## Problem 2.10 Loci of Points – In the figure given below, there is a horizontal channel PS which is fixed. And two rods PQ 80 mm long and QR 80 mm long glide in the channel PS such that the two rods are hinged at the point Q as shown in the figure below. Draw the locus of the midpoint of the rod QR.

**Procedure:**

**Procedure:**

* Step-1* First draw a horizontal line of length equal to the length of the rods PQ & QR; which 80 mm + 80 mm=160 mm.

* Step-2* Then mark a point P on the right hand end of the horizontal line, and from the point P draw a vertical line of the length 80mm. Now with the point P as center and radius equal to 80 mm draw an arc between the previously drawn vertical and horizontal lines.

* Step-3* Now with the point Pas center and radius equal to 80 mm cut the previously drawn arc in to any random number of divisions. And give the notations as Q

_{0}, Q

_{1}, Q

_{2}etc. as shown in the figure.

* Step-4* With the points Q

_{0}, Q

_{1}, Q

_{2}etc. as centers and radius equal to 80 mm, cut the previously drawn horizontal line such that the cuts should be on the outer side of the previously drawn arc, and give the notations as R

_{0}, R

_{1}R

_{2}etc. respectively.

* Step-5* Connects the points Q

_{0}, Q

_{1}, Q

_{2}etc. with the point P with straight lines. And also connect the points Q

_{0}, Q

_{1}, Q

_{2}etc. with the points R

_{0}, R

_{1}R

_{2}etc. respectively with straight lines as shown in the figure.

* Step-6* Mark the mid points of the lines Q

_{0}R

_{0}, Q

_{1}R

_{1}, Q

_{2}R

_{2}etc. and give the notations as N

_{0}, N

_{1}, N

_{2}etc. respectively as shown in the figure.

* Step-7* Now draw a medium dark smooth free hand curve passing through the points N

_{0}, N

_{1}, N

_{2 }etc. in sequence, which is the locus of the point N.

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