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  Some Quickies! Basic geometrical exercises.
  • Involutes: The spiral formed by a point on a cord as it unwinds from a line or polygon of any number of sides. Mouse-over image for instructions.
Involute of a line Involute of a triangle

Draw each 180 degree arc working from one end of the line to the other.

 Draw each arc with a span of 360/3 degrees as you work around the triangle
Involute of a square Involute of a circle
Draw each arc segment 90 degrees as you work around the square
Now try it with a pentagon and octagon.

  • Spiral of Archimedes: A curve for uniform motion cams. 

  • Divide circle into any number of parts by drawing radius line and using circular array.

  • Divide one radius line into that same number of segments using tickmark command.

  • Draw arcs from each tickmark to successive radius lines using line snap "K".

  • Draw curve starting at centerpoint.

  • Cycloidal Curve: The path a point on a circle makes as it rolls on a line.

  • Draw a circle (at left) and circular array a radius line 7 copies in 180 deg.

  • Distance between each vertical line is distance between points 0 and 1 on circle. (You can draw an arc centered on 0 and drawn from 1 down to the horizontal baseline) Array the vertical lines that distance.

  • Project horizontal lines from where radius lines intersect circle.

  • Since DC doesn't have an arc by radius (YET) I just copied ("N") circles in the first example at each intersection on central horizontal line.

  • The lower one uses an arc with 22 deg setting and 'point control->custom distance' ("J") of radius after setting each first point. Arrows help you see the operation.

  • Where these intersect each successive line are the points for the curve. 

  • Double click the intersect snap button to keep it on so you can set all the curve points in easy succession. Make sure your "snap preview ("F10") is on!