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4.9 polynomial cam
- 1. Sanjivani Rural Education Society’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 4.9 Advanced Cam -3-4-5 Polynomial Cam 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. • 𝑥 = 𝐶0+ 𝐶1 𝜃 𝛽 + 𝐶2 𝜃 𝛽 2 + 𝐶3 𝜃 𝛽 3 + 𝐶4 𝜃 𝛽 4 + 𝐶5 𝜃 𝛽 5 • Boundry conditions • 𝜃 = 0, 𝑡ℎ𝑒𝑛 𝑥 = 0, 𝑣 = 0, 𝑎 = 0 • 𝜃 = 𝛽, 𝑡ℎ𝑒𝑛 𝑥 = ℎ, 𝑣 = 0, 𝑎 = 0 • 𝑣 = 1 𝛽 𝐶1 + 2 ∗ 𝐶2 𝜃 𝛽 + 3 ∗ 𝐶3 𝜃 𝛽 2 + 4 ∗ 𝐶4 𝜃 𝛽 3 + 5 ∗ 𝐶5 𝜃 𝛽 4 • 𝑎 = 1 𝛽2 2 ∗ 𝐶2 + 6 ∗ 𝐶3 ∗ 𝜃 𝛽 + 12 ∗ 𝐶4 ∗ 𝜃 𝛽 2 + 20 ∗ 𝐶5 ∗ 𝜃 𝛽 3 Advanced Cam -3-4-5 Polynomial Cam
- 3. • 𝑥 = 𝐶0+ 𝐶1 𝜃 𝛽 + 𝐶2 𝜃 𝛽 2 + 𝐶3 𝜃 𝛽 3 + 𝐶4 𝜃 𝛽 4 + 𝐶5 𝜃 𝛽 5 • 𝜃 = 0, 𝑡ℎ𝑒𝑛 𝑥 = 0, • 0 = 𝐶0 1 • 𝜃 = 𝛽, 𝑡ℎ𝑒𝑛 𝑥 = ℎ • 𝑥 = 𝐶0+ 𝐶1 + 𝐶2 + 𝐶3 + 𝐶4 + 𝐶5 • ℎ = 𝐶1 + 𝐶2 + 𝐶3 + 𝐶4 + 𝐶5 2 Advanced Cam -3-4-5 Polynomial Cam
- 4. • 𝜃 = 0, 𝑡ℎ𝑒𝑛 𝑣 = 0, • 𝑣 = 1 𝛽 𝐶1 + 2 ∗ 𝐶2 𝜃 𝛽 + 3 ∗ 𝐶3 𝜃 𝛽 2 + 4 ∗ 𝐶4 𝜃 𝛽 3 + 5 ∗ 𝐶5 𝜃 𝛽 4 • 𝐶1 = 0 3 • 𝜃 = 𝛽, 𝑡ℎ𝑒𝑛 𝑣 = 0, • 𝑣 = 1 𝛽 𝐶1 + 2 ∗ 𝐶2 𝜃 𝛽 + 3 ∗ 𝐶3 𝜃 𝛽 2 + 4 ∗ 𝐶4 𝜃 𝛽 3 + 5 ∗ 𝐶5 𝜃 𝛽 4 • 0 = 𝐶1 + 2 ∗ 𝐶2 + 3 ∗ 𝐶3 + 4 ∗ 𝐶4 + 5 ∗ 𝐶5 • 0 = 2 ∗ 𝐶2 + 3 ∗ 𝐶3 + 4 ∗ 𝐶4 + 5 ∗ 𝐶5 4 Advanced Cam -3-4-5 Polynomial Cam
- 5. • 𝑎 = 1 𝛽2 2 ∗ 𝐶2 + 6 ∗ 𝐶3 ∗ 𝜃 𝛽 + 12 ∗ 𝐶4 ∗ 𝜃 𝛽 2 + 20 ∗ 𝐶5 ∗ 𝜃 𝛽 3 • 𝜃 = 0, 𝑡ℎ𝑒𝑛 𝑎 = 0, • 0 = 𝐶2 5 • 𝜃 = 𝛽, 𝑡ℎ𝑒𝑛 𝑎 = 0, • 0 = 2 ∗ 𝐶2 + 6 ∗ 𝐶3 + 12 ∗ 𝐶4 + 20 ∗ 𝐶5 • 0 = 6 ∗ 𝐶3 + 12 ∗ 𝐶4 + 20 ∗ 𝐶5 6 Advanced Cam -3-4-5 Polynomial Cam
- 6. ℎ = 𝐶3 + 𝐶4 + 𝐶5 2 0 = 3 ∗ 𝐶3 + 4 ∗ 𝐶4 + 5 ∗ 𝐶5 4 0 = 6 ∗ 𝐶3 + 12 ∗ 𝐶4 + 20 ∗ 𝐶5 6 By Solving Above Simultaneous equations • 𝐶3 = 10ℎ, • 𝐶4 = −15ℎ, • 𝐶5 = 6ℎ • 𝑥 = 10. ℎ 𝜃 𝛽 3 − 15. ℎ. 𝜃 𝛽 4 + 6ℎ 𝜃 𝛽 5 • 𝑥 = ℎ 10 𝜃 𝛽 3 − 15. 𝜃 𝛽 4 + 6 𝜃 𝛽 5 • 𝑣 = ℎ 30 𝜃 𝛽 2 − 60. 𝜃 𝛽 3 + 30 𝜃 𝛽 4 • 𝑎 = ℎ 60 𝜃 𝛽 1 − 180. 𝜃 𝛽 2 + 120 𝜃 𝛽 3 Advanced Cam -3-4-5 Polynomial Cam
- 7. Advanced Cam -3-4-5 Polynomial Cam
- 8. 8Subject :- Theory of Machines II