Question

2.11. Locate the cognates of the following mechanisms. (a) 0,08 = 13.0 04A= 6.0 ORB = 9.0 AB = 10.0 AC = 4.5 BC= 8.5

Answer 1

Cognate linkages

Cognate linkages are the three different linkages that generate same coupler curve

Here OAABOB be the original linkage with coupler point C attached to AB.

Drawing instructions

1. First draw the space configuration diagram as shown with suitable scale.

2. Read the angles α, β and γ as shown in the figure

3. To find O1 , Draw line OA O1 making an angle α with OA OB, draw the line OB O1 making an angle β with OA OB. The intersection of these line be the point O1. This is the third fixed point. The line as drawn as chain line.

4. To find the point A1, draw parallel lines OAA1 and CA1 to OAA and AC correspondingly. The intersection is A1

5. To find P1, draw the lines A1P1 and CP1 with the angle α and β from A1C, the intersection is P1

6. To find the point B2, draw parallel lines OBB2 and CB2 to OBB and BC correspondingly, The intersection is B2

7. To find P2, draw the lines CP2 and B2P2 with the angle α and β from CB2, the intersection is P2

8. Connect P1 O1 and P2 O1

9. The lines between the fixed pivot points are chain lines and all other construction lines of cognate linkages are doted lines

The cognate linkages are

                1. OAABOB – original linkage

                2.OAA1P1O1 – cognate linkage

                3. OBB2P2O1 – cognate linkage