Spiral | Problems on Spiral

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Spiral: 


Important approach for construction spiral...


Find total angular and total linear displacement and divide both into the same number of equal parts.here some problems on spiral to draw one and two convolution spirals.


1 ] Draw a spiral of one convolution. Take a radius as 40 mm.

Solution Steps

  1. With a 40 mm radius draw a circle and divide it into 8 parts. Name those 1, 2, 3, up to 8.

  2. Similarly divided line OP also in 8 parts and name those 1, 2, 3 up to 8.( because here it is one convolution we divide OP in same  parts as we divide a circle, here it is 8 so we divide OP into 8 parts, if you divide the circle into 12 parts then for one convolution we divide radius(OP) of the circle into 12 parts)

  3. Take O1 distance from the OP line and draw an arc up to the O1 radius vector. Name the Point P1.

  4. Similarly mark points P2, P3, P4 up to P8. And join those in a smooth curve.

  5. It is a SPIRAL of one convolution.


one convolution spiral

2 ] Point P is 80 mm from point O. It starts moving towards O and reaches it in two revolutions around it.  Draw revolutions around it and Draw locus of point P ( To draw a spiral of TWO convolutions ).

  • Total angular displacement here is two revolutions And total displacement here is distance OP.

  • Just divide the circle into 8 parts. means total angular displacement in 16 parts for two revolutions.

  • Divide OP also in 16 parts ( 8×2 for two revolutions).


Solution Steps

  1. With an 80 mm radius draw a circle and divide it into 8 parts. Name those 1, 2, 3, up to 8.

  2. Similarly divided line OP also in 16 parts and name those 1, 2, 3 up to 8.( because here it is two convolutions we divide OP in twice of parts as we divide a circle, here it is 8 so we divide OP into 16 parts, if you divide the circle into 12 parts then for two convolutions we divide radius(OP) of the circle into 24 parts.)

  3. Take O1 distance from the OP line and draw an arc up to the O1 radius vector. Name the Point P1.

  4. Similarly mark points P2, P3, P4 up to P16. And join those in a smooth curve.

  5. It is a SPIRAL of two convolutions.


spiral of two convolutions
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