# Problem 2.11 Loci of Points

Problem 2.11a Loci of Points – A circular disc of 72 mm diameter rotates about its center in the clockwise direction. While the disc completes one revolution, an insect walks across the diameter of the disc. Plot the locus of insect, assuming both the rotation of disc and movement of insect as uniform.

OR

Problem 2.11b Loci of Points – A link AB of 72 mm length rotates about its center in the clockwise direction while the link completes one revolution the insect walks across the link from one end to another. Plot the locus of insect assuming rotation of link and movement of insect as uniform.

## Procedure 2.11a:

Step-1 Draw a circle of diameter 72 mm with a center O which will be circular disc given in the data.

Step-2 As per given in data we have to assume that movement of insect and rotation of disc as uniform, so if we give one step rotation to disc than we have to give one step movement to insect. So to show this all movements we have to divide circle or circular disc into twelve equal parts (as a standard, you can divide in 24 parts or whatever number you like). If you have divided circle in 12 equal parts then it means total movements of disc and insect will be 12. So it is required to make 12 equal parts of insect’s path (which is diameter of disc) too. And give the notations A0-B0, A1-B1, A2-B2 etc., as shown into the figure.

Note:-You can give notations only in clockwise direction as disc rotates clockwise.

Step-3 With O as center and radius equal to O0, O1, O2, O3, O4, O5 on the horizontal axis draw circles that gives intersection points of horizontal center line of disc and circles. Like in the same way draw all arcs. And give the notations as P0, P1, P2 etc. as shown in the figure.

Step-4 Draw a smooth medium dark free hand curve passing through the points P0, P1, P2…P12 etc. as shown in the figure. This is the required answer or locus of insect moving uniformly with rotation of disc.

## Procedure 2.11b:

Step-1 Draw a circle of diameter 72 mm with a center O which will be link’s end points locus given in the data.

Step-2 As per given in data we have to assume that movement of insect and rotation of link as uniform, so if we give one step rotation to link than we have to give one step movement to insect. So to show this all movements we have to divide circle or link’s end points locus into twelve equal parts (as a standard, you can divide in 24 parts or whatever number you like). If you have divided circle in 12 equal parts then it means total movements of link and insect will be 12. So it is required to make 12 equal parts of insect’s path (which is length of link) too. And give the notations A0-B0, A1-B1, A2-B2 etc., as shown into the figure.

Note:-You can give notations only in clockwise direction as link rotates clockwise.

Step-3 With O as center and radius equal to O0, O1, O2, O3, O4, O5 on the horizontal axis draw circles that gives intersection points of horizontal center line of link and circles. Like in the same way draw all arcs. And give the notations as P0, P1, P2 etc. as shown in the figure.

Step-4 Draw a smooth medium dark free hand curve passing through the points P0, P1, P2…P12 etc. as shown in the figure. This is the required answer or locus of insect moving uniformly with rotation of link.

Step-5 Give the dimensions by any one method of dimensions and give the name of the components by leader lines wherever necessary.