## Problem 2.8 Loci of Points – In a four bar chain mechanism O_{1}O_{2} is a fixed link. O_{1}A 70 mm long is a driving crank, and the O_{2}B 80 mm long is a driven crank and both the cranks are oscillating. The ends of both these links are connected with a link AB 60 mm long. And the initial position of the links are given in the figure below. Find the locus of the point P which is midpoint of the link AB.

**Procedure:**

**Procedure:**

* Step-1* First draw a horizontal line of length equal to the length of driving crank O

_{1}A, which is 70 mm. Then draw a line AB at the angle 110° with the line O

_{1}A of the length 60 mm as shown in the figure. And then draw a horizontal line BO

_{2 }of the length equal to 80 mm as shown in the figure above.

* Step-2* With the point O

_{1}as center and radius equal to 60 mm draw a part of circle, like in the same way draw another part of a circle with the center O

_{2}and radius equal to 80 mm.

* Step-3* Now with center O

_{1}and radius equal to the length of the links O

_{1}A & AB which is 70mm + 60mm = 130mm, cut the part of the opposite circle; of the radius O2B; on two sides upper and lower as shown in the figure.

* Step-4* Like in the way you used previously, with center O

_{2 }and radius equal to the length of the links O

_{2}B & AB which is 80 mm + 60 mm = 140 mm, cut the part of the opposite circle; of the radius O1A; on two sides upper and lower as shown in the figure.

* Step-5* Divide the part of the circle O

_{1}A intoany random number of divisions and give the notations as A

_{1, }A

_{2}, A

_{3}etc. to the circle as shown into the figure.

* Step-6* With A

_{1, }A

_{2}, A

_{3 }etc. as centers and radius equal to length of the link AB, which is 60 mm, cut the part of the circle O

_{2}B in such a way that the cuts should be between the two extreme cuts previously done and when the link AB oscillates in downward or upward manner, the cuts should follow the motion accordingly.

* Step-7* Then connect the points A

_{1}B

_{1}, A

_{2}B

_{2}, A

_{3}B

_{3 }etc. with straight lines. And fins its mid points & give the notations P

_{1}, P

_{2}, P

_{3}etc. as shown into the figure.

* Step-8* Now draw a medium dark smooth free hand curve passing through the points P

_{1}, P

_{2}, P

_{3}etc. in sequence, which is the locus of the mid-point of link AB.

* Step-9* Give the dimensions by any one method of dimensions and give the name of the components by leader lines wherever necessary.