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Basic trigonometric lesson for CNC Machine operators and programmers, as well as other machine shop personnel.
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Disclaimer: All research materials are internet based. I do not own anything. Video links are included (from youtube).
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Modern precision manufacturing demands extreme dimensional accuracy and surface finish.Such performance is very difficult to achieve manually, if not impossible, even with expert operators. In cases where it is possible, it takes much higher time due to the need for frequent dimensional measurement to prevent overcutting. It is thus obvious that automated motion control would replace manual “handwheel” control in modern manufacturing. Development of computer numerically controlled (CNC) machines has also made possible the automation of the machining processes with flexibility to handle production of small to medium batch of parts. In the 1940s when the U.S. Air Force perceived the need to manufacture complex parts for highspeed aircraft. This led to the development of computer-based automatic machine tool controls also known as the Numerical Control (NC) systems. Commercial production of NC machine tools started around the fifties and sixties around the world. Note that at this time the microprocessor has not yet been invented. Initially, the CNC technology was applied on lathes, milling machines, etc. which could perform a single type of metal cutting operation. Later, attempt was made to handle a variety of workpieces that may require several different types machining operations and to finish them in a single set-up. Thus CNC machining Centres capable of performing multiple operations were developed. To start with, CNC machining centres were developed for machining prismatic components combining operations like milling, drilling, boring and tapping. Gradually machines for manufacturing cylindrical components, called turning centers were developed.
Automatically controlling a machine tool based on a set of pre-programmed machining and movement instructions is known as numerical control, or NC.In a typical NC system the motion and machining instructions and the related numerical data, together called a part program, used to be written on a punched tape. The part program is arranged in the form of blocks of information, each related to a particular operation in a sequence
of operations needed for producing a mechanical component. The punched tape used to be read one block at a time. Each block contained, in a particular syntax, information needed for processing a particular machining instruction such as, the segment length, its cutting speed, feed, etc. These pieces of information were related to the final dimensions of the workpiece (length, width, and radii of circles) and the contour forms (linear, circular, or other) as per the drawing. Based on these dimensions, motion commands were given separately for each axis of motion. Other instructions and related machining parameters, such as cutting speed, feed rate, as well as auxiliary functions related to coolant flow, spindle speed, part clamping, are also provided in part programs depending on manufacturing specifications such as tolerance and surface finish. Punched tapes are mostly obsolete.
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This document provides information about geometric dimensioning and tolerancing (GD&T). It defines GD&T as a method for defining the geometry of a part beyond simple tolerance dimensions. Feature control frames modify a part's geometry and include the geometric tolerance symbol, datum, and modifiers. Geometric characteristic symbols indicate the type of tolerance such as flatness, circularity, or perpendicularity. Datums establish the reference frame for measurements and include primary, secondary, and tertiary datums indicated on drawings.
Basic Geometrical Dimensioning & Tolerancing Tranning
A basic 2 day training on understanding of GDnT,Geometrical Dimensioning & Tolerancing to Technical & Egineering Group as a common language in understanding Drawings.
Trainer & Speaker
Timothy Wooi,
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Transposition an application of changing the lens power from one to another.
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Transposition is very important for optometrist who deals with retinoscopy and dispensing with this power point presentation you can easily transpose the lens power.
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Transposition
Transposition involves rewriting lens prescriptions while maintaining the same optical power. There are two types: simple transposition and toric transposition. Simple transposition follows three steps - adding the sphere and cylinder powers, changing the cylinder sign, and rotating the cylinder axis by 90 degrees. Toric transposition first uses simple transposition, then separates the prescription into a spherical power and cylindrical base curve with an additional cylinder at 90 degrees to the base curve. The crossed cylinder form combines two cylinders at perpendicular axes into an abbreviated format to describe total optical power.
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Transposition
Hy friends thank you all of you for your love. please see my slideshare. I have made simple and easy to understand for all students. and aslo i have been present same slide on my youtube channel "optometrist Nepal" so if you have any difficult to understand visit in my channel.
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https://itscnc.com/fadal-manuals
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Fadal Rotary Axes - User Manual | ITSCNC.COM
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Fadal Parts Manual
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Fadal rotary axes user manual
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Deflection of curved beam |Strength of Material Laboratory
SAIF ALDIN ALI MADIN
سيف الدين علي ماضي
S96aif@gmail.com
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Shop math trig
- 1. Shop Math Right Triangle Applications For CNC Programming 12/11/2014 By Richard Wade
- 2. 12/11/2014 You will need a calculator similar to this…
- 3. unless you would rather work out the trigonometric functions on a circle. This is how they were constructed before calculators. 12/11/2014
- 4. Remember two things about Right Triangles: = 90 ̊ The angles of all three corners for any triangle will add up to 180 ̊ One of the corners must be exactly 90 degrees. 12/11/2014
- 5. If one of the corners is exactly 90 degrees… The other two corners must add up to exactly 90 degrees! 12/11/2014 22° 68° 90° - 22° = 68°
- 6. Three Basic Trigonometry Functions: 12/11/2014 Sine Cosine Tangent
- 7. The two most common applications of Right Triangle Trigonometry in CNC Machining: 12/11/2014 1. Bolt Circle calculations. 2. Turning chamfers and/or angles.
- 8. A Bolt Circle is a method for defining hole position using a theoretical circle that passes through the center of a series of holes. 12/11/2014
- 9. 12/11/2014 4 HOLES EQ SPCD ON A Ø3.25 B.C. 20° Typical Information Given
- 10. 12/11/2014 One can almost imagine an arrow notched in the bow.
- 11. 12/11/2014 4 HOLES EQ SPCD ON A Ø3.25 B.C. 20° You can easily find the hypotenuse from the data given… (the bolt circle dimension is a diameter, so divide it in half to get the radius, which is also the hypotenuse of the triangle)
- 12. but the machine’s control uses X and Y coordinates. 12/11/2014
- 13. 3.25 ÷ 2 = 1.625 12/11/2014 20° 70° 90° – 20° = 70° What can be deduced from the information given on the part print.
- 14. 12/11/2014 20° 70° When going around the Corner, use Cosine! 0.5558 1.625 x 70 COS = 0.55578
- 15. When going around the Corner, use Cosine! 12/11/2014 20° 70° 0.5558 1.5270 1.625 x 20 COS = 1.5270
- 16. X=-1.5270 Y= 0.5558 12/11/2014 X= 0.5558 Y= 1.5270 X= 1.5270 Y=-0.5558 X=-0.5558 Y=-1.5270
- 17. 12/11/2014 Practice If the hypotenuse of a right triangle is 6.375, and one corner is shown to have a 32° angle, what is the other angle? What are the lengths of the two other sides? When you have your answer, press the Enter key.
- 18. 12/11/2014 Practice If the hypotenuse of a right triangle is 6.375, and one corner is shown to have a 32° angle, what is the other angle? 58° What are the lengths of the two other sides? 5.4063 and 3.3782
- 19. 12/11/2014
- 20. 12/11/2014 15° .270 ? The Tangent function is used to solve for an unknown side when there is a known side and a known non-ninety degree angle.
- 21. 1.250 12/11/2014 Typical Information Given 0.250 3.125 15° (side view of a round part)
- 22. Endpoint X = 1.250 Z = -0.250 12/11/2014 0.250 15° 1.250 Start-point X = ? Z = 0.00?
- 23. Endpoint X = 1.250 Z = -0.250 12/11/2014 0.250 15° 1.250 Start-point X = ? Z = 0.020 0.250 + 0.020 = 0.270
- 24. 12/11/2014 15° .270 0.0724 When crossing the triangle, cross a “T” with Tangent! 0.270 x 15 TAN = 0.07235
- 25. 12/11/2014 0.0724 x 2 = 0.1448 Double the Result… And Subtract from the X axis Endpoint. 1.250 – (0.0724 x 2) = 1.1052
- 26. Endpoint X = 1.250 Z = -0.250 12/11/2014 0.250 15° 1.250 Start-point X = 1.1052 Z = 0.020 1. Find and Solve the Triangle 2. Double X-axis Result 3. Subtract Dia. From X-Endpoint 4. Plug Data into Program
- 27. 12/11/2014 17° 7.750 ? Practice What is the length of the unknown side? When you have your answer, press the Enter key.
- 28. 12/11/2014 17° 7.750 ? Practice What is the length of the unknown side? 2.3694
- 29. 12/11/2014 Review When using the Hypotenuse (longest side of a triangle) and the angle on the corner you’re going around, use the Cosine function. When using a known side and an adjacent angle to get the opposite side (so you have to cross the triangle), use the Tangent function.
- 30. 12/11/2014