4.6 cycloidal motion
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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 Education Societyβs Sanjivani College of Engineering, Kopargaon-423603 ( An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune) NAAC βAβ 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 ο· S= Stroke length ο· π = π¨ππππππ ππππππππ ππ πͺππ ο· π = πͺππ πππππ ο· π πΆ = πΆππππππππ πππππ ο· π π«πΆ = π«ππππ πππππ πΆππππππππ πππππ ο· π πΉ = πΉππππππ πΊπππππ πππππ ο· π π«πΉ = π«ππππ πππππ πΉπππππ ππππππ πππππ
- 3. Cycloidal Motion-Graphical Method STEP 1. Draw horizontal line of 180mm Which denotes cam angle of 360Λ O
- 4. STEP 2. Draw vertical line length= stroke length Cycloidal Motion-Graphical Method
- 5. S STEP 2. Draw vertical line length= stroke length Vertical line denotes Displacement of Follower Cycloidal Motion-Graphical Method
- 6. S STEP 2. Draw vertical line length= stroke length Cam Angle π³ Cycloidal Motion-Graphical Method
- 7. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 3. Divide Horizontal line into 4 parts Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 8. π³ π =90Λ π³ π·π =120Λπ³ π·π=30Λπ³π=120Λ S STEP 3. Divide Horizontal line into 4 parts Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 9. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 3. Divide Horizontal line into 4 parts Take π π=60mm, π π«π=20mm, π π=60mm, π π=40mm, Cycloidal Motion-Graphical Method
- 10. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 4. Divide π π and π πΉ ππππ π πππππ πππππ 1part= 10mm Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 11. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 5. Give the numbers to the divided parts start from 0 and will end at 14. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 12. STEP 6. Draw vertical lines through divided parts Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ Cycloidal Motion-Graphical Method
- 13. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 7. Take a midpoint of Stroke length (Shown) Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 14. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 8. Draw one diagonal line Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 15. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 9. Consider any point on Diagonal line and draw on circle whos radius will be r= π 2πΉ Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 16. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ Cycloidal Motion-Graphical Method
- 17. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 10. Divide this circle with 6 equal part, dive circle by taking angle from horizontal line. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 18. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 11. Draw vertical line through the center of the circle. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 19. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 12. Join the circle division points by horizontal lines. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 20. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 13. Give numbering to the division points. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 21. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 14. Mark the points where horizontal line intersects the vertical line. And draw the line parallel to diagonal line. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 22. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 15. Parallel line intersects vertical divisions of outstroke angle 1 at a and 2 at b. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 23. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 16. In the same way you to draw the parallel line and mark the points. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 24. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 17. Draw the curve through the points a-b-c-d-e-f Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 25. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 18. Draw the diagonal line for return stroke angle. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 26. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 19. Again draw the circle with radius r= π 2πΉ and divide it in to 6 equal parts. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 27. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 19. Draw horizontal lines through the circle division points. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 28. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 21. Give the numbers to the division points and draw parallel line to diagonal line which intersects outstroke angle division points.. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 29. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ STEP 22. Draw a curve through the points g-h-i-j-k-l-m.. Take π³π=60mm, π³ π·π=20mm, π³π=60mm, π³π=40mm, Cycloidal Motion-Graphical Method
- 30. π³ π π³ π·π π³ π·ππ³π S Cam Angle π³ Final cycloidal curve. Cycloidal Motion-Graphical Method
- 31. Thank Youβ¦. 31Subject :- Theory of Machines II