 17.00mm 21.00mm 25.00mm 31.50mm 37.50mm 44.00mm 50.00mm 1.80mm 2.20mm 2.70mm 3.40mm 4.40mm 5.40mm 6.40mm 8.40mm 10.50mm 12.50mm 14.50mm 16.50mm 20.50mm 24.50mm 31.00mm 37.00mm 43.00mm 49.00mm D CLEARANCE DIA COUNTERBORED HOLES USA SOCKET-HEAD CAP SCREWS

9 GEOMETRIC SYMBOLS AND DEFINITIONS M A A A1 A2 A M L S.005 P 7

10 GEOMETRIC CHARACTERISTICS Flatness 8

11 GEOMETRIC CHARACTERISTICS Linear Profile 9

12 GEOMETRIC CHARACTERISTICS Perpendicularity (Squareness) 10

13 GEOMETRIC CHARACTERISTICS Circular Runout.005 A.375 4X M A 11

14 TYPICAL SURFACE FINISHES PRODUCED BY VARIOUS PRODUCTION METHODS Roughness Average 12

15 CLAMPING FORCE OF STANDARD CLAMP STRAPS USA Tensile Recommended Clamping Force Stud Torque* Force in Stud Size (ft.-lbs.) (lbs.) (lbs.) # / / / / / / / METRIC M M M M M M M *Clean, dry clamping stud torqued to approximately 33% of its 100,000 psi yield strength (2:1 lever ratio). 13

16 AISI/SAE NUMBERING SYSTEM FOR CARBON AND ALLOY STEELS 14

17 MACHINABILITY COMPARISON* Carbon Steels: % % % % 15

18 APPROXIMATE HARDNESS CONVERSIONS FOR STEEL 16

19 APPROXIMATE HARDNESS CONVERSIONS FOR STEEL 17

20 APPROXIMATE HARDNESS CONVERSIONS FOR STEEL 18

21 APPROXIMATE HARDNESS CONVERSIONS FOR STEEL 19

22 APPROXIMATE HARDNESS CONVERSIONS FOR STEEL 20

23 APPROXIMATE HARDNESS CONVERSIONS FOR STEEL 21

24 SINGLE-ACTING DOUBLE-ACTING ADJUSTABLE DETENT EXPANDING LIFTING BALL LOCK PINS BALL LOCK PINS BALL LOCK PINS PINS PINS PINS SINGLE-ACTING BALL LOCK PINS Precision ground locating pin. Press button to insert or remove. Positive locking until released by pressing button. Available in four handle styles. Two locking balls standard, with four balls available for greater pull-out strength. 3/16 to 1" diameters standard. Available in alloy or stainless steel. DOUBLE-ACTING BALL LOCK PINS Similar to a single-acting pin, except you release by pulling or pushing the handle. Positive locking. Choice of three handle styles. Available with drive-out option (internal spindle extends beyond the shank end). This feature lets you remove a pin under shear loading by tapping the shank end with a hammer. ADJUSTABLE BALL LOCK PINS Single-acting ball lock pin with adjustable grip length (1/2- inch range). Adjust grip by turning handle, then lock with the knurled locknut. Available in three handle styles. DETENT PINS Economical locating pin. Locking balls are spring loaded, not positive locking. Simply push pin to insert, pull to remove. 3/16 to 1" diameters standard. Available in alloy or stainless steel. EXPANDING PINS Precision alignment pin. Diameter expands up to.006 inches by moving handle. Positive cam action expands split bushings to lock pin in place. LIFTING PINS Single-acting ball lock pin with one-piece body and four balls for high tension loads. Sturdy forged shackle for heavy lifting. 22

25 METRIC PREFIXES 23

26 CONVERSION FACTORS Multiply By To Obtain A 24

27 Multiply By To Obtain Baryls 1 Dynes/sq. centimeter Board feet 144 Cubic inches Bolts (US Cloth) 40 Yards B.T.U x10 Ergs 25

28 Multiply By To Obtain Calories (kilogram) Kilogram-meters Calories (kilogram) Kilowatt-hours Candela/sq. centimeter Lamberts Candela/sq. inch.4869 Lamberts 26

29 Multiply By To Obtain Coulombs/sq. inch.1550 Coulombs/sq. cm Cubic centimeters 3.531x10 Cubic feet Cubic centimeters Cubic inches Cubic centimeters Cubic meters 27

30 Multiply By To Obtain Cubic yards.7646 Cubic meters Cubic yards Gallons Cubic yards Liters Cubic yards 1616 Pints (liquid) 28

31 Multiply By To Obtain Em (Pica).4233 Centimeters E 29

32 Multiply By To Obtain Feet/minute.3048 Meters/minute Feet/minute Miles/hour Feet/second Centimeters/second Feet/second Kilometers/hour 30

33 Multiply By To Obtain Gallons 8 Pints (liquid) Gallons Pounds of water Gallons 4 Quarts (liquid) Gallons (Imperial) Gallons 31

34 Multiply By To Obtain Grams/liter 1000 Parts/million Grams/sq. centimeter Pounds/sq. foot H 32

35 Multiply By To Obtain Inches 25.4 Millimeters Inches 1,000 Mils Inches Yards Inches of mercury Atmospheres 33

36 Multiply By To Obtain Kilograms Pounds Kilograms Tons Kilograms/cu. meter.001 Grams/cu. centimeter Kilograms/cu. meter Pounds/cu. foot 34

37 Multiply By To Obtain Kilowatts Horsepower Kilowatts Kilocalories/minute Kilowatts 1000 Watts Knots Feet/second 35

38 Multiply By To Obtain Meter-kilograms Pound-feet Meters 100 Centimeters Meters Feet Meters Inches 36

39 Multiply By To Obtain Miles/hour/sec Centimeters/sec./sec. Miles/hour/sec Feet/sec./sec. Miles/hour/sec Kilometers/hr./sec. 37

40 Multiply By To Obtain Oersteds Amperes/meter O 38

41 Multiply By To Obtain Poise 1 Grams/centimeter-sec. Pound-feet 13,560,000 Centimeter-dynes Pound-feet 13,825 Centimeter-grams Pound-feet.1383 Meter-kilograms 39

42 Multiply By To Obtain Pounds/sq. inch Atmospheres Pounds/sq. inch Bars Pounds/sq. inch Feet of water Pounds/sq. inch Inches of mercury 40

43 Multiply By To Obtain Revolutions/minute Revolutions/second Revolutions/min./min Radians/sec./sec. Revolutions/min./min x10 Revolutions/sec./sec. Revolutions/second 360 Degrees/second 41

44 Multiply By To Obtain Square meters Square yards Square miles 640 Acres Square miles 27,878,400 Square feet Square miles Square kilometers 42

45 Multiply By To Obtain W W 1 Watts 43

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48 RIGHT TRIANGLES c B a A C = 90 b Known Sides and Angles Unknown Sides and Angles Area a and b c = a 2 + b 2 A = arc tan a b B = arc tan b a a x b 2 a and c b = c 2 - a 2 A = arc sin a c B = arc cos a c a x c 2 - a 2 2 b and c a = c 2 - b 2 A = arc cos b c B = arc sin b c b x c 2 - b 2 2 a and A a b = tan A c = a sin A B = 90 - A a 2 2 x tan A a and B b = a x tan B - c = a cos B A = 90 - B a 2 x tan B 2 b and A a = b x tan A c = b cos A B = 90 - A b 2 x tan A 2 b and B a = b tan B c = b sin B A = 90 - B b 2 2 x tan B c and A a = c x sin A b = c x cos A B = 90 - A c 2 sin A cos A 2 c and B a = c x cos B b = c x sin B A = 90 B c 2 cos B sin B 2 46

49 OBLIQUE TRIANGLES c B a A C b Known Sides and Angles Unknown Sides and Angles Area All three sides a, b, c A = b arc cos 2 + c 2 - a 2 2bc arc sin B = b x sin A a C = A - B a x b x sin C 2 Two sides and the angle between them a, b, C c = a 2 +b 2 -(2abxcos C) A = arc tan a x sin C b-(a x cosc) B = A - C a x b x sin C 2 Two sides and the angle opposite one of the sides a, b, A ( B less than 90 ) arc sin B = b x sin A a C = A - B c = a x sin C sin A a x b x sin C 2 Two sides and the angle opposite one of the sides a, b, A ( B greater than 90 ) arc sin B = b x sin A a C = A - B c = a x sin C sin A a x b x sin C 2 One side and two angles a, A, B b = a x sin B sin A C = A - B c = a x sin C sin A a x b x sin C 2 47

50 SYSTEM Same great product, but with these advantages: Exclusively made in the USA Complete interchangeability with all components of the similar mounting system previously offered by Carr Lane Now lower price! CarrLane.com/Featured

51 5-AXIS + QUICK CHANGE = MAXIMUM UTILIZATION Use Carr Lane s Quintus quick-change riser to mount vises, fixture plates, or your custom clamping device By design, the CL5 system accepts our German-built, extremely accurate vises on precision plates made in the USA Achieve 5-side part access and quick-change flexibility Numerous jaw types and sizes available CarrLane.com/Featured

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99 DECIMAL EQUIVALENTS