## Problem 2.7 Loci of Points – A four bar chain mechanism has a fixed link O_{1}O_{2} 130 mm long. The O_{1}A 30 mm long is a driving crank revolving in clockwise manner. The driven crank O_{2}B 60 mm long is oscillating about the center O_{2}. The link AB 110 mm long is attached with the driving and driven crank. Draw the locus of the point P which is midpoint of the link AB.

**Procedure:**

**Procedure:**

* Step-1* First draw a horizontal center line of sufficient length.

* Step-2* Mark a point named O

_{1 }on the horizontal center line & O

_{2}at the distance 130 mm from O

_{1.}

* Step-3* Draw two circles with center points O

_{1 }& O

_{2 }with radii equal to the length of the crank O

_{1}A & O

_{2}B, which is 30 mm & 60 mm respectively.

* Step-4* Divide the circle O

_{1}A into 8 equal divisions and give the notations as A

_{1, }A

_{2}, A

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

* Step-5* With A

_{1, }A

_{2}, A

_{3 }etc. as centers and radius equal to the length of the connecting rod AB, which is 110 mm, cut the circle O

_{2}B in such a way that the cuts should be on the side which is above the horizontal center line.

* Step-6* 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-7* 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 connecting rod AB.

* Step-8* Give the dimensions by any one method of dimensions and give the name of the components by leader lines wherever necessary.