Locus - Problems on Fork & Slider, Oscillating Link, and Rotating Link

Problems on Fork & Slider, Oscillating Link, and Rotating Link

Fork & Slider

 6 ] Two points A and B are 100 mm apart. There is a point P, moving in a plane such that the difference of its distances from A and B always remains constant and equals to 40 mm. Draw locus of point P.  

Solution Steps:

1. Mark the lowermost position of M on the extension of AB by taking distance MN ( 40 mm ) from point B ( because N can not go beyond B ).


2.  Divide line ( M initial and M lowermost ) into eight to ten parts and mark them M₁, M₂, M₃, up to the last position of M.


3. Now take MN ( 40 mm ) as fixed distance in compass, M₁ center cut line CB in N₁.


4. Mark point P₁ on M₁N₁ with the same distance of MP from M_1.


5. Similarly locate M₂P_2, M₃P₃, M₄P₄, and join all P points.


6. It will be the locus of P.

Oscillating Link

7 ] A line OA, 80 mm long oscillates around O, 60º to the right side, and returns to its initial vertical position with uniform velocity. Meanwhile point P initially on O starts sliding downwards and reaches end A with uniform velocity. Draw locus of point P.

Solution Steps:

1. Point p - Reaches End A ( Downwards)


2. Divide OA  in Eight equal parts from O to A after O names 1, 2, 3, 4 up to 8. ( i.e. up to point A ).


3. Divide 60 angle into four parts ( 15 each ) and mark each point by A1, A2, A3, A4, and for return A5, A6, A7, and A8 ( initial point ).


4. Take center O, distance in compass O1 draw an arc up to OA1. Name this point as P1.


5. Similarly O center O2  distance mark P2 on the line OA2.


6. This way locate P3, P4, P4, P5 up to P8, and join them. ( it will be described locus of P )

 8 ]  A line OA, 80 mm long oscillates around O, 60º to right side, 120º to left and returns to its initial vertical position with uniform velocity. Meanwhile point P initially on O start sliding downwards, reaches end A, and returns to O again with uniform velocity. Draw locus of point P.

Solution Steps:

( Preaches A i.e moving downwards & return to O again I.e moves upwards)

1. Here distance traveled by point  P is PA. plus AP. Hence divide it into eight equal parts. ( So total linear displacement gets divided in 16 parts) Name those as shown.


2. Link OA goes 60º to right, comes back to original ( vertical ) position, goes 60º to left and returns to an original vertical position. Hence total angular displacement is 240º.  Divide this also in 16 parts. ( 15º each ) Name as per the previous problem. ( A, A1, A2 etc )


3. Take center O, distance in compass O1 draw an arc up to OA1. Name this point as P1.


4. Similarly O center O2  distance mark P2 on the line OA2.


5. This way locate P3, P4, P4, P5 up to P16, and join them. ( it will be described locus of P )

 Rotating Link

9 ] Rod AB, 100 mm long, revolves in a clockwise direction for one revolution. Meanwhile point P, initially on A starts moving towards B and reaches B. Draw locus of point P.

Solution Steps:

1. AB rod revolves around center O for revolution and point P slides along AB rod and reaches and B in one revolution.


2. Divide circle in 8 number of equal parts and name in arrow direction after A-A1, A2, A3, up to A8.


3. Distance traveled by point P is AB mm. Divide this also into 8 equal parts.


4. Initially P is on end A. When A moves to A1. point P goes one linear division ( part ) away from A1 and name the point P1.


5. When A moves to A2, P will be two parts away from A2 ( Name it P2 ). Mark it as above from A2.


6. From A3 mark P3 three parts aways from P3.


7. Similarly locate P4, P5, P6, P7, and P8 which will be eight parts away from A8. ( Means P has reached B ).


8. Join all p points by a smooth curve. it will be the locus of P.

10 ] Rod AB, 100 mm long, revolves in the clockwise direction for one revolution. Meanwhile point P, initially on A starts moving towards B, reaches B, and returns to A in one revolution of the rod. Draw locus of point P.

Solution Steps:

1. AB rod revolves around center O for one revolution and point P slides along rod AB reaches end B and returns to A.


2. Divide the circle in 8 number of equal parts and name in arrow direction after A-A1, A2, A3 up to A8.


3. Distance traveled by point P is AB plus AB mm. Divide AB in 4 parts so those will be 8 equal parts on return.


4. Initially P is on end A. When A moves to A1, point P goes one linear division ( part ) away from A1. Mark it from A1 and name the point P1.


5. When A moves to A2, P will be two parts aways from A2 ( Name it P2 ). Mark it as above from A2.


6. From A3 mark P3 three parts away from P3.


7. Similarly locate P4, P5, P6, P7, and P8 which will be eight parts away from A8. ( Means P has reached B ).


8. Join all P points by a smooth curve. It will be the locus of P.

The locus will follow the loop path two times in one revolution.

Please write comments if you find anything incorrect and if you have any queries about this topic or you want to share more information about the topic discussed above.