Method Of Drawing Tangent & Normal Part II
Tangent & Normal In Involute, Cycloid, And Spiral.
1 ] Involute
Steps
- Draw Involute as usual.
- Mark point Q on it as directed.
- Join Q to the center of circle C. Considering CQ diameter, Draw a semicircle as shown.
- Mark point of intersection of this semicircle and pole circle and join it to Q.
- This will be normal to involute.
- Draw a line at the right angle to this line from Q.
- it will be tangent to involute.
2 ] Cycloid
Steps
- Draw Cycloid as usual.
- Mark point Q on it as directed.
- With CP distance, From Q. Cut the point on the locus of C And join it to Q.
- From this point drop a perpendicular on the ground line and name it N.
- Join N with Q. This will be NORMAL to cycloid.
- Draw a line at the right angle to this line from Q.
- It will be TANGENT to cycloid.
3 ] Spiral
constant of the curve = [katex]\frac{\ Difference\ in\ length\ of\ any\ radius\ vectors}{\ Angle\ between\ the\ corresponding\ radius\ vector\ in\ radian\ }[/katex]
= [katex]\frac{\ \ OP\ {-\ OP2\ \ }}{\frac{\pi}{2}}[/katex]
=[katex]\frac{\ OP\ {-\ \ OP2\ }}{1.57}[/katex]
=3.185 mm.
Steps
- Draw spiral as usual.
- Draw a small circle of radius equal to the constant curve calculated above.
- Located point Q as described in problem and through it draw a tangent to this smaller circle. This is a normal to the spiral.
- Draw a line at the right angle.
- To this line from Q.
- It will be tangent to cycloid.
