A New General Theory of the Teeth of Wheels

3d Point 4th Point analytic curve angular motion angular velocities assumed axes axis circumference co-ordinates compute condition of contact continue contour curvature cutter cycloidal disc whose centre divisor draw ellipse epicycloid equal equation five contacts friction geometrical give Hence hour-glass curve indeterminate equation intersection involute limits line of centres linear velocity metacentric distance normal number of contacts number of teeth obliquity obtain orbit osculates outline parallel permutability perpendicular pinion pitch line pitch point Plate plerotic contact point of contact point Q porism position pragmatic action pragmatic contacts radii radius ratio result seven contacts shew shewn in figure side straight line straight rack suppose tangent teeth of wheels three contacts tion tooth tracing point Truncated wheel-work whence wherefore zero