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Pro/ENGINEER Wildfire 3.0 Tips and Tricks - Involute Gears

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Tham khảo tài liệu 'pro/engineer wildfire 3.0 tips and tricks - involute gears', công nghệ thông tin, đồ họa - thiết kế - flash phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Pro ENGINEER Wildfire 3.0 Tips and Tricks Involute Gears Involute Gears Introduction This lesson covers the development of involute gears. An involute gear is based on an involute curve which is a mathematical shape. To understand what an involute is consider a simple cylinder and a string as shown below. Wrap the string around the cylinder. While maintaining tension on the string trace the path that the end of the string makes while un-wrapping it around the cylinder. This path is an involute curve. A simple cylinder and a string. Pull Pull the string tight and keep it tangent to the cylinder. Wrap the string around the cylinder. Trace the end of the string while un-wrapping it around the cylinder. The resulting trajectory is an involute curve. There are two key parameters that control the involute curve the diameter of the cylinder and the angle that the string is un-wrapped around the cylinder. In the example above the string is unwrapped 90 around the cylinder. Copyright 2008 CADquest Inc. Page 1 Involute Gears Pro ENGINEER Wildfire 3.0 Tips and Tricks The Involute Curve Development of the mathematical equations for the involute curve uses simple trigonometry. We will develop the equations for 90 of one full involute. In other words we are un-wrapping the string 90 around the cylinder in a counterclockwise direction. The circumference of a circle is defined by c 2 n r One quarter 90 of the circumference of a circle is then c n r 2 In the figure below the line s is the same length as the part of the circumference the string has been un-wrapped s . Using trigonometry we find that xc r cos 9 yc r sin 9 x xc s sin 9 y yc - s cos 9 Page 2 Copyright 2008 CADquest Inc. Pro ENGINEER Wildfire 3.0 Tips and Tricks Involute Gears Datum Curves From Equation In Pro ENGINEER datum curves can be defined using mathematical equations. When using this feature a system variable t is used that varies from 0 to 1 over the length of the curve. For the involute curve let the angle ang