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4.6 cycloidal motion
This document provides a 22 step graphical method for drawing a cycloidal cam profile. It involves dividing the cam angle into sections for the outstroke, dwell after outstroke, return stroke, and dwell after return stroke. Circles are drawn using the stroke length to determine the radius, and divided into equal parts. Parallel lines are drawn to connect the circle divisions to angular divisions on the cam base circle, and curves are drawn through the connected points to generate the cycloidal cam profile for the outstroke and return stroke sections.
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4.6 cycloidal motion
- 1. Sanjivani Rural EducationSociety’s Sanjivani College of Engineering, Kopargaon-423603 ( An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune) NAAC ‘A’ Grade Accredited, ISO 9001:2015 Certified Subject :- Theory of Machines II T.E. Mechanical (302043) Unit 4 Cam and Follower 4.6 Cycloidal Motion -Graphical Method By Prof. K. N. Wakchaure(Asst Professor) Department of Mechanical Engineering Sanjivani College of Engineering (An Autonomous Institute) Kopargaon, Maharashtra Email: wakchaurekiranmech@Sanjivani.org.in Mobile:- +91-7588025393
- 2. NOMENCLATUR E S= Strokelength 𝝎 = 𝑨𝒏𝒈𝒖𝒍𝒂𝒓 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒐𝒇 𝑪𝒂𝒎 𝜭 = 𝑪𝒂𝒎 𝒂𝒏𝒈𝒍𝒆 𝜭 𝑶 = 𝑶𝒖𝒕𝒔𝒕𝒓𝒐𝒌𝒆 𝒂𝒏𝒈𝒍𝒆 𝜭 𝑫𝑶 = 𝑫𝒘𝒆𝒍𝒍 𝒂𝒇𝒕𝒆𝒓 𝑶𝒖𝒕𝒔𝒕𝒓𝒐𝒌𝒆 𝒂𝒏𝒈𝒍𝒆 𝜭 𝑹 = 𝑹𝒆𝒕𝒖𝒓𝒏𝒔 𝑺𝒕𝒓𝒐𝒌𝒆 𝒂𝒏𝒈𝒍𝒆 𝜭 𝑫𝑹 = 𝑫𝒘𝒆𝒍𝒍 𝒂𝒇𝒕𝒆𝒓 𝑹𝒆𝒕𝒖𝒓𝒏 𝒔𝒕𝒓𝒐𝒌𝒆 𝒂𝒏𝒈𝒍𝒆
- 3. Cycloidal Motion-Graphical Method STEP1. Draw horizontal line of 180mm Which denotes cam angle of 360˚ O
- 4. STEP 2. Drawvertical line length= stroke length Cycloidal Motion-Graphical Method
- 5. S STEP 2. Drawvertical line length= stroke length Vertical line denotes Displacement of Follower Cycloidal Motion-Graphical Method
- 6. S STEP 2. Drawvertical line length= stroke length Cam Angle 𝛳 Cycloidal Motion-Graphical Method
- 7. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 3. Divide Horizontal line into 4 parts Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 8. 𝛳 𝑅=90˚ 𝛳𝐷𝑅=120˚𝛳 𝐷𝑜=30˚𝛳𝑜=120˚ S STEP 3. Divide Horizontal line into 4 parts Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 9. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 3. Divide Horizontal line into 4 parts Take 𝜭 𝒐=60mm, 𝜭 𝑫𝒐=20mm, 𝜭 𝒐=60mm, 𝜭 𝒐=40mm, Cycloidal Motion-Graphical Method
- 10. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 4. Divide 𝜭 𝒐 and 𝜭 𝑹 𝒊𝒏𝒕𝒐 𝟔 𝒆𝒒𝒖𝒂𝒍 𝒑𝒂𝒓𝒕𝒔 1part= 10mm Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 11. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 5. Give the numbers to the divided parts start from 0 and will end at 14. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 12. STEP 6. Drawvertical lines through divided parts Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 Cycloidal Motion-Graphical Method
- 13. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 7. Take a midpoint of Stroke length (Shown) Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 14. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 8. Draw one diagonal line Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 15. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 9. Consider any point on Diagonal line and draw on circle whos radius will be r= 𝑠 2𝞹 Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 16. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 Cycloidal Motion-Graphical Method
- 17. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 10. Divide this circle with 6 equal part, dive circle by taking angle from horizontal line. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 18. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 11. Draw vertical line through the center of the circle. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 19. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 12. Join the circle division points by horizontal lines. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 20. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 13. Give numbering to the division points. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 21. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 14. Mark the points where horizontal line intersects the vertical line. And draw the line parallel to diagonal line. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 22. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 15. Parallel line intersects vertical divisions of outstroke angle 1 at a and 2 at b. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 23. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 16. In the same way you to draw the parallel line and mark the points. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 24. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 17. Draw the curve through the points a-b-c-d-e-f Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 25. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 18. Draw the diagonal line for return stroke angle. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 26. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 19. Again draw the circle with radius r= 𝑠 2𝞹 and divide it in to 6 equal parts. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 27. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 19. Draw horizontal lines through the circle division points. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 28. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 21. Give the numbers to the division points and draw parallel line to diagonal line which intersects outstroke angle division points.. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 29. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 STEP 22. Draw a curve through the points g-h-i-j-k-l-m.. Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm, Cycloidal Motion-Graphical Method
- 30. 𝛳 𝑅 𝛳𝐷𝑅𝛳 𝐷𝑜𝛳𝑜 S Cam Angle 𝛳 Final cycloidal curve. Cycloidal Motion-Graphical Method
- 31. Thank You…. 31Subject :-Theory of Machines II