## Problem 2.2 Loci of Points – O_{1}ABO_{2} is a Four Bar Chain with the link O_{1}O_{2} as the fixed link. Driving crank O_{1}A is 30 mm long. Driven crank O_{2}B is also 30 mm long. Connecting link AB is 80 mm long. Distance between O_{1} and O_{2} is 80 mm. Two cranks are revolving in opposite direction. Draw the loci of points M and N for one complete revolution of the driving crank. The point M is the mid-point of the connecting link AB and the point N is 30 mm from B on AB extended.

*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 80 mm from O

_{1.}

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

_{1 }& O

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

_{1}A & O

_{2}B, which is 30 mm.

* Step-4* Divide the circle O1 into 12 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 connecting rod AB, which is 80 mm, cut the circle O

_{2 }in such a way that if center point of the arc is above the center line than the cut should be below the center line and vice versa as shown into the figure. And give the notations B

_{1}, B

_{2}, B

_{3}etc. as per the figure.

* 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 M

_{1}, M

_{2}, M

_{3}etc. as shown into the figure. These are the mid points of the connecting rod AB.

* Step-7* Now draw a medium dark smooth curve passing from the points M

_{1}, M

_{2}, M

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

* Step-8* To get the locus of the point N, extends the lines A

_{1}B

_{1}, A

_{2}B

_{2}, A

_{3}B

_{3 }etc. in the direction from A to B as shown into the figure & give the notations as N

_{1}, N

_{2}, N

_{3 }etc. respectively.

* Step-9* Connects the points N

_{1}, N

_{2}, N

_{3 }etc. into sequence by a medium dark smooth curve, which is the locus of the point N.

* Step-10* Give the dimensions by any one method of dimensions and give the name of the components by leader lines wherever necessary.