Problem on cycloidal motion - construction of displacement diagram for cycloidal motion

1. Department of Mechanical Engineering
JSS Academy of Technical Education, Bangalore-560060
Kinematics of Machines
(Course Code:18ME44)

2. Kinematics of Machines
Module 4: Numerical problems on Cams
(Cycloidal Motion)

3. Numerical
Q1
Draw the profile of the cam when the roller follower moves with cycloidal motion during out
stroke and return stroke, as given below :
1. Out stroke with maximum displacement of 31.4 mm during 180° of cam rotation,
2. Return stroke for the next 150° of cam rotation,
3. Dwell for the remaining 30° of cam rotation.
The minimum radius of the cam is 15 mm and the roller diameter of the follower is 10 mm.
The axis of the roller follower is offset by 10 mm towards right from the axis of cam shaft.
Scale: 20 = 1cm
Rolling circle radius

4. Steps involved in construction of Displacement diagram for cycloidal motion
Step 1: Construct displacement diagram taking lift (S) = 31.4 mm on vertical axis and angular
displacement of cam on horizontal axis with suitable scale (in this case, scale 20 = 1 cm)
Step 2: Divide the Outstroke and return stroke into equal no. of division (say 6 division in this case)
Step 3: No Dwell exist between outstroke and return stroke in this case.

5. Steps involved in construction of Displacement diagram for cycloidal motion
Step 4: Construct the rolling circle at the left bottom corner of the displacement diagram taking
rolling circle radius = 5 mm
Step 5: Divide the rolling circle into 6 equal parts and label each division as show in fig.

6. Steps involved in construction of Displacement diagram for cycloidal motion
Step 6: From the centre of the rolling circle, draw a line that connects to the top most position of the
displacement diagram (to 6th division) on the outstroke. (As shown in fig.)

7. Steps involved in construction of Displacement diagram for cycloidal motion
Step 7: From the centre of the division 1 and 2, draw a line up to the 2nd division. This line must be
parallel to the previously drawn line (shown in red) (As shown in fig.)

8. Steps involved in construction of Displacement diagram for cycloidal motion
Step 8: From the centre of the division 4 and 5, draw a line up to the 5th division. This line must be
parallel to the previously lines (As shown in fig.)

9. Steps involved in construction of Displacement diagram for cycloidal motion
Step 9: Now, transfer the displacement from each vertical division, say 1, 2, 3, 4, 5 and 6 from
outstroke to the return stroke, by drawing horizontal projectors (thin line) as shown in fig.
Or
* Also, use scale or compass to transfer the corresponding displacement from the outstroke to the
return stroke, instead of horizontal projectors.

10. Steps involved in construction of Displacement diagram for cycloidal motion
Step 10: Now, join the corresponding division i.e. 1-1, 2-2 …etc. ,with a smooth curve as shown in fig.
This is the procedure for constructing the displacement diagram.

11. • The rolling circle can be drawn, either towards left or right bottom corner of the displacement diagram.
• In this case rolling circle is drawn at the mid portion of the displacement diagram, as dwell not exist
between the outstroke and return stroke.

12. 1. In this case rolling circle is drawn at the mid portion of the displacement diagram.
2. Divide the rolling circle into six equal parts and from these points draw horizontal
lines to meet the vertical diameter at a ′ , G and b ′ .
3. Join AG and GN.
4. From point a′ , draw lines parallel to AG and GN to intersect the vertical lines
drawn through 1, 2, 4′ and 5′ at B, C, L and M respectively.
5. Similarly draw parallel lines from b′ intersecting the vertical lines through 4, 5, 1′
and 2′ at E, F, H and J respectively.
Steps involved in construction of Displacement diagram for cycloidal motion

13. Cam profile: offset
1. Draw a base circle with centre O and radius = 15mm.
2. Draw a prime circle with centre O and radius = radius of cam + radius of roller = 15 + 10/2 = 20 mm
3. Draw an offset circle with centre O and radius = 10 mm.
4. Drawn the cam profile in the similar way as discussed in previous problem.
Steps involved in construction of cam

14. Cam profile: offset

15. End of Module