## Problem 2.9 Loci of Points – In a top view of a folding door mechanism, two rods PQ 110 mm long and QR 70 mm long are welded at the point Q. The angle PQR is 80°. The rod PQ is constrained to slide in a vertical and horizontal guide respectively as shown in the figure given below. For the motion of the rod AB vertically and horizontally, draw the locus of the point R and the point T; which is midpoint of the rod AB.

**Procedure:**

**Procedure:**

* Step-1* First draw a horizontal line of length equal to the length of horizontal channel, which is 110 mm long. And draw a vertical perpendicular line of the length 110 mm from the left hand end of the previously drawn horizontal line.

* Step-2* Then divide the horizontal line into 12 equal divisions, and give the notations as P

_{0}, P

_{1}, P

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

* Step-3* Now with the points P

_{0}, P

_{1}, P

_{2}etc. as centers and length equal to 110 mm, cut the vertical line and give the notations as Q

_{0}, Q

_{1}, Q

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

* Step-4* Find out the midpoints of the lines P

_{0}Q

_{0}, P

_{1}Q

_{1}, P

_{2}Q

_{2}etc. as shown in the figure and give the notations T

_{0}, T

_{1}, T

_{2}etc.

* Step-5* Connects these points T

_{0}, T

_{1}, T

_{2}etc. in sequence with a medium dark free hand smooth curve. This is the locus of the midpoint of the link PQ.

* 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 draw lines of the length 70 mm from the end points Q

_{0}, Q

_{1}, Q

_{2}etc. such that these lines should make an angle of 80° with the lines P

_{0}Q

_{0}, P

_{1}Q

_{1}, P

_{2}Q

_{2}etc. respectively as shown in the figure. And give the notations as R

_{0}, R

_{1}, R

_{2}etc.

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

_{0}, R

_{1}, R

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

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