This document outlines the graphical method for determining the motion of a follower using a cam with uniform velocity. It involves drawing a horizontal line representing the cam angle, a vertical line for stroke length, and dividing the lines into sections representing the outstroke, dwell after outstroke, return stroke, and dwell after return stroke angles. A semicircle is drawn through the midpoint of the stroke length and divided into equal parts, and horizontal lines are drawn through the division points to create a cam profile representing uniform velocity of the follower over the operating angles of the 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
4.4 Simple Harmonic 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= Stroke length
 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. Uniform Velocity- Graphical Method
STEP 1. Draw horizontal line of 180mm
Which denotes cam angle of 360˚
O

4. Uniform Velocity- Graphical Method
STEP 2. Draw vertical line length= stroke length

5. Uniform Velocity- Graphical Method
S
STEP 2. Draw vertical line length= stroke length
Vertical line denotes Displacement of Follower

6. Uniform Velocity- Graphical Method
S
STEP 2. Draw vertical line length= stroke length
Cam Angle 𝛳

7. Uniform Velocity- Graphical Method
𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳
STEP 3. Divide Horizontal line into 4 parts
Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm,

8. 𝛳 𝑅=90˚ 𝛳 𝐷𝑅=120˚𝛳 𝐷𝑜=30˚𝛳𝑜=120˚
Uniform Velocity- Graphical Method
S
STEP 3. Divide Horizontal line into 4 parts
Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm,

9. Uniform Velocity- Graphical Method
𝛳 𝑅 𝛳 𝐷𝑅𝛳 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,

10. Uniform Velocity- Graphical Method
𝛳 𝑅 𝛳 𝐷𝑅𝛳 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,

11. Uniform Velocity- Graphical Method
𝛳 𝑅 𝛳 𝐷𝑅𝛳 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,

12. Uniform Velocity- Graphical Method
STEP 6. Draw vertical lines through divided parts
Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm,
𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳

13. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳
STEP 7. Take a midpoint of Stroke length (Shown)
Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm,

14. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳
STEP 8 Draw a semicircle through midpoint with radius S/2
Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm,

15. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳
STEP 9. Divide Semicircle in 6 equal parts with angle 30˚
Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm,

16. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳
STEP 10. Divide Semicircle in 6 equal parts with angle 30˚
Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm,

17. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳
STEP 11. Draw horizontal line through the point which divides
circle into 6 equal parts.
Take 𝛳𝑜=60mm, 𝛳 𝐷𝑜=20mm, 𝛳𝑜=60mm, 𝛳𝑜=40mm,

18. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳

19. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳

20. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳

21. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳

22. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳

23. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳

24. 𝛳 𝑅 𝛳 𝐷𝑅𝛳 𝐷𝑜𝛳𝑜
S
Cam Angle 𝛳

25. 25Subject :- Theory of Machines II