A CIRCLE ( RADIUS = 1 ) ROLLING ( 1 REV ) AROUND THE CONVEX SIDE OF ANOTHER CIRCLE ( RADIUS = 4 ).
THE DISTANCE THE CENTER REFERENCE POINT OF THE SMALLER CIRCLE TRAVELS IS 2Pi(4+1)=10Pi
ANY ONE CHOSEN REFERENCE POINT, ON THE CIRCUMFERENCE OF THE SMALLER CIRCLE, WILL TRAVEL A DISTANCE OF
2Pi(1) x 5REV = 10Pi.
THE CIRCUMFERENCE OF THE LARGER CIRCLE IS 2Pi(4)=8Pi.
THE CIRCUMFERENCE OF THE SMALLER CIRCLE IS 2PI(1)=2Pi.
The emphasis on reference points is to keep your attention on what the reference points are doing and not on the length of the two circumferences, which are not reference points.
The point of contact between the two circles is not a reference point,
that point of contact is a start-stop reference.
Any point on the circumference of the smaller circle is a reference point.
The two circle centers are reference points.
Will any one point anywhere on the
unit circle travel 10Pi after 5 revolutions?